| Title: | Time Series Analysis |
|---|---|
| Description: | Contains R functions and datasets detailed in the book "Time Series Analysis with Applications in R (second edition)" by Jonathan Cryer and Kung-Sik Chan. |
| Authors: | Kung-Sik Chan, Brian Ripley |
| Maintainer: | Kung-Sik Chan <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.3.1 |
| Built: | 2024-11-29 09:05:50 UTC |
| Source: | CRAN |
Contains R functions and datasets detailed in the book "Time Series Analysis with Applications in R (second edition)" by J.D. Cryer and K.S. Chan
| Package: | TSA |
| Type: | Package |
| Version: | 1.3 |
| Date: | 2020-9-9 |
| License: | GPL version 2 or newer |
Kung-Sik Chan, Brian Ripley
This function calls the acf function in the stats package and processes to drop lag-0 of the acf. It only works for univariate time series, so x below should be 1-dimensional.
acf(x, lag.max = NULL, type = c("correlation", "covariance", "partial")[1], plot = TRUE, na.action = na.fail, demean = TRUE, drop.lag.0 = TRUE, ...)acf(x, lag.max = NULL, type = c("correlation", "covariance", "partial")[1], plot = TRUE, na.action = na.fail, demean = TRUE, drop.lag.0 = TRUE, ...)
x |
a univariate or multivariate (not ccf) numeric time series object or a numeric vector or matrix, or an "acf" object. |
lag.max |
maximum number of lags at which to calculate the acf. Default is 10*log10(N/m) where N is the number of observations and m the number of series. |
type |
character string giving the type of acf to be computed. Allowed values are "correlation" (the default), "covariance" or "partial". |
plot |
logical. If TRUE (the default) the acf is plotted. |
na.action |
function to be called to handle missing values. na.pass can be used. |
demean |
logical. Should the covariances be about the sample means? |
drop.lag.0 |
logical. Should lag 0 be dropped |
... |
further arguments to be passed to plot.acf. |
An object of class "acf", which is a list with the following elements:
lag |
A three dimensional array containing the lags at which the acf is estimated. |
acf |
An array with the same dimensions as lag containing the estimated acf. |
type |
The type of correlation (same as the type argument). |
n.used |
The number of observations in the time series. |
series |
The name of the series x. |
snames |
The series names for a multivariate time series. |
Original authors of stats:::acf are: Paul Gilbert, Martyn Plummer, B.D. Ripley. This wrapper is written by Kung-Sik Chan
~put references to the literature/web site here ~
plot.acf, ARMAacf for the exact autocorrelations of a given ARMA process.
data(rwalk) model1=lm(rwalk~time(rwalk)) summary(model1) acf(rstudent(model1),main='')data(rwalk) model1=lm(rwalk~time(rwalk)) summary(model1) acf(rstudent(model1),main='')
Monthly U.S. airline passenger-miles: 01/1996 - 05/2005.
data(airmiles)data(airmiles)
The format is: 'ts' int [1:113, 1] 30983174 32147663 38342975 35969113 36474391 38772238 40395657 41738499 33580773 36389842 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr "airmiles" - attr(*, "tsp")= num [1:3] 1996 2005 12
www.bts.gov/xml/air_traffic/src/index.xml#MonthlySystem
data(airmiles) ## maybe str(airmiles) ; plot(airmiles) ...data(airmiles) ## maybe str(airmiles) ; plot(airmiles) ...
Monthly total international airline passengers from 01/1960- 12/1971.
data(airpass)data(airpass)
The format is: Time-Series [1:144] from 1960 to 1972: 112 118 132 129 121 135 148 148 136 119 ...
Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1994) Time Series Analysis, Forecasting and Control. Second Edition. New York: Prentice-Hall.
data(airpass) ## maybe str(airpass) ; plot(airpass) ...data(airpass) ## maybe str(airpass) ; plot(airpass) ...
A simulated AR(1) series with the AR coefficient equal to 0.4.
data(ar1.2.s)data(ar1.2.s)
The format is: Time-Series [1:60] from 1 to 60: -0.0678 1.4994 0.4888 0.3987 -0.5162 ...
The model is Y(t)=0.4*Y(t-1)+e(t) where the e's are iid standard normal.
data(ar1.2.s) ## maybe str(ar1.2.s) ; plot(ar1.2.s) ...data(ar1.2.s) ## maybe str(ar1.2.s) ; plot(ar1.2.s) ...
A simulated AR(1) series with the AR coefficient equal to 0.9.
data(ar1.s)data(ar1.s)
The format is: Time-Series [1:60] from 1 to 60: -1.889 -1.691 -1.962 -0.566 -0.627 ...
The model is Y(t)=0.9*Y(t-1)+e(t) where the e's are iid standard normal.
data(ar1.s) ## maybe str(ar1.s) ; plot(ar1.s) ...data(ar1.s) ## maybe str(ar1.s) ; plot(ar1.s) ...
Asimulated AR(2) series with AR coefficients being equal to 1.5 and -0.75
data(ar2.s)data(ar2.s)
The format is: Time-Series [1:120] from 1 to 120: -2.064 -1.937 0.406 2.039 2.953 ...
The model is Y(t)=1.5*Y(t-1)-0.75*Y(t-2)+e(t) where the e's are iid standard normal random variables.
data(ar2.s) ## maybe str(ar2.s) ; plot(ar2.s) ...data(ar2.s) ## maybe str(ar2.s) ; plot(ar2.s) ...
This function is identical to the arimax function which builds on and
extends the capability of the arima function in R stats by allowing the
incorporation of transfer functions, and innovative and additive outliers.
For backward compatitibility, the function is also named arima.
Note in the computation of AIC, the number of parameters excludes the noise
variance. This function is heavily based on
the arima function of the stats core
of R, see the help page of this function for details on arguments
x to kappa.
arima(x, order = c(0, 0, 0), seasonal = list(order = c(0, 0, 0), period = NA), xreg = NULL, include.mean = TRUE, transform.pars = TRUE, fixed = NULL, init = NULL, method = c("CSS-ML", "ML", "CSS"), n.cond, optim.control = list(), kappa = 1e+06, io = NULL, xtransf, transfer = NULL)arima(x, order = c(0, 0, 0), seasonal = list(order = c(0, 0, 0), period = NA), xreg = NULL, include.mean = TRUE, transform.pars = TRUE, fixed = NULL, init = NULL, method = c("CSS-ML", "ML", "CSS"), n.cond, optim.control = list(), kappa = 1e+06, io = NULL, xtransf, transfer = NULL)
x |
time series response |
order |
regular ARIMA order |
seasonal |
seasonal ARIMA order |
xreg |
a dataframe containing covariates |
include.mean |
if true, an intercept term is incorporated in the model; applicable only to stationary models. |
transform.pars |
if true, the AR parameters are transformed to ensure stationarity |
fixed |
a vector indicating which coefficients are fixed or free |
init |
initial values |
method |
estimation method |
n.cond |
number of initial values to be conditioned on in a conditional analysis |
optim.control |
control parameters for the optimization procedure |
kappa |
prior variance; used in dealing with initial values |
io |
a list of time points at which the model may have an innovative outlier. The time point of the outlier can be given either as absolute time point or as c(a,b), i.e. at the b-th 'month' of the a-th 'year' where each year has frequency(x) months, assuming x is a time series. |
xtransf |
xtranf is a matrix with each column containing a covariate that affects
the time series response in terms of an ARMA filter of order (p,q), i.e.
if Z is one such covariate, its effect on the time series is
|
transfer |
a list consisting of the ARMA orders for each transfer (distributed lag) covariate. |
An Arimax object contining the model fit.
Original author of the arima function in R stats: Brian Ripley. The arimax function is based on the stats:::arima function, with modifications by Kung-Sik Chan.
data(hare) arima(sqrt(hare),order=c(3,0,0))data(hare) arima(sqrt(hare),order=c(3,0,0))
This function bootstraps time series according to the fitted ARMA(p,d,q) model supplied by the fitted object arima.fit, and estimate the same model using the arima function. Any bootstrap sample that has problem when fitted with the ARIMA model will be omitted from the final results and all error messages will be suppressed. You can check if there is any fitting problem by running the command geterrmessage().
arima.boot(arima.fit, cond.boot = FALSE, is.normal = TRUE, B = 1000, init, ntrans = 100)arima.boot(arima.fit, cond.boot = FALSE, is.normal = TRUE, B = 1000, init, ntrans = 100)
arima.fit |
a fitted object from the arima function (seasonal components not allowed) |
cond.boot |
whether or not the bootstrap is conditional on the (p+d) initial values; if it is set true. If false (default), the stationary bootstrap is used. |
is.normal |
if true (default), errors are normally distributed, otherwise errors are drawn randomly and with replacement from the residuals of the fitted model. |
B |
number of bootstrap replicates (1000, default) |
init |
initial values for the bootstrap; needed if cond.boot=True default values are the initial values of the time series of the fitted model. |
ntrans |
number of transient values for the stationary bootstrap. Default=100 |
a matrix each row of which consists of the coefficient estimates of a bootstrap time-series.
Kung-Sik Chan
data(hare) arima.hare=arima(sqrt(hare),order=c(3,0,0)) boot.hare=arima.boot(arima.hare,B=50,init=sqrt(hare)[1:3],ntrans=100) apply(boot.hare,2,quantile, c(.025,.975)) period.boot=apply(boot.hare,1,function(x){ roots=polyroot(c(1,-x[1:3])) min1=1.e+9 rootc=NA for (root in roots) { if( abs(Im(root))<1e-10) next if (Mod(root)< min1) {min1=Mod(root); rootc=root} } if(is.na(rootc)) period=NA else period=2*pi/abs(Arg(rootc)) period }) hist(period.boot) quantile(period.boot,c(0.025,.975))data(hare) arima.hare=arima(sqrt(hare),order=c(3,0,0)) boot.hare=arima.boot(arima.hare,B=50,init=sqrt(hare)[1:3],ntrans=100) apply(boot.hare,2,quantile, c(.025,.975)) period.boot=apply(boot.hare,1,function(x){ roots=polyroot(c(1,-x[1:3])) min1=1.e+9 rootc=NA for (root in roots) { if( abs(Im(root))<1e-10) next if (Mod(root)< min1) {min1=Mod(root); rootc=root} } if(is.na(rootc)) period=NA else period=2*pi/abs(Arg(rootc)) period }) hist(period.boot) quantile(period.boot,c(0.025,.975))
This function builds on and
extends the capability of the arima function in R stats by allowing the
incorporation of transfer functions, innovative and additive outliers.
For backward compatitibility, the function is also named arima.
Note in the computation of AIC, the number of parameters excludes the noise
variance. See the help page of arima in stats for details on arguments
x to kappa.
arimax(x, order = c(0, 0, 0), seasonal = list(order = c(0, 0, 0), period = NA), xreg = NULL, include.mean = TRUE, transform.pars = TRUE, fixed = NULL, init = NULL, method = c("CSS-ML", "ML", "CSS"), n.cond, optim.control = list(), kappa = 1e+06, io = NULL, xtransf, transfer = NULL)arimax(x, order = c(0, 0, 0), seasonal = list(order = c(0, 0, 0), period = NA), xreg = NULL, include.mean = TRUE, transform.pars = TRUE, fixed = NULL, init = NULL, method = c("CSS-ML", "ML", "CSS"), n.cond, optim.control = list(), kappa = 1e+06, io = NULL, xtransf, transfer = NULL)
x |
time series response |
order |
regular ARIMA order |
seasonal |
seasonal ARIMA order |
xreg |
a dataframe containing covariates |
include.mean |
if true, an intercept term is incorporated in the model; applicable only to stationary model. |
transform.pars |
if true, the AR parameters are transformed to ensure stationarity |
fixed |
a vector indicating which coefficients are fixed or free |
init |
initial values |
method |
estimation method |
n.cond |
number of initial values to be conditioned on a conditional analysis |
optim.control |
control parameters for the optimization procedure |
kappa |
prior variance; used in dealing with initial values |
io |
a list of time points at which the model may have an innovative outlier. The time point of the outlier can be given either as absolute time point or as c(a,b), i.e. at the b-th 'month' of the a-th 'year' where each year has frequency(x) months, assuming x is a time series. |
xtransf |
xtranf is a matrix with each column containing a covariate that affects
the time series response in terms of an ARMA filter of order (p,q), i.e.
if Z is one such covariate, its effect on the time series is
|
transfer |
a list consisting of the ARMA orders for each transfer (distributed lag) covariate. |
An Arimax object containing the model fit.
Original author of the arima function in R stats: Brian Ripley. The arimax function is based on the stats:::arima function, with modifications by Kung-Sik Chan.
data(airmiles) plot(log(airmiles),ylab='Log(airmiles)',xlab='Year', main='') acf(diff(diff(window(log(airmiles),end=c(2001,8)),12)),lag.max=48,main='') air.m1=arimax(log(airmiles),order=c(0,1,1),seasonal=list(order=c(0,1,1), period=12),xtransf=data.frame(I911=1*(seq(airmiles)==69), I911=1*(seq(airmiles)==69)), transfer=list(c(0,0),c(1,0)),xreg=data.frame(Dec96=1*(seq(airmiles)==12), Jan97=1*(seq(airmiles)==13),Dec02=1*(seq(airmiles)==84)),method='ML')data(airmiles) plot(log(airmiles),ylab='Log(airmiles)',xlab='Year', main='') acf(diff(diff(window(log(airmiles),end=c(2001,8)),12)),lag.max=48,main='') air.m1=arimax(log(airmiles),order=c(0,1,1),seasonal=list(order=c(0,1,1), period=12),xtransf=data.frame(I911=1*(seq(airmiles)==69), I911=1*(seq(airmiles)==69)), transfer=list(c(0,0),c(1,0)),xreg=data.frame(Dec96=1*(seq(airmiles)==12), Jan97=1*(seq(airmiles)==13),Dec02=1*(seq(airmiles)==84)),method='ML')
A simulated ARMA(1,1) series with the model given by:
where the e's are iid standard normal
random variables.
data(arma11.s)data(arma11.s)
The format is: Time-Series [1:100] from 1 to 100: -0.765 1.297 0.668 -1.607 -0.626 ...
data(arma11.s) ## maybe str(arma11.s) ; plot(arma11.s) ...data(arma11.s) ## maybe str(arma11.s) ; plot(arma11.s) ...
Computes and plots the theoretical spectral density function of a stationary ARMA model
ARMAspec(model, freq = seq(0, 0.5, 0.001), plot = TRUE, ...)ARMAspec(model, freq = seq(0, 0.5, 0.001), plot = TRUE, ...)
model |
an arma model |
freq |
vector of frequency over which the spectral density is computed |
plot |
if true, plot the spectral density function; default is true |
... |
other parameters to be passed to the plot function |
a list:
spec |
spectral density values |
freq |
same as freq in the input |
model |
the arma model |
Kung-Sik Chan
theta=.9 # Reset theta for other MA(1) plots ARMAspec(model=list(ma=-theta))theta=.9 # Reset theta for other MA(1) plots ARMAspec(model=list(ma=-theta))
This function finds a number of subset ARMA models. A "long" AR model is fitted to the data y to compute the residuals which are taken as a proxy of the error process. Then, an ARMA model is approximated by a regression model with the the covariates being the lags of the time series and the lags of the error process. Subset ARMA models may then be selected using the subset regression technique by leaps and bounds, via the regsubsets function of the leaps package in R.
armasubsets(y, nar, nma, y.name = "Y", ar.method = "ols", ...)armasubsets(y, nar, nma, y.name = "Y", ar.method = "ols", ...)
y |
time-series data |
nar |
maximum AR order |
nma |
maximum MA order |
y.name |
label of the time series |
ar.method |
method used for fitting the long AR model; default is ols with the AR order determined by AIC |
... |
arguments passed to the plot.armasubsets function |
An object of the armasubsets class to be processed by the plot.armasubsets function.
Kung-Sik Chan
set.seed(92397) test=arima.sim(model=list(ar=c(rep(0,11),.8),ma=c(rep(0,11),0.7)),n=120) res=armasubsets(y=test,nar=14,nma=14,y.name='test',ar.method='ols') plot(res)set.seed(92397) test=arima.sim(model=list(ar=c(rep(0,11),.8),ma=c(rep(0,11),0.7)),n=120) res=armasubsets(y=test,nar=14,nma=14,y.name='test',ar.method='ols') plot(res)
Monthly beer sales in millions of barrels, 01/1975 - 12/1990.
data(beersales)data(beersales)
The format is: Time-Series [1:192] from 1975 to 1991: 11.12 9.84 11.57 13.01 13.42 ...
Frees, E. W., Data Analysis Using Regression Models, Prentice Hall, 1996.
data(beersales) ## maybe str(beersales) ; plot(beersales) ...data(beersales) ## maybe str(beersales) ; plot(beersales) ...
Weekly unit sales (log-transformed) of Bluebird standard potato chips (New Zealand) and their price for 104 weeks.
data(bluebird)data(bluebird)
The format is: mts [1:104, 1:2] 11.5 11.5 11.8 11.9 11.3 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr [1:2] "log.sales" "price" - attr(*, "tsp")= num [1:3] 1 104 1 - attr(*, "class")= chr [1:2] "mts" "ts"
www.stat.auckland.ac.nz/~balemi/Assn3.xls
data(bluebird) ## maybe str(bluebird) ; plot(bluebird) ...data(bluebird) ## maybe str(bluebird) ; plot(bluebird) ...
Weekly unit sales (log-transformed) of Bluebird Lite potato chips (New Zealand) and their price for 104 weeks.
data(bluebirdlite)data(bluebirdlite)
A data frame with 104 observations on the following 2 variables.
log.salesa numeric vector
pricea numeric vector
www.stat.auckland.ac.nz/~balemi/Assn3.xls
data(bluebirdlite) ## maybe str(bluebirdlite) ; plot(bluebirdlite) ...data(bluebirdlite) ## maybe str(bluebirdlite) ; plot(bluebirdlite) ...
Monthly public transit boardings (mostly buses and light rail) and gasoline price (both log-transformed), Denver, Colorado region, 08/2000 - 03/2006.
Personal communication from Lee Cryer, Project Manager, Regional Transportation District, Denver, Colorado. Denver gasoline prices were obtained from the Energy Information Administration, U.S. Department of Energy, Washington, D.C.at www.eia.doe.gov
data(boardings) plot(boardings) ## maybe str(boardings) ; plot(boardings) ...data(boardings) plot(boardings) ## maybe str(boardings) ; plot(boardings) ...
Determine the appropriate power transformation for time-series data. The objective is to estimate the power transformation so that the transformed time series is approximately a Gaussian AR process.
BoxCox.ar(y, order, lambda = seq(-2, 2, 0.01), plotit = TRUE, method = c("mle", "yule-walker", "burg", "ols", "yw"), ...)BoxCox.ar(y, order, lambda = seq(-2, 2, 0.01), plotit = TRUE, method = c("mle", "yule-walker", "burg", "ols", "yw"), ...)
y |
univariate time series (must be positive) |
order |
AR order for the data; if missing, the order is determined by AIC for the log-transformed data |
lambda |
a vector of candidate power transformation values; if missing, it is set to be from -2 to 2, with increment .01 |
plotit |
logical value, if true, plot the profile log-likelihood for the power estimator |
method |
method of AR estimation; default is "mle" |
... |
other parameters to be passed to the ar function |
A list that contains the following:
lambda |
candidate power transformation parameter values |
loglike |
profile log-likelihood |
mle |
maximum likelihood estimate of the power transformation value |
ci |
95% C.I. of the power transformation value |
The procedure is very computer intensive. Be patient for the outcome
Kung-Sik Chan
data(hare) # hare.transf=BoxCox.ar(y=hare) # hare.transf$cidata(hare) # hare.transf=BoxCox.ar(y=hare) # hare.transf$ci
Monthly CO2 level at Alert, Northwest Territories, Canada, near the Artic Circle, 01/1994 - 12/2004.
data(co2)data(co2)
The format is: Time-Series [1:132] from 1994 to 2005: 363 364 365 364 364 ...
http://cdiac.ornl.gov/trends/co2/sio-alt.htm
data(co2) ## maybe str(co2) ; plot(co2) ...data(co2) ## maybe str(co2) ; plot(co2) ...
Color property from 35 consecutive batches in an industrial process.
data(color)data(color)
The format is: Time-Series [1:35] from 1 to 35: 67 63 76 66 69 71 72 71 72 72 ...
“The Estimation of Sigma for an X Chart”, Journal of Quality Technology, Vol. 22, No. 3 (July 1990), by Jonathan D. Cryer and Thomas P. Ryan.
data(color) ## maybe str(color) ; plot(color) ...data(color) ## maybe str(color) ; plot(color) ...
Daily values of one unit of the CREF (College Retirement Equity Fund) Stock fund, 08/26/04 - 08/15/06.
data(CREF)data(CREF)
The format is: Time-Series [1:501] from 1 to 501: 170 170 169 170 171 ...
www.tiaa-cref.org/performance/retirement/data/index.html
data(CREF) ## maybe str(CREF) ; plot(CREF) ...data(CREF) ## maybe str(CREF) ; plot(CREF) ...
Daily values of one unit of the CREF (College Retirement Equity Fund) Bond fund, 08/26/04 - 08/15/06.
data(CREF)data(CREF)
www.tiaa-cref.org/performance/retirement/data/index.html
data(CREF) ## maybe str(CREF) ; plot(CREF) ...data(CREF) ## maybe str(CREF) ; plot(CREF) ...
Accounts receivable data. Number of days until a distributor of Winegard Company products pays their account.
data(days)data(days)
The format is: Time-Series [1:130] from 1 to 130: 39 39 41 26 28 28 25 26 24 38 ...
Personal communication from Mark Selergren, Vice President, Winegard, Inc., Burlington, Iowa.
data(days) ## maybe str(days) ; plot(days) ...data(days) ## maybe str(days) ; plot(days) ...
82 consecutive values for the amount of deviation (in 0.000025 inch units) from a specified target value in an industrial machining process at Deere & Co.
data(deere1)data(deere1)
The format is: Time-Series [1:82] from 1 to 82: 3 0 -1 -4 7 3 7 3 3 -1 ...
Personal communication from William F. Fulkerson, Deere & Co. Technical Center, Moline, Illinois.
data(deere1) ## maybe str(deere1) ; plot(deere1) ...data(deere1) ## maybe str(deere1) ; plot(deere1) ...
102 consecutive values for the deviation (in 0.0000025 inch units) from a specified target value.
data(deere2)data(deere2)
The format is: Time-Series [1:102] from 1 to 102: -18 -24 -17 -27 -37 -34 -8 14 18 7 ...
Personal communication from William F. Fulkerson, Deere & Co. Technical Center, Moline, Illinois.
data(deere2) ## maybe str(deere2) ; plot(deere2) ...data(deere2) ## maybe str(deere2) ; plot(deere2) ...
Fifty seven consecutive values for the deviation (in 0.0000025 inch units) from a specified target value.
data(deere3)data(deere3)
The format is: Time-Series [1:57] from 1 to 57: -500 -1250 -500 -3000 -2375 ...
Personal communication from William F. Fulkerson, Deere & Co. Technical Center, Moline, Illinois.
data(deere3) ## maybe str(deere3) ; plot(deere3) ...data(deere3) ## maybe str(deere3) ; plot(deere3) ...
This function serves to detect whether there are any additive outliers
(AO). It implements the
test statistic proposed by Chang, Chen and Tiao (1988).
detectAO(object, alpha = 0.05, robust = TRUE)detectAO(object, alpha = 0.05, robust = TRUE)
object |
a fitted ARIMA model |
alpha |
family significance level (5% is the default) Bonferroni rule is used to control the family error rate. |
robust |
if true, the noise standard deviation is estimated by mean absolute residuals times sqrt(pi/2). Otherwise, it is the estimated by sqrt(sigma2) from the arima fit. |
A list containing the following components:
ind |
the time indices of potential AO |
lambda2 |
the corresponding test statistics |
Kung-Sik Chan
Chang, I.H., Tiao, G.C. and C. Chen (1988). Estimation of Time Series Parameters in the Presence of Outliers. Technometrics, 30, 193-204.
set.seed(12345) y=arima.sim(model=list(ar=.8,ma=.5),n.start=158,n=100) y[10] y[10]=10 y=ts(y,freq=1,start=1) plot(y,type='o') acf(y) pacf(y) eacf(y) m1=arima(y,order=c(1,0,0)) m1 detectAO(m1) detectAO(m1, robust=FALSE) detectIO(m1)set.seed(12345) y=arima.sim(model=list(ar=.8,ma=.5),n.start=158,n=100) y[10] y[10]=10 y=ts(y,freq=1,start=1) plot(y,type='o') acf(y) pacf(y) eacf(y) m1=arima(y,order=c(1,0,0)) m1 detectAO(m1) detectAO(m1, robust=FALSE) detectIO(m1)
This function serves to detect whether there are any innovative
outliers (IO). It implements the
test statistic proposed by Chang, Chen and Tiao (1988).
detectIO(object, alpha = 0.05, robust = TRUE)detectIO(object, alpha = 0.05, robust = TRUE)
object |
a fitted ARIMA model |
alpha |
family significance level (5% is the default) Bonferroni rule is used to control the family error rate. |
robust |
if true, the noise standard deviation is estimated by mean absolute residuals times sqrt(pi/2). Otherwise, it is the estimated by sqrt(sigma2) from the arima fit. |
A list containing the following components:
ind |
the time indices of potential AO |
lambda1 |
the corresponding test statistics |
Kung-Sik Chan
Chang, I.H., Tiao, G.C. and C. Chen (1988). Estimation of Time Series Parameters in the Presence of Outliers. Technometrics, 30, 193-204.
set.seed(12345) y=arima.sim(model=list(ar=.8,ma=.5),n.start=158,n=100) y[10] y[10]=10 y=ts(y,freq=1,start=1) plot(y,type='o') acf(y) pacf(y) eacf(y) m1=arima(y,order=c(1,0,0)) m1 detectAO(m1) detectAO(m1, robust=FALSE) detectIO(m1)set.seed(12345) y=arima.sim(model=list(ar=.8,ma=.5),n.start=158,n=100) y[10] y[10]=10 y=ts(y,freq=1,start=1) plot(y,type='o') acf(y) pacf(y) eacf(y) m1=arima(y,order=c(1,0,0)) m1 detectAO(m1) detectAO(m1, robust=FALSE) detectIO(m1)
Computes the sample extended acf (ESACF) for the time series stored in z. The matrix of ESACF with the AR order up to ar.max and the MA order up to ma.max is stored in the matrix EACFM.
eacf(z, ar.max = 7, ma.max = 13)eacf(z, ar.max = 7, ma.max = 13)
z |
the time series data |
ar.max |
maximum AR order; default=7 |
ma.max |
maximum MA order; default=13 |
A list containing the following two components:
eacf |
a matrix of sample extended ACF |
symbol |
corresponding matrix of symbols indicating the significance of the ESACF |
Side effect of the eacf function: The function prints a coded ESACF table with significant values denoted by * and nosignificant values by 0.
Kung-Sik Chan
Tsay, R. and Tiao, G. (1984). "Consistent Estimates of Autoregressive Parameters and Extended Sample Autocorrelation Function for Stationary and Nonstationary ARMA Models." Journal of the American Statistical Association, 79 (385), pp. 84-96.
data(arma11.s) eacf(arma11.s)data(arma11.s) eacf(arma11.s)
An electroencephalogram (EEG) is a noninvasive test used to detect and record the electrical activity generated in the brain. These data were measured at a frequency of 256 per second and came from a patient suffering a seizure. This a portion of a series on the website of Professor Richard Smith, University of North Carolina. His source: Professors Mike West and Andrew Krystal, Duke University.
data(eeg)data(eeg)
The format is: ts [1:13000, 1] -3.08 -20.15 -45.05 -69.95 -94.57 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr "eeg" - attr(*, "tsp")= num [1:3] 2001 15000 1
http://www.stat.unc.edu/faculty/rs/s133/Data/datadoc.html
data(eeg) ## maybe str(eeg) ; plot(eeg) ...data(eeg) ## maybe str(eeg) ; plot(eeg) ...
Monthly U.S. electricity generation (in millions of kilowatt hours) of all types: coal, natural gas, nuclear, petroleum, and wind, 01/1973 - 12/2005.
data(electricity)data(electricity)
The format is: 'ts' int [1:396, 1] 160218 143539 148158 139589 147395 161244 173733 177365 156875 154197 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr "electricity" - attr(*, "tsp")= num [1:3] 1973 2006 12
Source: www.eia.doe.gov/emeu/mer/elect.html
data(electricity) ## maybe str(electricity) ; plot(electricity) ...data(electricity) ## maybe str(electricity) ; plot(electricity) ...
A digitized sound file of about 0.4 seconds of a B flat just below middle C played on a euphonium by one of the authors (JDC), a member of the group Tempered Brass.
data(euph)data(euph)
The format is: Time-Series [1:1105] from 1 to 1105: 0.244 0.635 0.712 0.608 0.317 ...
data(euph) ## maybe str(euph) ; plot(euph) ...data(euph) ## maybe str(euph) ; plot(euph) ...
A simulated AR(1) series with the AR(1) coefficient being 3.
data(explode.s)data(explode.s)
The format is: Time-Series [1:8] from 1 to 8: 0.63 0.64 3.72 12.67 39.57 ...
data(explode.s) ## maybe str(explode.s) ; plot(explode.s) ...data(explode.s) ## maybe str(explode.s) ; plot(explode.s) ...
Computes the fitted values of an arima model.
## S3 method for class 'Arima' fitted(object,...)## S3 method for class 'Arima' fitted(object,...)
object |
a fitted model from the arima function. |
... |
other arguments; not used here but kept to be consistent with the generic method |
fitted values
Kung-Sik Chan
data(hare) hare.m1=arima(sqrt(hare),order=c(3,0,0)) fitted(hare.m1)data(hare) hare.m1=arima(sqrt(hare),order=c(3,0,0)) fitted(hare.m1)
Flow data (in cubic feet per second) for the Iowa river measured at Wapello, Iowa for the period 09/1958 - 08/2006.
data(flow)data(flow)
http://waterdata.usgs.gov/ia/nwis/sw
data(flow) ## maybe str(flow) ; plot(flow) ...data(flow) ## maybe str(flow) ; plot(flow) ...
Simulate a GARCH process.
garch.sim(alpha, beta, n = 100, rnd = rnorm, ntrans = 100,...)garch.sim(alpha, beta, n = 100, rnd = rnorm, ntrans = 100,...)
alpha |
The vector of ARCH coefficients including the intercept term as the first element |
beta |
The vector of GARCH coefficients |
n |
sample size |
rnd |
random number generator for the noise; default is normal |
ntrans |
burn-in size, i.e. number of initial simulated data to be discarded |
... |
parameters to be passed to the random number generator |
Simulate data from the GARCH(p,q) model:
where is iid,
independent of past , and
simulated GARCH time series of size n.
Kung-Sik Chan
set.seed(1235678) garch01.sim=garch.sim(alpha=c(.01,.9),n=500) plot(garch01.sim,type='l', main='',ylab=expression(r[t]),xlab='t')set.seed(1235678) garch01.sim=garch.sim(alpha=c(.01,.9),n=500) plot(garch01.sim,type='l', main='',ylab=expression(r[t]),xlab='t')
Perform a goodness-of-fit test for the GARCH model by checking whether the standardized residuals are iid based on the ACF of the absolute residuals or squared residuals.
gBox(model, lags = 1:20, x, method = c("squared", "absolute")[1], plot = TRUE)gBox(model, lags = 1:20, x, method = c("squared", "absolute")[1], plot = TRUE)
model |
fitted model from the garch function of the tseries library |
lags |
a vector of maximum ACF lags to be used in the test |
x |
time series data to which the GARCH model is fitted |
method |
"squared": test is based on squared residuals; "absolute": test is based on absolute residuals |
plot |
logical variable, if TRUE, the p-values of the tests are plotted |
lags |
lags in the input |
pvalue |
a vector of p-values of the tests |
method |
method used |
x |
x |
Kung-Sik Chan
"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan
require(tseries) # need to uncomment this line when running the example data(CREF) r.cref=diff(log(CREF))*100 m1=tseries::garch(x=r.cref,order=c(1,1)) summary(m1) gBox(m1,x=r.cref,method='squared')require(tseries) # need to uncomment this line when running the example data(CREF) r.cref=diff(log(CREF))*100 m1=tseries::garch(x=r.cref,order=c(1,1)) summary(m1) gBox(m1,x=r.cref,method='squared')
Daily price of gold (in $ per troy ounce) for the 252 trading days of 2005
data(gold)data(gold)
The format is: Time-Series [1:252] from 1 to 252: 427 426 426 423 421 ...
www.lbma.org.uk/2005dailygold.htm
data(gold) ## maybe str(gold) ; plot(gold) ...data(gold) ## maybe str(gold) ; plot(gold) ...
Daily returns of the google stock from 08/20/04 - 09/13/06.
data(google)data(google)
The format is: Time-Series [1:521] from 1 to 521: 0.0764 0.0100 -0.0423 0.0107 0.0179 ...
http://finance.yahoo.com/q/hp?s=GOOG
data(google) ## maybe str(google) ; plot(google) ...data(google) ## maybe str(google) ; plot(google) ...
Annual number of hare data.
data(hare)data(hare)
The format is: Time-Series [1:31] from 1905 to 1935: 50 20 20 22 27 50 55 78 70 59 ...
These are yearly hare abundances for the main drainage of the Hudson Bay, based on trapper questionnaires.
MacLulich, D. A. (1937) Fluctuations in the Number of the Varying Hare (Lepus americanus) (Univ. of Toronto Press, Toronto)
Stenseth, N. C., Falck, W., Bjornstad, O. N. and Krebs. C. J. (1997) Population regulation in snowshoe hare and Canadian lynx: Asymmetric food web configurations between hare and lynx. Proc. Natl. Acad. Sci., 94, 5147-5152.
data(hare)data(hare)
The function creates a matrix of the first m pairs of harmonic functions for fitting a harmonic trend (cosine-sine trend, Fourier regresssion) models with the response being x, a time series.
harmonic(x, m = 1)harmonic(x, m = 1)
x |
a time series |
m |
the number of pairs of harmonic functions to be created; 2m must be less than or equal to the frequency of x |
a matrix consisting of
excluding any zero functions.
Kung-Sik Chan
data(tempdub) # first creates the first pair of harmonic functions and then fit the model har.=harmonic(tempdub,1) model4=lm(tempdub~har.) summary(model4)data(tempdub) # first creates the first pair of harmonic functions and then fit the model har.=harmonic(tempdub,1) model4=lm(tempdub~har.) summary(model4)
Average hours worked (times 10) in U.S. manufacturing sector, from 07/1982 - 06/1987
data(hours)data(hours)
The format is: Time-Series [1:60] from 1983 to 1987: 389 390 389 390 393 397 392 388 396 398 ...
Cryer, J. D. Time Series Analysis, Duxbury Press, 1986.
data(hours) ## maybe str(hours) ; plot(hours) ...data(hours) ## maybe str(hours) ; plot(hours) ...
A simulated IMA(2,2) series with theta1=1 and theta2=-0.6
data(ima22.s)data(ima22.s)
The format is: Time-Series [1:62] from 1 to 62: 0.00000 0.00000 -0.00569 2.12404 2.15337 ...
data(ima22.s) ## maybe str(ima22.s) ; plot(ima22.s) ...data(ima22.s) ## maybe str(ima22.s) ; plot(ima22.s) ...
Quarterly earnings per share for 1960Q1 to 1980Q4 of the U.S. company, Johnson & Johnson, Inc.
data(JJ)data(JJ)
The format is: Time-Series [1:84] from 1960 to 1981: 0.71 0.63 0.85 0.44 0.61 0.69 0.92 0.55 0.72 0.77 ...
http://www.stat.pitt.edu/stoffer/tsa2/
data(JJ) ## maybe str(JJ) ; plot(JJ) ...data(JJ) ## maybe str(JJ) ; plot(JJ) ...
Carry out Keenan's 1-degree test for nonlinearity against the null hypothesis that the time series follows some AR process.
Keenan.test(x, order, ...)Keenan.test(x, order, ...)
x |
time series |
order |
working AR order; if missing, it is estimated by minimizing AIC via the ar function. |
... |
user-supplied options to the ar function. |
The test is designed to have optimal local power against depature from the linear autoregressive function in the direction of the square of the linear autoregressive function.
A list containing the following components
test.stat |
The observed test statistic |
p.value |
p-value of the test |
order |
working AR order |
Kung-Sik Chan
Keenan, D. M. (1985), A Tukey nonadditivity-type test for time series Nonlinearity, Biometrika, 72, 39-44.
data(spots) Keenan.test(sqrt(spots))data(spots) Keenan.test(sqrt(spots))
Computes the Kurtosis.
kurtosis(x, na.rm = FALSE)kurtosis(x, na.rm = FALSE)
x |
data |
na.rm |
logical variable, if true, missing values are excluded from analysis |
Given data , the sample kurtosis is
defined by the formula:
The function returns the kurtosis of the data.
Kung-Sik Chan
data(CREF) r.cref=diff(log(CREF))*100 kurtosis(r.cref)data(CREF) r.cref=diff(log(CREF))*100 kurtosis(r.cref)
Computes and plots the nonparametric regression function of a time series against its various lags.
lagplot(x, lag.max = 6, deg = 1, nn = 0.7, method = c("locfit", "gam", "both")[1])lagplot(x, lag.max = 6, deg = 1, nn = 0.7, method = c("locfit", "gam", "both")[1])
x |
time series |
lag.max |
maximum lag |
deg |
degree of local polynomial, needed only for the locfit method |
nn |
fraction of nearest data contained in a window, needed only for the locfit method |
method |
Two methods for nonparametric estimation: "locfit" is
the default which
uses the local polynomial approach via the locfit library to estimate the
conditional mean function of |
Side effects: The nonparametric lagged regression functions are plotted lag by lag, with the raw data superimposed on the plots.
Kung-Sik Chan
"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan
set.seed(2534567) par(mfrow=c(3,2)) y=arima.sim(n=61,model=list(ar=c(1.6,-0.94),ma=-0.64)) # lagplot(y)set.seed(2534567) par(mfrow=c(3,2)) y=arima.sim(n=61,model=list(ar=c(1.6,-0.94),ma=-0.64)) # lagplot(y)
Annual precipitation (in inches) in Los Angeles, 1878-1992.
data(larain)data(larain)
The format is: Time-Series [1:115] from 1778 to 1892: 20.86 17.41 18.65 5.53 10.74 ...
Personal communication from Professor Donald Bentley,
Pomona College, Claremont, California. For more data see
http://www.wrh.noaa.gov/lox/climate/cvc.php
data(larain) ## maybe str(larain) ; plot(larain) ...data(larain) ## maybe str(larain) ; plot(larain) ...
This function modifies the Box.test function in the stats package, and it computes the Ljung-Box or Box-Pierce tests checking whether or not the residuals appear to be white noise.
LB.test(model, lag = 12, type = c("Ljung-Box", "Box-Pierce"), no.error = FALSE, omit.initial = TRUE)LB.test(model, lag = 12, type = c("Ljung-Box", "Box-Pierce"), no.error = FALSE, omit.initial = TRUE)
model |
model fit from the arima function |
lag |
number of lags of the autocorrelation of the residuals to be included in the test statistic. (default=12) |
type |
either Ljung-Box or Box-Pierce |
no.error |
a system variable; normally it is not changed |
omit.initial |
if true, (d+Ds) initial residuals are omitted from the test |
a list:
statistics |
test statistic |
p.value |
p-value |
parameter |
d.f. of the Chi-square test |
lag |
no of lags |
Kung-Sik Chan, based on A. Trapletti's work on the Box.test function in the stats package
Box, G. E. P. and Pierce, D. A. (1970), Distribution of residual correlations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association, 65, 15091526.
Ljung, G. M. and Box, G. E. P. (1978), On a measure of lack of fit in time series models. Biometrika 65, 553564.
data(color) m1.color=arima(color,order=c(1,0,0)) LB.test(m1.color)data(color) m1.color=arima(color,order=c(1,0,0)) LB.test(m1.color)
A simulated MA(1) series with the MA(1) coefficient equal to 0.9.
data(ma1.1.s)data(ma1.1.s)
The format is: Time-Series [1:120] from 1 to 120: 0.182 -0.748 -0.355 1.014 -2.363 ...
The model is where the e's are iid standard normal.
data(ma1.1.s) ## maybe str(ma1.1.s) ; plot(ma1.1.s) ...data(ma1.1.s) ## maybe str(ma1.1.s) ; plot(ma1.1.s) ...
A simulated MA(1) series with the MA(1) coefficient equal to -0.9.
data(ma1.2.s)data(ma1.2.s)
The format is: Time-Series [1:120] from 1 to 120: 1.511 1.821 0.957 -1.538 -2.888 ...
The model is where the e's are iid standard normal.
data(ma1.2.s) ## maybe str(ma1.2.s) ; plot(ma1.2.s) ...data(ma1.2.s) ## maybe str(ma1.2.s) ; plot(ma1.2.s) ...
A simulated MA(2) series with MA coefficients being 1 and -0.6.
data(ma2.s)data(ma2.s)
The format is: Time-Series [1:120] from 1 to 120: -0.4675 0.0815 0.9938 -2.6959 2.8116 ...
The model is where the e's are iid standard normal
random variables.
data(ma2.s) ## maybe str(ma2.s) ; plot(ma2) ...data(ma2.s) ## maybe str(ma2.s) ; plot(ma2) ...
Perform the McLeod-Li test for conditional heteroscedascity (ARCH).
McLeod.Li.test(object, y, gof.lag, col = "red", omit.initial = TRUE, plot = TRUE, ...)McLeod.Li.test(object, y, gof.lag, col = "red", omit.initial = TRUE, plot = TRUE, ...)
object |
a fitted Arima model, ususally the output from the arima function. If supplied, then the Mcleod-Li test is applied to the residuals of the model, and the y-argument is ignored. |
y |
time series data with which one wants to test for the presence of conditional heteroscedascity |
gof.lag |
maximum number of lags for which the test is carried out. |
col |
color of the reference line |
omit.initial |
suppress the initial (d+Ds) residuals if set to be TRUE |
plot |
suppress plotting if set to be FALSE |
... |
other arguments to be passed to the plot function |
The test checks for the presence of conditional heteroscedascity by computing the Ljung-Box (portmanteau) test with the squared data (if y is supplied and object suppressed) or with the squared residuals from an arima model (if an arima model is passed to the function via the object argument.)
pvlaues |
the vector of p-values for the Ljung-Box test statistics
computed using the first |
Kung-Sik Chan
McLeod, A. I. and W. K. Li (1983). Diagnostic checking ARMA time series models using squared residual autocorrelations. Journal of Time Series Analysis, 4, 269273.
data(CREF) r.cref=diff(log(CREF))*100 McLeod.Li.test(y=r.cref)data(CREF) r.cref=diff(log(CREF))*100 McLeod.Li.test(y=r.cref)
Average monthly milk production per cow in the US, 01/1994 - 12/2005
data(milk)data(milk)
The format is: 'ts' int [1:144, 1] 1343 1236 1401 1396 1457 1388 1389 1369 1318 1354 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr "milk" - attr(*, "tsp")= num [1:3] 1994 2006 12
data(milk) str(milk) plot(milk)data(milk) str(milk) plot(milk)
Monthly spot price for crude oil, Cushing, OK (in U.S. dollars per barrel), 01/1986 - 01/2006.
data(oil.price)data(oil.price)
The format is: Time-Series [1:241] from 1986 to 2006: 22.9 15.4 12.6 12.8 15.4 ...
tonto.eia.doe.gov/dnav/pet/hist/rwtcM.htm
data(oil.price) ## maybe str(oil.price) ; plot(oil.price) ...data(oil.price) ## maybe str(oil.price) ; plot(oil.price) ...
Monthly wholesale specialty oil filters sales, Deere & Co, 07/1983 - 06/1987.
data(oilfilters)data(oilfilters)
The format is: Time-Series [1:48] from 1984 to 1987: 2385 3302 3958 3302 2441 3107 5862 4536 4625 4492 ... - attr(*, "freq")= num 12 - attr(*, "start")= num [1:2] 1987 7
Data courtesy of William F. Fulkerson, Deere & Company, Technical Center, Moline, Illinois.
data(oilfilters) ## maybe str(oilfilters) ; plot(oilfilters) ...data(oilfilters) ## maybe str(oilfilters) ; plot(oilfilters) ...
This is a wrapper that computes the periodogram
periodogram(y,log='no',plot=TRUE,ylab="Periodogram", xlab="Frequency",lwd=2,...)periodogram(y,log='no',plot=TRUE,ylab="Periodogram", xlab="Frequency",lwd=2,...)
y |
A univariate time series |
log |
if set to "yes", the periodogram is plotted on the log-scale; default="no" |
plot |
The periodogram is plotted if it is set to be TRUE which is the default |
ylab |
label on the y-axis |
xlab |
label on the x-axis |
lwd |
thickness of the periodogram lines |
... |
other arguments to be passed to the plot function |
A list that contains the following elements:
freq |
Vector of frequencies at which the spectral density is estimated. (Possibly approximate Fourier frequencies. |
spec |
Vector of estimates of the periodogram at frequencies corresponding to freq. |
Bloomfield, P. (1976) Fourier Analysis of Time Series: An Introduction. Wiley.
Brockwell, P. J. and Davis, R. A. (1991) Time Series: Theory and Methods. Second edition. Springer.
data(star) plot(star,xlab='Day',ylab='Brightness') periodogram(star,ylab='Variable Star Periodogram'); abline(h=0)data(star) plot(star,xlab='Day',ylab='Brightness') periodogram(star,ylab='Variable Star Periodogram'); abline(h=0)
Plots the time series data and its predictions with 95% prediction bounds.
## S3 method for class 'Arima' plot(x, n.ahead = 12, col = "black", ylab = object$series, lty = 2, n1, newxreg, transform, Plot=TRUE, ...)## S3 method for class 'Arima' plot(x, n.ahead = 12, col = "black", ylab = object$series, lty = 2, n1, newxreg, transform, Plot=TRUE, ...)
x |
a fitted arima model |
n.ahead |
number of prediction steps ahead (default=12) |
col |
color of the prediction bounds |
ylab |
label of the y-axis |
lty |
line type of the point predictor; default=dashed lines |
n1 |
starting time point of the plot (default=earliest time point) |
newxreg |
a matrix of covariate(s) over the period of prediction |
transform |
function used to transform the forecasts and their prediction bounds; if missing, no transformation will be carried out. This option is useful if the model was fitted to the transformed data and it is desirable to obtain the forecasts on the original scale. For example, if the model was fitted with the logarithm of the data, then transform = exp will plot the forecasts and their prediction bounds on the original scale. |
Plot |
Plotting will be suppressed if Plot is set to be FALSE; default is TRUE |
... |
additional parameters passed to the plot function |
Side effects of the function: plot the forecasts and their 95% prediction bounds, unless Plot is set to be FALSE. The part of the observed series is plotted with all data plotted as open circles and linked by a smooth line. By default the predicted values are plotted as open circles joined up by a dashed line. The plotting style of the predicted values can be altered by supplying relevant plotting options, e.g specifying the options type='o', pch=19 and lty=1 will plot the predicted values as solid circles that are overlaid on the connecting smooth solid line. The prediction limits are plotted as dotted lines, with default color being black. However, the prediction limits can be drawn in other colors. For example, setting col='red' paints the prediction limits in red. An interesting use of the col argument is setting col=NULL which has the effect of not drawing the prediction limits.
The function returns an invisible list containing the following components.
pred |
the time series of predicted values |
lpi |
the corresponding lower 95% prediction limits |
upi |
the corresponding upper 95% prediction limits |
Kung-Sik Chan
data(oil.price) oil.IMA11alt=arima(log(oil.price),order=c(0,1,1), # create the design matrix of the covariate for prediction xreg=data.frame (constant=seq(oil.price))) n=length(oil.price) n.ahead=24 newxreg=data.frame(constant=(n+1):(n+n.ahead)) # do the prediction and plot the results plot(oil.IMA11alt,n.ahead=n.ahead,newxreg=newxreg, ylab='Log(Oil Price)',xlab='Year',n1=c(2000,1)) # do the same thing but on the orginal scale plot(oil.IMA11alt,n.ahead=n.ahead,newxreg=newxreg, ylab='Oil Price',xlab='Year',n1=c(2000,1),transform=exp,pch=19, lty=1,type='o') # Setting pch=19 plots the predicted values as solid circles. res=plot(oil.IMA11alt,n.ahead=n.ahead,newxreg=newxreg, ylab='Oil Price',xlab='Year',n1=c(2000,1),transform=exp,pch=19,col=NULL) # Setting col=NULL will make the prediction bands invisible. Try col='red'. res # prints the predicted values and their 95% prediction limits.data(oil.price) oil.IMA11alt=arima(log(oil.price),order=c(0,1,1), # create the design matrix of the covariate for prediction xreg=data.frame (constant=seq(oil.price))) n=length(oil.price) n.ahead=24 newxreg=data.frame(constant=(n+1):(n+n.ahead)) # do the prediction and plot the results plot(oil.IMA11alt,n.ahead=n.ahead,newxreg=newxreg, ylab='Log(Oil Price)',xlab='Year',n1=c(2000,1)) # do the same thing but on the orginal scale plot(oil.IMA11alt,n.ahead=n.ahead,newxreg=newxreg, ylab='Oil Price',xlab='Year',n1=c(2000,1),transform=exp,pch=19, lty=1,type='o') # Setting pch=19 plots the predicted values as solid circles. res=plot(oil.IMA11alt,n.ahead=n.ahead,newxreg=newxreg, ylab='Oil Price',xlab='Year',n1=c(2000,1),transform=exp,pch=19,col=NULL) # Setting col=NULL will make the prediction bands invisible. Try col='red'. res # prints the predicted values and their 95% prediction limits.
This function is adapted from the plot.regsubsets function of the leaps package, and its main use is to plot the output from the armasubsets function.
## S3 method for class 'armasubsets' plot(x, labels = obj$xnames, main = NULL, scale = c("BIC", "AICc", "AIC", "Cp", "adjR2", "R2"), col = gray(c(seq(0.4, 0.7, length = 10), 0.9)), draw.grid = TRUE, axis.at.3 = TRUE, ...)## S3 method for class 'armasubsets' plot(x, labels = obj$xnames, main = NULL, scale = c("BIC", "AICc", "AIC", "Cp", "adjR2", "R2"), col = gray(c(seq(0.4, 0.7, length = 10), 0.9)), draw.grid = TRUE, axis.at.3 = TRUE, ...)
x |
an object of class armasubsets |
labels |
variable names |
main |
title for plot |
scale |
which summary statistic to use for ordering plots |
col |
the last color should be close to but distinct from white |
draw.grid |
a logical argument; if it is true (default), gray grid lines are superimposed on the graph. |
axis.at.3 |
a logical argument; if if it is true (default), the x-labels are drawn on the upper horizontal axis. |
... |
other arguments |
Plot the few best subset ARMA models.
Kung-Sik Chan, based on previoud work by Thomas Lumley and Merlise Clyde
armasubsets
set.seed(53331) test=arima.sim(model=list(ar=c(rep(0,11),.8),ma=c(rep(0,11),0.7)),n=120) res=armasubsets(y=test,nar=14,nma=14,y.name='test',ar.method='ols') plot(res)set.seed(53331) test=arima.sim(model=list(ar=c(rep(0,11),.8),ma=c(rep(0,11),0.7)),n=120) res=armasubsets(y=test,nar=14,nma=14,y.name='test',ar.method='ols') plot(res)
A workhorse function for the acf function in the TSA pacakage.
Kung-Sik Chan
Predictions based on a fitted TAR model. The errors are assumed to be normally distributed. The predictive distributions are approximated by simulation.
## S3 method for class 'TAR' predict(object, n.ahead = 1, n.sim = 1000,...)## S3 method for class 'TAR' predict(object, n.ahead = 1, n.sim = 1000,...)
object |
a fitted TAR model from the tar function |
n.ahead |
number of prediction steps ahead |
n.sim |
simulation size |
... |
other arguments; not used here but kept for consistency with the generic method |
fit |
a vector of medians of the 1-step to n.ahead-step predictive distributions |
pred.interval |
a matrix whose i-th row consists of the 2.5 and 97.5 precentiles of the i-step predictive distribution |
pred.matrix |
a matrix whose j-th column consists of all simulated values from the j-step predictive distribution |
Kung-Sik Chan
"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan
data(prey.eq) prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE) set.seed(2357125) pred.prey=predict(prey.tar.1,n.ahead=60,n.sim=1000) yy=ts(c(log(prey.eq),pred.prey$fit),frequency=1,start=1) plot(yy,type='n',ylim=range(c(yy,pred.prey$pred.interval)),ylab='Log Prey', xlab=expression(t)) lines(log(prey.eq)) lines(window(yy, start=end(prey.eq)[1]+1),lty=2) lines(ts(pred.prey$pred.interval[2,],start=end(prey.eq)[1]+1),lty=2) lines(ts(pred.prey$pred.interval[1,],start=end(prey.eq)[1]+1),lty=2)data(prey.eq) prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE) set.seed(2357125) pred.prey=predict(prey.tar.1,n.ahead=60,n.sim=1000) yy=ts(c(log(prey.eq),pred.prey$fit),frequency=1,start=1) plot(yy,type='n',ylim=range(c(yy,pred.prey$pred.interval)),ylab='Log Prey', xlab=expression(t)) lines(log(prey.eq)) lines(window(yy, start=end(prey.eq)[1]+1),lty=2) lines(ts(pred.prey$pred.interval[2,],start=end(prey.eq)[1]+1),lty=2) lines(ts(pred.prey$pred.interval[1,],start=end(prey.eq)[1]+1),lty=2)
Monthly U.S. average prescription costs for the months 08/1986 - 03/1992.
data(prescrip)data(prescrip)
The format is: Time-Series [1:68] from 1987 to 1992: 14.5 14.7 14.8 14.6 14.3 ...
Frees, E. W., Data Analysis Using Regression Models, Prentice Hall, 1996.
data(prescrip) ## maybe str(prescrip) ; plot(prescrip) ...data(prescrip) ## maybe str(prescrip) ; plot(prescrip) ...
The bivariate time series are prewhitened according to an AR model fitted to the x-component of the bivariate series. Alternatively, if an ARIMA model is provided, it will be used to prewhiten both series. The CCF of the prewhitened bivariate series is then computed and plotted.
prewhiten(x, y, x.model = ar.res,ylab="CCF", ...)prewhiten(x, y, x.model = ar.res,ylab="CCF", ...)
x |
first component series |
y |
second component series |
x.model |
an ARIMA model; if provided, it is used to prewhiten both series. Otherwise, an AR model is fitted to the x-series and used to prewhiten both series.The AR order is chosen by minimizing the AIC and the fit carried out by the ar.ols function. |
ylab |
label of y-axis; default is "CCF" |
... |
additional parameters to be passed to the ar.ols and the ccf function. |
A list containing the following components:
ccf |
Output from the ccf function on the prewhitened data. |
ar |
The AR model fit to the x-series, or x.model if it is provided. |
Kung-Sik Chan
data(milk) data(electricity) milk.electricity=ts.intersect(milk,log(electricity)) plot(milk.electricity,yax.flip=TRUE,main='') ccf(as.numeric(milk.electricity[,1]),as.numeric(milk.electricity[,2]), main='milk & electricity',ylab='CCF') me.dif=ts.intersect(diff(diff(milk,12)),diff(diff(log(electricity),12))) prewhiten(as.numeric(me.dif[,1]),as.numeric(me.dif[,2]), ,ylab='CCF' )data(milk) data(electricity) milk.electricity=ts.intersect(milk,log(electricity)) plot(milk.electricity,yax.flip=TRUE,main='') ccf(as.numeric(milk.electricity[,1]),as.numeric(milk.electricity[,2]), main='milk & electricity',ylab='CCF') me.dif=ts.intersect(diff(diff(milk,12)),diff(diff(log(electricity),12))) prewhiten(as.numeric(me.dif[,1]),as.numeric(me.dif[,2]), ,ylab='CCF' )
The stationary part of the Didinium series in the veilleux data frame.
data(prey.eq)data(prey.eq)
The format is: Time-Series [1:57] from 7 to 35: 26.9 53.2 65.6 81.2 143.9 ...
data(prey.eq) ## maybe str(prey.eq) ; plot(prey.eq) ...data(prey.eq) ## maybe str(prey.eq) ; plot(prey.eq) ...
Simulates a first-order quadratic AR model with normally distributed noise.
qar.sim(const = 0, phi0 = 0, phi1 = 0.5, sigma = 1, n = 20, init = 0)qar.sim(const = 0, phi0 = 0, phi1 = 0.5, sigma = 1, n = 20, init = 0)
const |
intercept |
phi0 |
coefficient of the lag 1 |
phi1 |
coefficient of the squared lag 1 |
sigma |
noise standard deviation |
n |
sample size |
init |
number of burn-in values |
The quadratic AR(1) model specifies that
where are iid normally distributed with zero mean and standard
deviation . If , the model is deterministic.
A simulated series from the quadratic AR(1) model, as a vector
Kung-Sik Chan
set.seed(1234567) plot(y=qar.sim(n=15,phi1=.5,sigma=1),x=1:15,type='l',ylab=expression(Y[t]),xlab='t') y=qar.sim(n=100,const=0.0,phi0=3.97, phi1=-3.97,sigma=0,init=.377) plot(y,x=1:100,type='l',ylab=expression(Y[t]),xlab='t') acf(y,main='')set.seed(1234567) plot(y=qar.sim(n=15,phi1=.5,sigma=1),x=1:15,type='l',ylab=expression(Y[t]),xlab='t') y=qar.sim(n=100,const=0.0,phi0=3.97, phi1=-3.97,sigma=0,init=.377) plot(y,x=1:100,type='l',ylab=expression(Y[t]),xlab='t') acf(y,main='')
Monthly total UK (United Kingdom) retail sales (non-food stores in billions of pounds), 01/1983 - 12/1987.
data(retail)data(retail)
The format is: Time-Series [1:60] from 1983 to 1988: 81.3 78.9 93.8 94 97.8 1.6 99.6 1.2 98 1.7 ...
www.statistics.gov.uk/statbase/TSDdownload1.asp
data(retail) ## maybe str(retail) ; plot(retail) ...data(retail) ## maybe str(retail) ; plot(retail) ...
Final position in the x direction of an industrial robot put through a series of planned exercises many times.
data(robot)data(robot)
The format is: Time-Series [1:324] from 1 to 324: 0.0011 0.0011 0.0024 0 -0.0018 0.0055 0.0055 -0.0015 0.0047 -1e-04 ...
Personal communication from William F. Fulkerson, Deere & Co. Technical Center, Moline, Illinois.
data(robot) ## maybe str(robot) ; plot(robot) ...data(robot) ## maybe str(robot) ; plot(robot) ...
Computes the internally standardized residuals from a fitted ARIMA model.
## S3 method for class 'Arima' rstandard(model,...)## S3 method for class 'Arima' rstandard(model,...)
model |
model fitted by the arima function |
... |
not used; kept here for consistency with the generic method |
residuals/(error std. dev.)
time series of standarized residuals
data(oil.price) m1.oil=arima(log(oil.price),order=c(0,1,1)) plot(rstandard(m1.oil),ylab='Standardized residuals',type='l') abline(h=0)data(oil.price) m1.oil=arima(log(oil.price),order=c(0,1,1)) plot(rstandard(m1.oil),ylab='Standardized residuals',type='l') abline(h=0)
Test the independence of a sequence of random variables by checking whether there are too many or too few runs above (or below) the median.
runs(x,k=0)runs(x,k=0)
x |
time series |
k |
the value above or below which runs are counted; default is zero, so data is assumed to have zero median |
The runs test examines the data in sequence to look for patterns that would give evidence against independence. Runs above or below k are counted. A small number of runs would indicate that neighboring values are positively dependent and tend to hang together over time. On the other hand, too many runs would indicate that the data oscillate back and forth across their median of zero. Then neighboring residuals are negatively dependent. So either too few or too many runs lead us to reject independence. When applied to residuals, the runs test is useful for model diagnostics.
pvalue |
p-value of the test |
observed.runs |
observed number of runs |
expected.runs |
expected number of runs |
n1 |
number of data less than or equal to k |
n2 |
number of data above k |
Kung-Sik Chan
data(tempdub) month.=season(tempdub) # the period sign is included to make the printout from # the following command clearer. model3=lm(tempdub~month.) # intercept is automatically included so one month (Jan) is dropped summary(model3) runs(rstudent(model3))data(tempdub) month.=season(tempdub) # the period sign is included to make the printout from # the following command clearer. model3=lm(tempdub~month.) # intercept is automatically included so one month (Jan) is dropped summary(model3) runs(rstudent(model3))
A simulated random walk with standard normal increments
data(rwalk)data(rwalk)
data(rwalk) ## maybe str(rwalk) ; plot(rwalk) ...data(rwalk) ## maybe str(rwalk) ; plot(rwalk) ...
Extract the season info from a equally spaced time series and create a vector of the season info. For example for monthly data, the function outputs a vector containing the months of the data.
season(x, labels)season(x, labels)
x |
a time series |
labels |
the user supplied labels for the seasons |
The time series must have frequency greater than 1, otherwise the function will stop and issue an error message. If labels is missing, labels will be set as follows: It is set to be c("1Q","2Q","3Q","4Q) if the frequency of x equals 4, c("January",...,"December") if the frequency equals 12, and c("Monday",...,"Sunday") if frequency equals 7. Otherwise, it is set to be c("S1",...)
An invisible vector containing the seasons of the data
Kung-Sik Chan
data(tempdub) month.=season(tempdub) # the period sign is included to make the printout from # the commands two line below clearer; ditto below. model2=lm(tempdub~month.-1) # -1 removes the intercept term summary(model2)data(tempdub) month.=season(tempdub) # the period sign is included to make the printout from # the commands two line below clearer; ditto below. model2=lm(tempdub~month.-1) # -1 removes the intercept term summary(model2)
Computes the skewness of the data
skewness(x, na.rm = FALSE)skewness(x, na.rm = FALSE)
x |
data |
na.rm |
logical variable, if true, missing values are excluded from analysis |
Given data , the sample skewness is
defined by the formula:
The function returns the skewness of the data.
Kung-Sik Chan
data(CREF) r.cref=diff(log(CREF))*100 skewness(r.cref)data(CREF) r.cref=diff(log(CREF))*100 skewness(r.cref)
Quarterly S&P Composite Index, 1936Q1 - 1977Q4.
data(SP)data(SP)
The format is: Time-Series [1:168] from 1936 to 1978: 149 148 160 172 179 ...
Frees, E. W., Data Analysis Using Regression Models, Prentice Hall, 1996.
data(SP) ## maybe str(SP) ; plot(SP) ...data(SP) ## maybe str(SP) ; plot(SP) ...
This is a wrapper that allows the user to invoke either the spec.pgram function or the spec.ar function in the stats pacakge. Note that the seasonal attribute of the data, if it exists, will be removed, for our preferred way of presenting the output.
spec(x, taper = 0, detrend = FALSE, demean = TRUE, method = c("pgram", "ar")[1], ci.plot = FALSE, ylim = range(c(lower.conf.band, upper.conf.band)), ...)spec(x, taper = 0, detrend = FALSE, demean = TRUE, method = c("pgram", "ar")[1], ci.plot = FALSE, ylim = range(c(lower.conf.band, upper.conf.band)), ...)
A list that contains the following:
x |
A univariate or multivariate time series |
taper |
amount of taper; 0 is the default |
detrend |
logical; if True, the data are detrended; default is False |
demean |
logical; if True, the data are centered; default is True |
method |
String specifying the method used to estimate the spectral density. Allowed methods are "pgram" (the default) and "ar". |
ci.plot |
logical; if True, the 95% confidence band will be plotted. |
ylim |
Plotting parameter vector specifying the minimum and maximum of the y-axis. |
... |
other arguments |
The output is from the spec.pgram function or spec.ar function, and the following description of the output is taken from the help manual of the spec function in the stats package. An object of class "spec", which is a list containing at least the following components:
freq |
Vector of frequencies at which the spectral density is estimated. (Possibly approximate Fourier frequencies.) The units are the reciprocal of cycles per unit time (and not per observation spacing): see Details below. |
spec |
Vector (for univariate series) or matrix (for multivariate series) of estimates of the spectral density at frequencies corresponding to freq. coh NULL for univariate series. For multivariate time series, a matrix containing the squared coherency between different series. Column i + (j - 1) * (j - 2)/2 of coh contains the squared coherency between columns i and j of x, where i < j. |
phase |
NULL for univariate series. For multivariate time series a matrix containing the cross-spectrum phase between different series. The format is the same as coh. |
series |
The name of the time series. |
snames |
For multivariate input, the names of the component series. |
method |
The method used to calculate the spectrum. |
The result is returned invisibly if plot is true.
Bloomfield, P. (1976) Fourier Analysis of Time Series: An Introduction. Wiley.
Brockwell, P. J. and Davis, R. A. (1991) Time Series: Theory and Methods. Second edition. Springer.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S-PLUS. Fourth edition. Springer. (Especially pages 3927.)
set.seed(271435); n=200; phi=-0.6 y=arima.sim(model=list(ar=phi),n=n) k=kernel('daniell',m=15) sp=spec(y,kernel=k,main='',sub='',xlab='Frequency', ylab='Log(Smoothed Sample Spectrum)',ci.plot=TRUE,ci.col='black') lines(sp$freq,ARMAspec(model=list(ar=phi),sp$freq,plot=FALSE)$spec,lty=4) abline(h=0)set.seed(271435); n=200; phi=-0.6 y=arima.sim(model=list(ar=phi),n=n) k=kernel('daniell',m=15) sp=spec(y,kernel=k,main='',sub='',xlab='Frequency', ylab='Log(Smoothed Sample Spectrum)',ci.plot=TRUE,ci.col='black') lines(sp$freq,ARMAspec(model=list(ar=phi),sp$freq,plot=FALSE)$spec,lty=4) abline(h=0)
Annual American (relative) sunspot numbers collected from 1945 to 2007. The annual (relative) sunspot number is a weighted average of solar activities measured from a network of observatories.
data(spots)data(spots)
The format is: Time-Series [1:61] from 1945 to 2005: 32.3 99.9 170.9 166.6 174.1 ...
http://www.ngdc.noaa.gov/stp/SOLAR/ftpsunspotnumber.html#american
"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan
data(spots) ## maybe str(spots) ; plot(spots) ...data(spots) ## maybe str(spots) ; plot(spots) ...
Annual international sunspot numbers, NOAA National Geophysical Data Center, 1700 - 2005.
data(spots1)data(spots1)
The format is: ts [1:306, 1] 5 11 16 23 36 58 29 20 10 8 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr "spots" - attr(*, "tsp")= num [1:3] 1700 2005 1
ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/YEARLY.PLT
data(spots1) ## maybe str(spots1) ; plot(spots1) ...data(spots1) ## maybe str(spots1) ; plot(spots1) ...
Brightness (magnitude) of a particular star at midnight on 600 consecutive nights.
data(star)data(star)
Whittaker, E. T. and Robinson, G., (1924). The Calculus of Observations. London: Blackie and Son.
data(star) ## maybe str(star) ; plot(star) ... data(star) plot(star,xlab='Day',ylab='Brightness')data(star) ## maybe str(star) ; plot(star) ... data(star) plot(star,xlab='Day',ylab='Brightness')
Add the calculation of AIC and AICc. See the help manual of regsubsets function of the leaps package
## S3 method for class 'armasubsets' summary(object, all.best = TRUE, matrix = TRUE, matrix.logical = FALSE, df = NULL, ...)## S3 method for class 'armasubsets' summary(object, all.best = TRUE, matrix = TRUE, matrix.logical = FALSE, df = NULL, ...)
object |
armasubsets object |
all.best |
Show all the best subsets or just one of each size |
matrix |
Show a matrix of the variables in each model or just summary statistics |
matrix.logical |
With matrix=TRUE, the matrix is logical TRUE/FALSE or string "*"/code" " |
df |
Specify a number of degrees of freedom for the summary statistics. The default is n-1 |
... |
Other arguments for future methods |
Kung-Sik Chan, based on previous work of Thomas Lumley
Estimation of a two-regime TAR model.
tar(y, p1, p2, d, is.constant1 = TRUE, is.constant2 = TRUE, transform = "no", center = FALSE, standard = FALSE, estimate.thd = TRUE, threshold, method = c("MAIC", "CLS")[1], a = 0.05, b = 0.95, order.select = TRUE, print = FALSE)tar(y, p1, p2, d, is.constant1 = TRUE, is.constant2 = TRUE, transform = "no", center = FALSE, standard = FALSE, estimate.thd = TRUE, threshold, method = c("MAIC", "CLS")[1], a = 0.05, b = 0.95, order.select = TRUE, print = FALSE)
y |
time series |
p1 |
AR order of the lower regime |
p2 |
AR order of the upper regime |
d |
delay parameter |
is.constant1 |
if True, intercept included in the lower regime, otherwise the intercept is fixed at zero |
is.constant2 |
similar to is.constant1 but for the upper regime |
transform |
available transformations: "no" (i.e. use raw data), "log", "log10" and "sqrt" |
center |
if set to be True, data are centered before analysis |
standard |
if set to be True, data are standardized before analysis |
estimate.thd |
if True, threshold parameter is estimated, otherwise it is fixed at the value supplied by threshold |
threshold |
known threshold value, only needed to be supplied if estimate.thd is set to be False. |
method |
"MAIC": estimate the TAR model by minimizing the AIC; "CLS": estimate the TAR model by the method of Conditional Least Squares. |
a |
lower percent; the threshold is searched over the interval defined by the a*100 percentile to the b*100 percentile of the time-series variable |
b |
upper percent |
order.select |
If method is "MAIC", setting order.select to True will enable the function to further select the AR order in each regime by minimizing AIC |
print |
if True, the estimated model will be printed |
The two-regime Threshold Autoregressive (TAR) model is given by the following formula:
where r is the threshold and d the delay.
A list of class "TAR" which can be further processed by the by the predict and tsdiag functions.
Kung-Sik Chan
Tong, H. (1990) "Non-linear Time Series, a Dynamical System Approach," Clarendon Press Oxford
"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan
predict.TAR,
tsdiag.TAR,
tar.sim,
tar.skeleton
data(prey.eq) prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE)data(prey.eq) prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE)
Simulate a two-regime TAR model.
tar.sim(object, ntransient = 500, n = 500, Phi1, Phi2, thd, d, p, sigma1, sigma2, xstart = rep(0, max(p,d)), e)tar.sim(object, ntransient = 500, n = 500, Phi1, Phi2, thd, d, p, sigma1, sigma2, xstart = rep(0, max(p,d)), e)
object |
a TAR model fitted by the tar function; if it is supplied, the model parameters and initial values are extracted from it |
ntransient |
the burn-in size |
n |
sample size of the simulated series |
Phi1 |
the coefficient vector of the lower-regime model |
Phi2 |
the coefficient vector of the upper-regime model |
thd |
threshold |
d |
delay |
p |
maximum autoregressive order |
sigma1 |
noise std. dev. in the lower regime |
sigma2 |
noise std. dev. in the upper regime |
xstart |
initial values for the simulation |
e |
standardized noise series of size equal to length(xstart)+ntransient+n; if missing, it will be generated as some normally distributed errors |
The two-regime Threshold Autoregressive (TAR) model is given by the following formula:
where r is the threshold and d the delay.
A list containing the following components:
y |
simulated TAR series |
e |
the standardized errors |
...
Kung-Sik Chan
Tong, H. (1990) "Non-linear Time Series, a Dynamical System Approach," Clarendon Press Oxford "Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan
set.seed(1234579) y=tar.sim(n=100,Phi1=c(0,0.5), Phi2=c(0,-1.8),p=1,d=1,sigma1=1,thd=-1, sigma2=2)$y plot(y=y,x=1:100,type='b',xlab="t",ylab=expression(Y[t]))set.seed(1234579) y=tar.sim(n=100,Phi1=c(0,0.5), Phi2=c(0,-1.8),p=1,d=1,sigma1=1,thd=-1, sigma2=2)$y plot(y=y,x=1:100,type='b',xlab="t",ylab=expression(Y[t]))
The skeleton of a TAR model is obtained by suppressing the noise term from the TAR model.
tar.skeleton(object, Phi1, Phi2, thd, d, p, ntransient = 500, n = 500, xstart, plot = TRUE,n.skeleton = 50)tar.skeleton(object, Phi1, Phi2, thd, d, p, ntransient = 500, n = 500, xstart, plot = TRUE,n.skeleton = 50)
object |
a TAR model fitted by the tar function; if it is supplied, the model parameters and initial values are extracted from it |
ntransient |
the burn-in size |
n |
sample size of the skeleton trajectory |
Phi1 |
the coefficient vector of the lower-regime model |
Phi2 |
the coefficient vector of the upper-regime model |
thd |
threshold |
d |
delay |
p |
maximum autoregressive order |
xstart |
initial values for the iteration of the skeleton |
plot |
if True, the time series plot of the skeleton is drawn |
n.skeleton |
number of last n.skeleton points of the skeleton to be plotted |
The two-regime Threshold Autoregressive (TAR) model is given by the following formula:
where r is the threshold and d the delay.
A vector that contains the trajectory of the skeleton, with the burn-in discarded.
Kung-Sik Chan
Tong, H. (1990) "Non-linear Time Series, a Dynamical System Approach," Clarendon Press Oxford. "Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan
data(prey.eq) prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE) tar.skeleton(prey.tar.1)data(prey.eq) prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE) tar.skeleton(prey.tar.1)
A digitized sound file of about 0.4 seconds of a B flat just below middle C played on a tenor trombone by Chuck Kreeb, a member of Tempered Brass and a friend of one of the authors.
data(tbone)data(tbone)
The format is: Time-Series [1:17689] from 1 to 17689: 0.0769 0.0862 0.0961 0.1050 0.1129 ...
data(tbone) ## maybe str(tbone) ; plot(tbone) ...data(tbone) ## maybe str(tbone) ; plot(tbone) ...
Monthly average temperature (in degrees Fahrenheit) recorded in Dubuque 1/1964 - 12/1975.
data(tempdub)data(tempdub)
The format is: Time-Series [1:144] from 1964 to 1976: 24.7 25.7 30.6 47.5 62.9 68.5 73.7 67.9 61.1 48.5 ...
http://mesonet.agron.iastate.edu/climodat/index.phtml?station=ia2364&report=16
data(tempdub) ## maybe str(tempdub) ; plot(tempdub) ...data(tempdub) ## maybe str(tempdub) ; plot(tempdub) ...
Carry out the likelihood ratio test for threshold nonlinearity, with the null hypothesis being a normal AR process and the alternative hypothesis being a TAR model with homogeneous, normally distributed errors.
tlrt(y, p, d = 1, transform = "no", a = 0.25, b = 0.75,...)tlrt(y, p, d = 1, transform = "no", a = 0.25, b = 0.75,...)
y |
time series |
p |
working AR order |
d |
delay |
transform |
available transformations: "no" (i.e. use raw data), "log", "log10" and "sqrt" |
a |
lower percent; the threshold is searched over the interval defined by the a*100 percentile to the b*100 percentile of the time-series variable |
b |
upper percent |
... |
other arguments to be passed to the ar function which determines the Ar order, if p is missing |
The search for the threshold parameter may be narrower than that defined by the user as the function attempts to ensure adequate sample size in each regime of the TAR model. The p-value of the test is based on large-sample approximation and also is more reliable for small p-values.
p.value |
p-value of the test |
test.statistic |
likelihood ratio test statistic |
a |
the actual lower fraction that defines the interval of search for the threshold; it may differ from the a specified by the user |
b |
the actual upper fraction that defines the interval of search for the threshold |
Kung-Sik Chan
Chan, K.S. (1990). Percentage points of likelihood ratio tests for threshold autoregression. Journal of Royal Statistical Society, B 53, 3, 691-696.
data(spots) pvaluem=NULL for (d in 1:5){ res=tlrt(sqrt(spots),p=5,d=d,a=0.25,b=0.75) pvaluem= cbind( pvaluem, round(c(d,signif(c(res$test.statistic, res$p.value))),3)) } rownames(pvaluem)=c('d','test statistic','p-value') pvaluemdata(spots) pvaluem=NULL for (d in 1:5){ res=tlrt(sqrt(spots),p=5,d=d,a=0.25,b=0.75) pvaluem= cbind( pvaluem, round(c(d,signif(c(res$test.statistic, res$p.value))),3)) } rownames(pvaluem)=c('d','test statistic','p-value') pvaluem
Carry out Tsay's test for quadratic nonlinearity in a time series.
Tsay.test(x, order, ...)Tsay.test(x, order, ...)
x |
time series |
order |
working linear AR order; if missing, it will be estimated via the ar function by minimizing AIC |
... |
options to be passed to the ar function |
The null hypothesis is that the true model is an AR process. The AR order, if missing, is estimated by minimizing AIC via the ar function, i.e. fitting autoregressive model to the data. The default fitting method of the ar function is "yule-walker."
A list containing the following components
test.stat |
The observed test statistic |
p.value |
p-value of the test |
order |
working AR order |
Kung-Sik Chan
Tsay, R. S. (1986), Nonlinearity test for time series, Biometrika, 73, 461-466.
data(spots) Tsay.test(sqrt(spots))data(spots) Tsay.test(sqrt(spots))
This function is modified from the tsdiag function of the stats package.
## S3 method for class 'Arimax' tsdiag(object, gof.lag, tol = 0.1, col = "red", omit.initial = TRUE,...)## S3 method for class 'Arimax' tsdiag(object, gof.lag, tol = 0.1, col = "red", omit.initial = TRUE,...)
object |
a fitted ARIMAX model |
gof.lag |
maximum lag used in ACF and Ljung-Box tests for the residuals |
tol |
tolerance (default=0.1); see below |
col |
color of some warning lines in the figures (default=red) |
omit.initial |
suppress the initial (d+Ds) residuals if true |
... |
other arguments to be passed to the acf function |
Side effects: Plot the time plot of the standardized residuals. Red dashed line at +/-qnorm(0.025/no of data) are added to the plot. Data beyond these lines are deemed outliers, based on the Bonferronni rule. The ACF of the standardized residuals is plotted. The p-values of the Ljung-Box test are plotted using a variety of the first K residuals. K starts at the lag on and beyond which the moving-average weights (in the MA(infinity) representation) are less than tol.
Kung-Sik Chan, based on the tsdiag function of the stats pacakage
data(color) m1.color=arima(color,order=c(1,0,0)) tsdiag(m1.color,gof=15,omit.initial=FALSE)data(color) m1.color=arima(color,order=c(1,0,0)) tsdiag(m1.color,gof=15,omit.initial=FALSE)
The time series plot and the sample ACF of the standardized residuals are plotted. Also, a portmanteau test for detecting residual correlations in the standardized residuals are carried out.
## S3 method for class 'TAR' tsdiag(object, gof.lag, col = "red",xlab = "t", ...)## S3 method for class 'TAR' tsdiag(object, gof.lag, col = "red",xlab = "t", ...)
object |
a fitted TAR model output from the tar function |
gof.lag |
number of lags of ACF to be examined |
col |
color of the lines flagging outliers, etc. |
xlab |
x labels for the plots |
... |
any additional user-supplied options to be passed to the acf function |
Side effects: plot the time-series plot of the standardized residuals, their sample ACF and portmanteau test for residual autocorrelations in the standardized errors.
Kung-Sik Chan
"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan
data(prey.eq) prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE) tsdiag(prey.tar.1)data(prey.eq) prey.tar.1=tar(y=log(prey.eq),p1=4,p2=4,d=3,a=.1,b=.9,print=TRUE) tsdiag(prey.tar.1)
A digitized sound file of about 0.4 seconds of a B flat an octave and one whole step below middle C played on a BB flat tuba by Linda Fisher, a member of Tempered Brass and a friend one of the authors.
data(tuba)data(tuba)
The format is: Time-Series [1:4402] from 1 to 4402: 0.217 0.209 0.200 0.195 0.196 ...
data(tuba) ## maybe str(tuba) ; plot(tuba) ...data(tuba) ## maybe str(tuba) ; plot(tuba) ...
Annual sales of certain large equipment, 1983 - 2005.
data(units)data(units)
The format is: ts [1:24, 1] 71.7 78.6 111.1 125.6 133.0 ... - attr(*, "tsp")= num [1:3] 1982 2005 1 - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr "Units"
Proprietary sales data from a large international company
data(units) ## maybe str(units) ; plot(units) ...data(units) ## maybe str(units) ; plot(units) ...
Daily USD/HKD (US dollar to Hong Kong dollar) exchange rate from January 1, 2005 to March 7, 2006
data(usd.hkd)data(usd.hkd)
A data frame with 431 observations on the following 6 variables.
rdaily returns of USD/HKD exchange rates
vestimated conditional variances based on an AR(1)+GARCH(3,1) model
hkratedaily USD/HKD exchange rates
outlier1dummy variable of day 203, corresponding to July 22, 2005
outlier2dummy variable of day 290, another possible outlier
daycalendar day
http://www.oanda.com/convert/fxhistory
"Time Series Analysis, with Applications in R" by J.D. Cryer and K.S. Chan
data(usd.hkd) ## maybe str(usd.hkd) ; plot(usd.hkd) ...data(usd.hkd) ## maybe str(usd.hkd) ; plot(usd.hkd) ...
A data frame consisting of bivariate time series from an experiment for studying prey-predator dynamics. The first time series consists of the numbers of prey individuals (Didinium natsutum) per ml measured every twelve hours over a period of 35 days; the second time series consists of the corresponding number of predators (Paramecium aurelia) per ml.
data(veilleux)data(veilleux)
The format is: mts [1:71, 1:2] 15.7 53.6 73.3 93.9 115.4 ... - attr(*, "dimnames")=List of 2 ..$ : NULL ..$ : chr [1:2] "Didinium" "Paramecium" - attr(*, "tsp")= num [1:3] 0 35 2 - attr(*, "class")= chr [1:2] "mts" "ts"
http://www-personal.buseco.monash.edu.au/~hyndman/TSDL/
Veilleux (1976) "The analysis of a predatory interaction between Didinium and Paramecium", Masters thesis, University of Alberta.
Jost & Ellner (2000) "Testing for predator dependence in predator-prey dynamics: a non-parametric approach", Proceedings of the Royal Society of London B, 267, 1611-1620.
data(veilleux) ## maybe str(veilleux) ; plot(veilleux) ...data(veilleux) ## maybe str(veilleux) ; plot(veilleux) ...
Average hourly wages in the apparel industry, from 07/1981 - 06/1987.
data(wages)data(wages)
The format is: Time-Series [1:72] from 1982 to 1987: 4.92 4.96 5.04 5.05 5.04 5.04 5.18 5.13 5.15 5.18 ...
Cryer, J. D. Time Series Analysis, Duxbury Press, 1986.
data(wages) ## maybe str(wages) ; plot(wages) ...data(wages) ## maybe str(wages) ; plot(wages) ...
Monthly unit sales of recreational vehicles from Winnebago, Inc., Forrest City, Iowa, from 11/1966 - 02/1972.
data(winnebago)data(winnebago)
The format is: Time-Series [1:64] from 1967 to 1972: 61 48 53 78 75 58 146 193 124 120 ...
Roberts, H. V., Data Analysis for Managers with Minitab, second edition, The Scientific Press, 1991.
data(winnebago) ## maybe str(winnebago) ; plot(winnebago) ...data(winnebago) ## maybe str(winnebago) ; plot(winnebago) ...
Computes the lag of a vector, with missing elements replaced by NA
zlag(x, d= 1)zlag(x, d= 1)
x |
vector |
d |
compute the lag d of x |
A vector whose k-th element equals x[k-d] with x[t]=NA for t<=0
Kung-Sik Chan
##---- Should be DIRECTLY executable !! ---- ##-- ==> Define data, use random, ##-- or do help(data=index) for the standard data sets. x=1:5 zlag(x,2)##---- Should be DIRECTLY executable !! ---- ##-- ==> Define data, use random, ##-- or do help(data=index) for the standard data sets. x=1:5 zlag(x,2)