, Blake LeBaron [ctb]
(BDS test code)| Title: | Time Series Analysis and Computational Finance |
|---|---|
| Description: | Time series analysis and computational finance. |
| Authors: | Adrian Trapletti [aut], Kurt Hornik [aut, cre]
, Blake LeBaron [ctb]
(BDS test code) |
| Maintainer: | Kurt Hornik <[email protected]> |
| License: | GPL-2 | GPL-3 |
| Version: | 0.10-58 |
| Built: | 2024-10-24 07:01:29 UTC |
| Source: | CRAN |
Computes the Augmented Dickey-Fuller test for the null that x has
a unit root.
adf.test(x, alternative = c("stationary", "explosive"), k = trunc((length(x)-1)^(1/3)))adf.test(x, alternative = c("stationary", "explosive"), k = trunc((length(x)-1)^(1/3)))
x |
a numeric vector or time series. |
alternative |
indicates the alternative hypothesis and must be
one of |
k |
the lag order to calculate the test statistic. |
The general regression equation which incorporates a constant and a
linear trend is used and the t-statistic for a first order
autoregressive coefficient equals one is computed. The number of lags
used in the regression is k. The default value of
trunc((length(x)-1)^(1/3)) corresponds to the suggested upper
bound on the rate at which the number of lags, k, should be
made to grow with the sample size for the general ARMA(p,q)
setup. Note that for k equals zero the standard Dickey-Fuller
test is computed. The p-values are interpolated from Table 4.2, p. 103
of Banerjee et al. (1993). If the computed statistic is outside the
table of critical values, then a warning message is generated.
Missing values are not allowed.
A list with class "htest" containing the following components:
statistic |
the value of the test statistic. |
parameter |
the lag order. |
p.value |
the p-value of the test. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name of the data. |
alternative |
a character string describing the alternative hypothesis. |
A. Trapletti
A. Banerjee, J. J. Dolado, J. W. Galbraith, and D. F. Hendry (1993): Cointegration, Error Correction, and the Econometric Analysis of Non-Stationary Data, Oxford University Press, Oxford.
S. E. Said and D. A. Dickey (1984): Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order. Biometrika 71, 599–607.
x <- rnorm(1000) # no unit-root adf.test(x) y <- diffinv(x) # contains a unit-root adf.test(y)x <- rnorm(1000) # no unit-root adf.test(x) y <- diffinv(x) # contains a unit-root adf.test(y)
Fit an ARMA model to a univariate time series by conditional least
squares. For exact maximum likelihood estimation see
arima0.
arma(x, order = c(1, 1), lag = NULL, coef = NULL, include.intercept = TRUE, series = NULL, qr.tol = 1e-07, ...)arma(x, order = c(1, 1), lag = NULL, coef = NULL, include.intercept = TRUE, series = NULL, qr.tol = 1e-07, ...)
x |
a numeric vector or time series. |
order |
a two dimensional integer vector giving the orders of the
model to fit. |
lag |
a list with components |
coef |
If given this numeric vector is used as the initial estimate of the ARMA coefficients. The preliminary estimator suggested in Hannan and Rissanen (1982) is used for the default initialization. |
include.intercept |
Should the model contain an intercept? |
series |
name for the series. Defaults to
|
qr.tol |
the |
... |
additional arguments for |
The following parametrization is used for the ARMA(p,q) model:
where is set to zero if no intercept is included. By using
the argument lag, it is possible to fit a parsimonious submodel
by setting arbitrary and to zero.
arma uses optim to minimize the conditional
sum-of-squared errors. The gradient is computed, if it is needed, by
a finite-difference approximation. Default initialization is done by
fitting a pure high-order AR model (see ar.ols).
The estimated residuals are then used for computing a least squares
estimator of the full ARMA model. See Hannan and Rissanen (1982) for
details.
A list of class "arma" with the following elements:
lag |
the lag specification of the fitted model. |
coef |
estimated ARMA coefficients for the fitted model. |
css |
the conditional sum-of-squared errors. |
n.used |
the number of observations of |
residuals |
the series of residuals. |
fitted.values |
the fitted series. |
series |
the name of the series |
frequency |
the frequency of the series |
call |
the call of the |
vcov |
estimate of the asymptotic-theory covariance matrix for the coefficient estimates. |
convergence |
The |
include.intercept |
Does the model contain an intercept? |
A. Trapletti
E. J. Hannan and J. Rissanen (1982): Recursive Estimation of Mixed Autoregressive-Moving Average Order. Biometrika 69, 81–94.
summary.arma for summarizing ARMA model fits;
arma-methods for further methods;
arima0, ar.
data(tcm) r <- diff(tcm10y) summary(r.arma <- arma(r, order = c(1, 0))) summary(r.arma <- arma(r, order = c(2, 0))) summary(r.arma <- arma(r, order = c(0, 1))) summary(r.arma <- arma(r, order = c(0, 2))) summary(r.arma <- arma(r, order = c(1, 1))) plot(r.arma) data(nino) s <- nino3.4 summary(s.arma <- arma(s, order=c(20,0))) summary(s.arma <- arma(s, lag=list(ar=c(1,3,7,10,12,13,16,17,19),ma=NULL))) acf(residuals(s.arma), na.action=na.remove) pacf(residuals(s.arma), na.action=na.remove) summary(s.arma <- arma(s, lag=list(ar=c(1,3,7,10,12,13,16,17,19),ma=12))) summary(s.arma <- arma(s, lag=list(ar=c(1,3,7,10,12,13,16,17),ma=12))) plot(s.arma)data(tcm) r <- diff(tcm10y) summary(r.arma <- arma(r, order = c(1, 0))) summary(r.arma <- arma(r, order = c(2, 0))) summary(r.arma <- arma(r, order = c(0, 1))) summary(r.arma <- arma(r, order = c(0, 2))) summary(r.arma <- arma(r, order = c(1, 1))) plot(r.arma) data(nino) s <- nino3.4 summary(s.arma <- arma(s, order=c(20,0))) summary(s.arma <- arma(s, lag=list(ar=c(1,3,7,10,12,13,16,17,19),ma=NULL))) acf(residuals(s.arma), na.action=na.remove) pacf(residuals(s.arma), na.action=na.remove) summary(s.arma <- arma(s, lag=list(ar=c(1,3,7,10,12,13,16,17,19),ma=12))) summary(s.arma <- arma(s, lag=list(ar=c(1,3,7,10,12,13,16,17),ma=12))) plot(s.arma)
Methods for fitted ARMA model objects.
## S3 method for class 'arma' coef(object, ...) ## S3 method for class 'arma' vcov(object, ...) ## S3 method for class 'arma' residuals(object, ...) ## S3 method for class 'arma' fitted(object, ...) ## S3 method for class 'arma' print(x, digits = max(3, getOption("digits") - 3), ...) ## S3 method for class 'arma' plot(x, ask = interactive(), ...)## S3 method for class 'arma' coef(object, ...) ## S3 method for class 'arma' vcov(object, ...) ## S3 method for class 'arma' residuals(object, ...) ## S3 method for class 'arma' fitted(object, ...) ## S3 method for class 'arma' print(x, digits = max(3, getOption("digits") - 3), ...) ## S3 method for class 'arma' plot(x, ask = interactive(), ...)
object, x
|
an object of class |
digits |
see |
ask |
Should the |
... |
further arguments passed to or from other methods. |
For coef, a numeric vector; for vcov, a numeric matrix;
for residuals and fitted a univariate time series;
for plot and print, the fitted ARMA model object.
A. Trapletti
Computes and prints the BDS test statistic for the null that x
is a series of i.i.d. random variables.
bds.test(x, m = 3, eps = seq(0.5 * sd(x), 2 * sd(x), length.out = 4), trace = FALSE)bds.test(x, m = 3, eps = seq(0.5 * sd(x), 2 * sd(x), length.out = 4), trace = FALSE)
x |
a numeric vector or time series. |
m |
an integer indicating that the BDS test statistic is computed
for embedding dimensions |
eps |
a numeric vector of epsilon values for close points. The
BDS test is computed for each element of |
trace |
a logical indicating whether some informational output is traced. |
This test examines the “spatial dependence” of the observed
series. To do this, the series is embedded in m-space and the
dependence of x is examined by counting “near” points.
Points for which the distance is less than eps are called
“near”. The BDS test statistic is asymptotically standard Normal.
Missing values are not allowed.
There is a special print method for objects of class "bdstest"
which by default uses 4 digits to format real numbers.
A list with class "bdstest" containing the following components:
statistic |
the values of the test statistic. |
p.value |
the p-values of the test. |
method |
a character string indicating what type of test was performed. |
parameter |
a list with the components |
data.name |
a character string giving the name of the data. |
B. LeBaron, Ported to R by A. Trapletti
J. B. Cromwell, W. C. Labys and M. Terraza (1994): Univariate Tests for Time Series Models, Sage, Thousand Oaks, CA, pages 32–36.
x <- rnorm(100) bds.test(x) # i.i.d. example x <- c(rnorm(50), runif(50)) bds.test(x) # not identically distributed x <- quadmap(xi = 0.2, a = 4.0, n = 100) bds.test(x) # not independentx <- rnorm(100) bds.test(x) # i.i.d. example x <- c(rnorm(50), runif(50)) bds.test(x) # not identically distributed x <- quadmap(xi = 0.2, a = 4.0, n = 100) bds.test(x) # not independent
Contains the well-known Beveridge Wheat Price Index which gives annual price data from 1500 to 1869, averaged over many locations in western and central Europe.
data(bev)data(bev)
A univariate time series with 370 observations. The object is of
class "ts".
This data provides an example of long memory time series which has the appearance of being nonstationary in levels and yet also appears overdifferenced. See, e.g., Baillie (1996).
Time Series Data Library: https://robjhyndman.com/TSDL/
R. T. Baillie (1996): Long Memory Processes and Fractional Integration in Econometrics. Journal of Econometrics, 73, 5–59.
Contains annual tree-ring measurements from Mount Campito from 3426 BC through 1969 AD.
data(camp)data(camp)
A univariate time series with 5405 observations. The object is of
class "ts".
This series is a standard example for the concept of long memory time series.
The data was produced and assembled at the Tree Ring Laboratory at the University of Arizona, Tuscon.
Time Series Data Library: https://robjhyndman.com/TSDL/
Fit a Generalized Autoregressive Conditional Heteroscedastic GARCH(p, q) time series model to the data by computing the maximum-likelihood estimates of the conditionally normal model.
garch(x, order = c(1, 1), series = NULL, control = garch.control(...), ...) garch.control(maxiter = 200, trace = TRUE, start = NULL, grad = c("analytical","numerical"), abstol = max(1e-20, .Machine$double.eps^2), reltol = max(1e-10, .Machine$double.eps^(2/3)), xtol = sqrt(.Machine$double.eps), falsetol = 1e2 * .Machine$double.eps, ...)garch(x, order = c(1, 1), series = NULL, control = garch.control(...), ...) garch.control(maxiter = 200, trace = TRUE, start = NULL, grad = c("analytical","numerical"), abstol = max(1e-20, .Machine$double.eps^2), reltol = max(1e-10, .Machine$double.eps^(2/3)), xtol = sqrt(.Machine$double.eps), falsetol = 1e2 * .Machine$double.eps, ...)
x |
a numeric vector or time series. |
order |
a two dimensional integer vector giving the orders of the
model to fit. |
series |
name for the series. Defaults to
|
control |
a list of control parameters as set up by |
maxiter |
gives the maximum number of log-likelihood function
evaluations |
trace |
logical. Trace optimizer output? |
start |
If given this numeric vector is used as the initial estimate
of the GARCH coefficients. Default initialization is to set the
GARCH parameters to slightly positive values and to initialize the
intercept such that the unconditional variance of the initial GARCH
is equal to the variance of |
grad |
character indicating whether analytical gradients or a numerical approximation is used for the optimization. |
abstol |
absolute function convergence tolerance. |
reltol |
relative function convergence tolerance. |
xtol |
coefficient-convergence tolerance. |
falsetol |
false convergence tolerance. |
... |
additional arguments for |
garch uses a Quasi-Newton optimizer to find the maximum
likelihood estimates of the conditionally normal model. The first
max(p, q) values are assumed to be fixed. The optimizer uses a hessian
approximation computed from the BFGS update. Only a Cholesky factor
of the Hessian approximation is stored. For more details see Dennis
et al. (1981), Dennis and Mei (1979), Dennis and More (1977), and
Goldfarb (1976). The gradient is either computed analytically or
using a numerical approximation.
A list of class "garch" with the following elements:
order |
the order of the fitted model. |
coef |
estimated GARCH coefficients for the fitted model. |
n.likeli |
the negative log-likelihood function evaluated at the coefficient estimates (apart from some constant). |
n.used |
the number of observations of |
residuals |
the series of residuals. |
fitted.values |
the bivariate series of conditional standard
deviation predictions for |
series |
the name of the series |
frequency |
the frequency of the series |
call |
the call of the |
vcov |
outer product of gradient estimate of the asymptotic-theory covariance matrix for the coefficient estimates. |
A. Trapletti, the whole GARCH part; D. M. Gay, the FORTRAN optimizer
A. K. Bera and M. L. Higgins (1993): ARCH Models: Properties, Estimation and Testing. J. Economic Surveys 7 305–362.
T. Bollerslev (1986): Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics 31, 307–327.
R. F. Engle (1982): Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica 50, 987–1008.
J. E. Dennis, D. M. Gay, and R. E. Welsch (1981): Algorithm 573 — An Adaptive Nonlinear Least-Squares Algorithm. ACM Transactions on Mathematical Software 7, 369–383.
J. E. Dennis and H. H. W. Mei (1979): Two New Unconstrained Optimization Algorithms which use Function and Gradient Values. J. Optim. Theory Applic. 28, 453–482.
J. E. Dennis and J. J. More (1977): Quasi-Newton Methods, Motivation and Theory. SIAM Rev. 19, 46–89.
D. Goldfarb (1976): Factorized Variable Metric Methods for Unconstrained Optimization. Math. Comput. 30, 796–811.
summary.garch for summarizing GARCH model fits;
garch-methods for further methods.
n <- 1100 a <- c(0.1, 0.5, 0.2) # ARCH(2) coefficients e <- rnorm(n) x <- double(n) x[1:2] <- rnorm(2, sd = sqrt(a[1]/(1.0-a[2]-a[3]))) for(i in 3:n) # Generate ARCH(2) process { x[i] <- e[i]*sqrt(a[1]+a[2]*x[i-1]^2+a[3]*x[i-2]^2) } x <- ts(x[101:1100]) x.arch <- garch(x, order = c(0,2)) # Fit ARCH(2) summary(x.arch) # Diagnostic tests plot(x.arch) data(EuStockMarkets) dax <- diff(log(EuStockMarkets))[,"DAX"] dax.garch <- garch(dax) # Fit a GARCH(1,1) to DAX returns summary(dax.garch) # ARCH effects are filtered. However, plot(dax.garch) # conditional normality seems to be violatedn <- 1100 a <- c(0.1, 0.5, 0.2) # ARCH(2) coefficients e <- rnorm(n) x <- double(n) x[1:2] <- rnorm(2, sd = sqrt(a[1]/(1.0-a[2]-a[3]))) for(i in 3:n) # Generate ARCH(2) process { x[i] <- e[i]*sqrt(a[1]+a[2]*x[i-1]^2+a[3]*x[i-2]^2) } x <- ts(x[101:1100]) x.arch <- garch(x, order = c(0,2)) # Fit ARCH(2) summary(x.arch) # Diagnostic tests plot(x.arch) data(EuStockMarkets) dax <- diff(log(EuStockMarkets))[,"DAX"] dax.garch <- garch(dax) # Fit a GARCH(1,1) to DAX returns summary(dax.garch) # ARCH effects are filtered. However, plot(dax.garch) # conditional normality seems to be violated
Methods for fitted GARCH model objects.
## S3 method for class 'garch' predict(object, newdata, genuine = FALSE, ...) ## S3 method for class 'garch' coef(object, ...) ## S3 method for class 'garch' vcov(object, ...) ## S3 method for class 'garch' residuals(object, ...) ## S3 method for class 'garch' fitted(object, ...) ## S3 method for class 'garch' print(x, digits = max(3, getOption("digits") - 3), ...) ## S3 method for class 'garch' plot(x, ask = interactive(), ...) ## S3 method for class 'garch' logLik(object, ...)## S3 method for class 'garch' predict(object, newdata, genuine = FALSE, ...) ## S3 method for class 'garch' coef(object, ...) ## S3 method for class 'garch' vcov(object, ...) ## S3 method for class 'garch' residuals(object, ...) ## S3 method for class 'garch' fitted(object, ...) ## S3 method for class 'garch' print(x, digits = max(3, getOption("digits") - 3), ...) ## S3 method for class 'garch' plot(x, ask = interactive(), ...) ## S3 method for class 'garch' logLik(object, ...)
object, x
|
an object of class |
newdata |
a numeric vector or time series to compute GARCH
predictions. Defaults to |
genuine |
a logical indicating whether a genuine prediction should be made, i.e., a prediction for which there is no target observation available. |
digits |
see |
ask |
Should the |
... |
further arguments passed to or from other methods. |
predict returns +/- the conditional standard deviation
predictions from a fitted GARCH model.
coef returns the coefficient estimates.
vcov the associated covariance matrix estimate (outer product of gradients estimator).
residuals returns the GARCH residuals, i.e., the time series
used to fit the model divided by the computed conditional standard
deviation predictions for this series. Under the assumption of
conditional normality the residual series should be i.i.d. standard
normal.
fitted returns +/- the conditional standard deviation
predictions for the series which has been used to fit the model.
plot graphically investigates normality and remaining ARCH
effects for the residuals.
logLik returns the log-likelihood value of the GARCH(p, q)
model represented by object evaluated at the estimated
coefficients. It is assumed that first max(p, q) values are fixed.
For predict a bivariate time series (two-column matrix) of
predictions.
For coef, a numeric vector, for residuals and
fitted a univariate (vector) and a bivariate time series
(two-column matrix), respectively.
For plot and print, the fitted GARCH model object.
A. Trapletti
Download historical financial data from a given data provider over the WWW.
get.hist.quote(instrument = "^gdax", start, end, quote = c("Open", "High", "Low", "Close"), provider = c("yahoo"), method = NULL, origin = "1899-12-30", compression = "d", retclass = c("zoo", "ts"), quiet = FALSE, drop = FALSE)get.hist.quote(instrument = "^gdax", start, end, quote = c("Open", "High", "Low", "Close"), provider = c("yahoo"), method = NULL, origin = "1899-12-30", compression = "d", retclass = c("zoo", "ts"), quiet = FALSE, drop = FALSE)
instrument |
a character string giving the name of the quote symbol to download. See the web page of the data provider for information about the available quote symbols. |
start |
an R object specifying the date of the start of the
period to download. This must be in a form which is recognized by
|
end |
an R object specifying the end of the download period, see above. Defaults to yesterday. |
quote |
a character string or vector indicating whether to
download opening, high, low, or closing quotes, or volume. For the
default provider, this can be specified as |
provider |
a character string with the name of the data
provider. Currently, only |
method |
No longer used. |
origin |
an R object specifying the origin of the Julian dates, see above. Defaults to 1899-12-30 (Popular spreadsheet programs internally also use Julian dates with this origin). |
compression |
Governs the granularity of the retrieved data;
|
retclass |
character specifying which class the return value
should have: can be either |
quiet |
logical. Should status messages (if any) be suppressed? |
drop |
logical. If |
A time series containing the data either as a "zoo" series
(default) or a "ts" series. The "zoo" series is created
with zoo and has an index of class "Date".
If a "ts" series is returned, the index is in physical time,
i.e., weekends, holidays, and missing days are filled with NAs
if not available. The time scale is given in Julian dates (days since
the origin).
A. Trapletti
getSymbols for downloads from various
providers;
zoo,
ts,
as.Date,
as.POSIXct,
tryCatch({ x <- get.hist.quote(instrument = "^gspc", start = "1998-01-01", quote = "Close") plot(x) x <- get.hist.quote(instrument = "ibm", quote = c("Cl", "Vol")) plot(x, main = "International Business Machines Corp") spc <- get.hist.quote(instrument = "^gspc", start = "1998-01-01", quote = "Close") ibm <- get.hist.quote(instrument = "ibm", start = "1998-01-01", quote = "Adj") require("zoo") # For merge() method. x <- merge(spc, ibm) plot(x, main = "IBM vs S&P 500") }, error = identity)tryCatch({ x <- get.hist.quote(instrument = "^gspc", start = "1998-01-01", quote = "Close") plot(x) x <- get.hist.quote(instrument = "ibm", quote = c("Cl", "Vol")) plot(x, main = "International Business Machines Corp") spc <- get.hist.quote(instrument = "^gspc", start = "1998-01-01", quote = "Close") ibm <- get.hist.quote(instrument = "ibm", start = "1998-01-01", quote = "Adj") require("zoo") # For merge() method. x <- merge(spc, ibm) plot(x, main = "IBM vs S&P 500") }, error = identity)
Contains the Icelandic river data as presented in Tong (1990), pages 432–440.
data(ice.river)data(ice.river)
4 univariate time series flow.vat, flow.jok,
prec, and temp, each with 1095 observations and the
joint series ice.river.
The series are daily observations from Jan. 1, 1972 to Dec. 31, 1974
on 4 variables: flow.vat, mean daily flow of Vatnsdalsa river
(cms), flow.jok, mean daily flow of Jokulsa Eystri river (cms),
prec, daily precipitation in Hveravellir (mm), and mean daily
temperature in Hveravellir (deg C).
These datasets were introduced into the literature in a paper by Tong, Thanoon, and Gudmundsson (1985).
Time Series Data Library: https://robjhyndman.com/TSDL/
H. Tong (1990): Non-Linear Time Series, A Dynamical System Approach. Oxford University Press, Oxford.
H. Tong, B. Thanoon, and G. Gudmundsson (1985): Threshold time series modelling of two Icelandic riverflow systems. Water Resources Bulletin, 21, 651–661.
The function irts is used to create irregular time-series
objects.
as.irts coerces an object to an irregularly spaced
time-series. is.irts tests whether an object is an irregularly
spaced time series.
irts(time, value) as.irts(object) is.irts(object)irts(time, value) as.irts(object) is.irts(object)
time |
a numeric vector or a vector of class |
value |
a numeric vector or matrix representing the values of the irregular time-series object. |
object |
an R object to be coerced to an irregular time-series object or an R object to be tested whether it is an irregular time-series object. |
The function irts is used to create irregular time-series
objects. These are scalar or vector valued time series indexed by a
time-stamp of class "POSIXct". Unlike objects of class
"ts", they can be used to represent irregularly spaced
time-series.
A list of class "irts" with the following elements:
time |
a vector of class |
value |
a numeric vector or matrix. |
A. Trapletti
ts,
POSIXct,
irts-methods,
irts-functions
n <- 10 t <- cumsum(rexp(n, rate = 0.1)) v <- rnorm(n) x <- irts(t, v) x as.irts(cbind(t, v)) is.irts(x) # Multivariate u <- rnorm(n) irts(t, cbind(u, v))n <- 10 t <- cumsum(rexp(n, rate = 0.1)) v <- rnorm(n) x <- irts(t, v) x as.irts(cbind(t, v)) is.irts(x) # Multivariate u <- rnorm(n) irts(t, cbind(u, v))
Basic functions related to irregular time-series objects.
daysecond(object, tz = "GMT") approx.irts(object, time, ...) is.businessday(object, tz = "GMT") is.weekend(object, tz = "GMT") read.irts(file, format = "%Y-%m-%d %H:%M:%S", tz = "GMT", ...) weekday(object, tz = "GMT") write.irts(object, file = "", append = FALSE, quote = FALSE, sep = " ", eol = "\n", na = "NA", dec = ".", row.names = FALSE, col.names = FALSE, qmethod = "escape", format = "%Y-%m-%d %H:%M:%S", tz = "GMT", usetz = FALSE, format.value = NULL, ...)daysecond(object, tz = "GMT") approx.irts(object, time, ...) is.businessday(object, tz = "GMT") is.weekend(object, tz = "GMT") read.irts(file, format = "%Y-%m-%d %H:%M:%S", tz = "GMT", ...) weekday(object, tz = "GMT") write.irts(object, file = "", append = FALSE, quote = FALSE, sep = " ", eol = "\n", na = "NA", dec = ".", row.names = FALSE, col.names = FALSE, qmethod = "escape", format = "%Y-%m-%d %H:%M:%S", tz = "GMT", usetz = FALSE, format.value = NULL, ...)
object |
an object of class |
format, tz, usetz
|
formatting related arguments, see
|
time |
an object of class |
file, append, quote, sep, eol, na, dec, row.names, col.names, qmethod
|
reading and writing related arguments, see
|
format.value |
a string which specifies the formatting of the
values when writing an irregular time-series object to a
file. |
... |
further arguments passed to or from other methods: for
|
daysecond and weekday return the number of seconds since
midnight (the same day) and the weekday as a decimal number (0-6,
Sunday is 0), respectively.
is.businessday and is.weekend test which entries of an
irregular time-series object are recorded on business days and
weekends, respectively.
approx.irts interpolates an irregularly spaced time-series at
prespecified times.
read.irts is the function to read irregular time-series
objects from a file.
write.irts is the function to write irregular time-series
objects to a file.
For daysecond and weekday a vector of decimal numbers
representing the number of seconds and the weekday, respectively.
For is.businessday and is.weekend a vector of
"logical" representing the test results for each time.
For approx.irts, read.irts and write.irts an
object of class "irts".
A. Trapletti
n <- 10 t <- cumsum(rexp(n, rate = 0.1)) v <- rnorm(n) x <- irts(t, v) daysecond(x) weekday(x) is.businessday(x) is.weekend(x) x approx.irts(x, seq(ISOdatetime(1970, 1, 1, 0, 0, 0, tz = "GMT"), by = "10 secs", length.out = 7), rule = 2) ## Not run: file <- tempfile() # To write an irregular time-series object to a file one might use write.irts(x, file = file) # To read an irregular time-series object from a file one might use read.irts(file = file) unlink(file) ## End(Not run)n <- 10 t <- cumsum(rexp(n, rate = 0.1)) v <- rnorm(n) x <- irts(t, v) daysecond(x) weekday(x) is.businessday(x) is.weekend(x) x approx.irts(x, seq(ISOdatetime(1970, 1, 1, 0, 0, 0, tz = "GMT"), by = "10 secs", length.out = 7), rule = 2) ## Not run: file <- tempfile() # To write an irregular time-series object to a file one might use write.irts(x, file = file) # To read an irregular time-series object from a file one might use read.irts(file = file) unlink(file) ## End(Not run)
Methods for irregular time-series objects.
## S3 method for class 'irts' lines(x, type = "l", ...) ## S3 method for class 'irts' plot(x, type = "l", plot.type = c("multiple", "single"), xlab = "Time", ylab = NULL, main = NULL, ylim = NULL, oma = c(6, 0, 5, 0), ...) ## S3 method for class 'irts' points(x, type = "p", ...) ## S3 method for class 'irts' print(x, format = "%Y-%m-%d %H:%M:%S", tz = "GMT", usetz = TRUE, format.value = NULL, ...) ## S3 method for class 'irts' time(x, ...) ## S3 method for class 'irts' value(x, ...) ## S3 method for class 'irts' x[i, j, ...]## S3 method for class 'irts' lines(x, type = "l", ...) ## S3 method for class 'irts' plot(x, type = "l", plot.type = c("multiple", "single"), xlab = "Time", ylab = NULL, main = NULL, ylim = NULL, oma = c(6, 0, 5, 0), ...) ## S3 method for class 'irts' points(x, type = "p", ...) ## S3 method for class 'irts' print(x, format = "%Y-%m-%d %H:%M:%S", tz = "GMT", usetz = TRUE, format.value = NULL, ...) ## S3 method for class 'irts' time(x, ...) ## S3 method for class 'irts' value(x, ...) ## S3 method for class 'irts' x[i, j, ...]
x |
an object of class |
type, plot.type, xlab, ylab, main, ylim, oma
|
graphical
arguments, see |
format, tz, usetz
|
formatting related arguments, see
|
format.value |
a string which specifies the formatting of the
values when printing an irregular time-series
object. |
i, j
|
indices specifying the parts to extract from an irregular time-series object. |
... |
further arguments passed to or from other methods: for
|
plot is the method for plotting irregular time-series objects.
points and lines are the methods for drawing a sequence
of points as given by an irregular time-series object and joining the
corresponding points with line segments, respectively.
print is the method for printing irregular time-series objects.
time and value are the methods for extracting the
sequence of times and the sequence of values of an irregular
time-series object.
[.irts is the method for extracting parts of irregular
time-series objects.
For time an object of class "POSIXct" representing the
sequence of times. For value a vector or matrix representing
the sequence of values.
For [.irts an object of class "irts" representing the
extracted part.
For plot, points, lines, and print the
irregular time-series object.
A. Trapletti
n <- 10 t <- cumsum(rexp(n, rate = 0.1)) v <- rnorm(n) x <- irts(t, v) x time(x) value(x) plot(x) points(x) t <- cumsum(c(t[1], rexp(n-1, rate = 0.2))) v <- rnorm(n, sd = 0.1) x <- irts(t, v) lines(x, col = "red") points(x, col = "red") # Multivariate t <- cumsum(rexp(n, rate = 0.1)) u <- rnorm(n) v <- rnorm(n) x <- irts(t, cbind(u, v)) x x[,1] x[1:3,] x[1:3,1] plot(x)n <- 10 t <- cumsum(rexp(n, rate = 0.1)) v <- rnorm(n) x <- irts(t, v) x time(x) value(x) plot(x) points(x) t <- cumsum(c(t[1], rexp(n-1, rate = 0.2))) v <- rnorm(n, sd = 0.1) x <- irts(t, v) lines(x, col = "red") points(x, col = "red") # Multivariate t <- cumsum(rexp(n, rate = 0.1)) u <- rnorm(n) v <- rnorm(n) x <- irts(t, cbind(u, v)) x x[,1] x[1:3,] x[1:3,1] plot(x)
Tests the null of normality for x using the Jarque-Bera
test statistic.
jarque.bera.test(x)jarque.bera.test(x)
x |
a numeric vector or time series. |
This test is a joint statistic using skewness and kurtosis coefficients.
Missing values are not allowed.
A list with class "htest" containing the following components:
statistic |
the value of the test statistic. |
parameter |
the degrees of freedom. |
p.value |
the p-value of the test. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name of the data. |
A. Trapletti
J. B. Cromwell, W. C. Labys and M. Terraza (1994): Univariate Tests for Time Series Models, Sage, Thousand Oaks, CA, pages 20–22.
x <- rnorm(100) # null jarque.bera.test(x) x <- runif(100) # alternative jarque.bera.test(x)x <- rnorm(100) # null jarque.bera.test(x) x <- runif(100) # alternative jarque.bera.test(x)
Computes the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test for the
null hypothesis that x is level or trend stationary.
kpss.test(x, null = c("Level", "Trend"), lshort = TRUE)kpss.test(x, null = c("Level", "Trend"), lshort = TRUE)
x |
a numeric vector or univariate time series. |
null |
indicates the null hypothesis and must be one of
|
lshort |
a logical indicating whether the short or long version of the truncation lag parameter is used. |
To estimate sigma^2 the Newey-West estimator is used.
If lshort is TRUE, then the truncation lag parameter is
set to trunc(4*(n/100)^0.25), otherwise
trunc(12*(n/100)^0.25) is used. The p-values are interpolated
from Table 1 of Kwiatkowski et al. (1992). If the computed statistic
is outside the table of critical values, then a warning message is
generated.
Missing values are not handled.
A list with class "htest" containing the following components:
statistic |
the value of the test statistic. |
parameter |
the truncation lag parameter. |
p.value |
the p-value of the test. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name of the data. |
A. Trapletti
D. Kwiatkowski, P. C. B. Phillips, P. Schmidt, and Y. Shin (1992): Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root. Journal of Econometrics 54, 159–178.
x <- rnorm(1000) # is level stationary kpss.test(x) y <- cumsum(x) # has unit root kpss.test(y) x <- 0.3*(1:1000)+rnorm(1000) # is trend stationary kpss.test(x, null = "Trend")x <- rnorm(1000) # is level stationary kpss.test(x) y <- cumsum(x) # has unit root kpss.test(y) x <- 0.3*(1:1000)+rnorm(1000) # is trend stationary kpss.test(x, null = "Trend")
This function computes the maximum drawdown or maximum loss of the
univariate time series (or vector) x.
maxdrawdown(x)maxdrawdown(x)
x |
a numeric vector or univariate time series. |
The max drawdown or max loss statistic is defined as the maximum
value drop after one of the peaks of x. For financial
instruments the max drawdown represents the worst investment loss for
a buy-and-hold strategy invested in x.
A list containing the following three components:
maxdrawdown |
double representing the max drawdown or max loss statistic. |
from |
the index (or vector of indices) where the max drawdown period starts. |
to |
the index (or vector of indices) where the max drawdown period ends. |
A. Trapletti
# Toy example x <- c(1:10, 9:7, 8:14, 13:8, 9:20) mdd <- maxdrawdown(x) mdd plot(x) segments(mdd$from, x[mdd$from], mdd$to, x[mdd$from], col="grey") segments(mdd$from, x[mdd$to], mdd$to, x[mdd$to], col="grey") mid <- (mdd$from + mdd$to)/2 arrows(mid, x[mdd$from], mid, x[mdd$to], col="red", length = 0.16) # Realistic example data(EuStockMarkets) dax <- log(EuStockMarkets[,"DAX"]) mdd <- maxdrawdown(dax) mdd plot(dax) segments(time(dax)[mdd$from], dax[mdd$from], time(dax)[mdd$to], dax[mdd$from], col="grey") segments(time(dax)[mdd$from], dax[mdd$to], time(dax)[mdd$to], dax[mdd$to], col="grey") mid <- time(dax)[(mdd$from + mdd$to)/2] arrows(mid, dax[mdd$from], mid, dax[mdd$to], col="red", length = 0.16)# Toy example x <- c(1:10, 9:7, 8:14, 13:8, 9:20) mdd <- maxdrawdown(x) mdd plot(x) segments(mdd$from, x[mdd$from], mdd$to, x[mdd$from], col="grey") segments(mdd$from, x[mdd$to], mdd$to, x[mdd$to], col="grey") mid <- (mdd$from + mdd$to)/2 arrows(mid, x[mdd$from], mid, x[mdd$to], col="red", length = 0.16) # Realistic example data(EuStockMarkets) dax <- log(EuStockMarkets[,"DAX"]) mdd <- maxdrawdown(dax) mdd plot(dax) segments(time(dax)[mdd$from], dax[mdd$from], time(dax)[mdd$to], dax[mdd$from], col="grey") segments(time(dax)[mdd$from], dax[mdd$to], time(dax)[mdd$to], dax[mdd$to], col="grey") mid <- time(dax)[(mdd$from + mdd$to)/2] arrows(mid, dax[mdd$from], mid, dax[mdd$to], col="red", length = 0.16)
Observations with missing values in some of the variables are removed.
na.remove(object, ...)na.remove(object, ...)
object |
a numeric matrix, vector, univariate, or multivariate time series. |
... |
further arguments to be passed to or from methods. |
For na.remove.ts this changes the “intrinsic” time scale. It
is assumed that both, the new and the old time scale are synchronized
at the first and the last valid observation. In between, the new
series is equally spaced in the new time scale.
An object without missing values. The attribute "na.removed"
contains the indices of the removed missing values in object.
A. Trapletti
x<-ts(c(5453.08,5409.24,5315.57,5270.53, # one and a half week stock index 5211.66,NA,NA,5160.80,5172.37)) # data including a weekend na.remove(x) # eliminate weekend and introduce ``business'' time scalex<-ts(c(5453.08,5409.24,5315.57,5270.53, # one and a half week stock index 5211.66,NA,NA,5160.80,5172.37)) # data including a weekend na.remove(x) # eliminate weekend and introduce ``business'' time scale
These are the extended Nelson-Plosser Data.
data(NelPlo)data(NelPlo)
14 macroeconomic time series: cpi, ip, gnp.nom,
vel, emp, int.rate, nom.wages,
gnp.def, money.stock, gnp.real,
stock.prices, gnp.capita, real.wages, and
unemp and the joint series NelPlo.
The series are of various lengths but all end in 1988. The data set contains the following series: consumer price index, industrial production, nominal GNP, velocity, employment, interest rate, nominal wages, GNP deflator, money stock, real GNP, stock prices (S&P500), GNP per capita, real wages, unemployment.
C. R. Nelson and C. I. Plosser (1982), Trends and Random Walks in Macroeconomic Time Series. Journal of Monetary Economics, 10, 139–162. doi:10.1016/0304-3932(82)90012-5.
Formerly in the Journal of Business and Economic Statistics data archive, currently at http://korora.econ.yale.edu/phillips/data/np&enp.dat.
G. Koop and M. F. J. Steel (1994), A Decision-Theoretic Analysis of the Unit-Root Hypothesis using Mixtures of Elliptical Models. Journal of Business and Economic Statistics, 12, 95–107. doi:10.1080/07350015.1994.10509993.
These data constitutes of Nino Region 3 and Nino Region 3.4 SST indices.
data(nino)data(nino)
Two univariate time series nino3 and nino3.4 with 598
observations and the joint series nino.
The measurements are given in degrees Celsius. The Nino 3 Region is bounded by 90W-150W and 5S-5N. The Nino 3.4 Region is bounded by 120W-170W and 5S-5N.
Climate Prediction Center: https://www.cpc.ncep.noaa.gov/data/indices/
Plots open-high-low-close bar chart of a (financial) time series.
plotOHLC(x, xlim = NULL, ylim = NULL, xlab = "Time", ylab, col = par("col"), bg = par("bg"), axes = TRUE, frame.plot = axes, ann = par("ann"), main = NULL, date = c("calendar", "julian"), format = "%Y-%m-%d", origin = "1899-12-30", ...)plotOHLC(x, xlim = NULL, ylim = NULL, xlab = "Time", ylab, col = par("col"), bg = par("bg"), axes = TRUE, frame.plot = axes, ann = par("ann"), main = NULL, date = c("calendar", "julian"), format = "%Y-%m-%d", origin = "1899-12-30", ...)
x |
a multivariate time series object of class |
xlim, ylim, xlab, ylab, col, bg, axes, frame.plot, ann, main
|
graphical arguments, see |
date |
a string indicating the type of x axis annotation. Default is calendar dates. |
format |
a string indicating the format of the x axis annotation if
|
origin |
an R object specifying the origin of the Julian dates
if |
... |
further graphical arguments passed to
|
Within an open-high-low-close bar chart, each bar represents price information for the time interval between the open and the close price. The left tick for each bar indicates the open price for the time interval. The right tick indicates the closing price for the time interval. The vertical length of the bar represents the price range for the time interval.
The time scale of x must be in Julian dates (days since the
origin).
A. Trapletti
plot.default,
format.POSIXct,
get.hist.quote
con <- url("https://finance.yahoo.com") if(!inherits(try(open(con), silent = TRUE), "try-error")) { close(con) ## Plot OHLC bar chart for the last 'nDays' days of the instrument ## 'instrument' nDays <- 50 instrument <- "^gspc" start <- strftime(as.POSIXlt(Sys.time() - nDays * 24 * 3600), format="%Y-%m-%d") end <- strftime(as.POSIXlt(Sys.time()), format = "%Y-%m-%d") x <- get.hist.quote(instrument = instrument, start = start, end = end, retclass = "ts") plotOHLC(x, ylab = "price", main = instrument) }con <- url("https://finance.yahoo.com") if(!inherits(try(open(con), silent = TRUE), "try-error")) { close(con) ## Plot OHLC bar chart for the last 'nDays' days of the instrument ## 'instrument' nDays <- 50 instrument <- "^gspc" start <- strftime(as.POSIXlt(Sys.time() - nDays * 24 * 3600), format="%Y-%m-%d") end <- strftime(as.POSIXlt(Sys.time()), format = "%Y-%m-%d") x <- get.hist.quote(instrument = instrument, start = start, end = end, retclass = "ts") plotOHLC(x, ylab = "price", main = instrument) }
Computes the Phillips-Ouliaris test for the null hypothesis that
x is not cointegrated.
po.test(x, demean = TRUE, lshort = TRUE)po.test(x, demean = TRUE, lshort = TRUE)
x |
a matrix or multivariate time series. |
demean |
a logical indicating whether an intercept is included in the cointegration regression or not. |
lshort |
a logical indicating whether the short or long version of the truncation lag parameter is used. |
The Phillips-Perron Z(alpha) statistic for a unit root in the
residuals of the cointegration regression is computed, see also
pp.test. The unit root is estimated from a regression of
the first variable (column) of x on the remaining variables of
x without a constant and a linear trend. To estimate
sigma^2 the Newey-West estimator is used. If lshort is
TRUE, then the truncation lag parameter is set to
trunc(n/100), otherwise trunc(n/30) is used. The
p-values are interpolated from Table Ia and Ib, p. 189 of Phillips and
Ouliaris (1990). If the computed statistic is outside the table of
critical values, then a warning message is generated.
The dimension of x is restricted to six variables. Missing
values are not handled.
A list with class "htest" containing the following components:
statistic |
the value of the test statistic. |
parameter |
the truncation lag parameter. |
p.value |
the p-value of the test. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name of the data. |
A. Trapletti
P. C. B. Phillips and S. Ouliaris (1990): Asymptotic Properties of Residual Based Tests for Cointegration. Econometrica 58, 165–193.
x <- ts(diffinv(matrix(rnorm(2000),1000,2))) # no cointegration po.test(x) x <- diffinv(rnorm(1000)) y <- 2.0-3.0*x+rnorm(x,sd=5) z <- ts(cbind(x,y)) # cointegrated po.test(z)x <- ts(diffinv(matrix(rnorm(2000),1000,2))) # no cointegration po.test(x) x <- diffinv(rnorm(1000)) y <- 2.0-3.0*x+rnorm(x,sd=5) z <- ts(cbind(x,y)) # cointegrated po.test(z)
Computes an efficient portfolio from the given return series x
in the mean-variance sense.
## Default S3 method: portfolio.optim(x, pm = mean(x), riskless = FALSE, shorts = FALSE, rf = 0.0, reslow = NULL, reshigh = NULL, covmat = cov(x), ...)## Default S3 method: portfolio.optim(x, pm = mean(x), riskless = FALSE, shorts = FALSE, rf = 0.0, reslow = NULL, reshigh = NULL, covmat = cov(x), ...)
x |
a numeric matrix or multivariate time series consisting of a series of returns. |
pm |
the desired mean portfolio return. |
riskless |
a logical indicating whether there is a riskless lending and borrowing rate. |
shorts |
a logical indicating whether shortsales on the risky securities are allowed. |
rf |
the riskfree interest rate. |
reslow |
a vector specifying the (optional) lower bound on allowed portfolio weights. |
reshigh |
a vector specifying the (optional) upper bound on allowed portfolio weights. |
covmat |
the covariance matrix of asset returns. |
... |
further arguments to be passed from or to methods. |
The computed portfolio has the desired expected return pm and
no other portfolio exists, which has the same mean return, but a
smaller variance. Inequality restrictions of the form can be imposed using the reslow and
reshigh vectors. An alternative covariance matrix estimate can
be supplied via the covmat argument. To solve the quadratic
program, solve.QP is used.
portfolio.optim is a generic function with methods for
multivariate "ts" and default for matrix.
Missing values are not allowed.
A list containing the following components:
pw |
the portfolio weights. |
px |
the returns of the overall portfolio. |
pm |
the expected portfolio return. |
ps |
the standard deviation of the portfolio returns. |
A. Trapletti
E. J. Elton and M. J. Gruber (1991): Modern Portfolio Theory and Investment Analysis, 4th Edition, Wiley, NY, pp. 65-93.
C. Huang and R. H. Litzenberger (1988): Foundations for Financial Economics, Elsevier, NY, pp. 59-82.
x <- rnorm(1000) dim(x) <- c(500,2) res <- portfolio.optim(x) res$pw require("zoo") # For diff() method. X <- diff(log(as.zoo(EuStockMarkets))) res <- portfolio.optim(X) ## Long only res$pw res <- portfolio.optim(X, shorts=TRUE) ## Long/Short res$pwx <- rnorm(1000) dim(x) <- c(500,2) res <- portfolio.optim(x) res$pw require("zoo") # For diff() method. X <- diff(log(as.zoo(EuStockMarkets))) res <- portfolio.optim(X) ## Long only res$pw res <- portfolio.optim(X, shorts=TRUE) ## Long/Short res$pw
Computes the Phillips-Perron test for the null hypothesis that
x has a unit root.
pp.test(x, alternative = c("stationary", "explosive"), type = c("Z(alpha)", "Z(t_alpha)"), lshort = TRUE)pp.test(x, alternative = c("stationary", "explosive"), type = c("Z(alpha)", "Z(t_alpha)"), lshort = TRUE)
x |
a numeric vector or univariate time series. |
alternative |
indicates the alternative hypothesis and must be
one of |
type |
indicates which variant of the test is computed and must
be one of |
lshort |
a logical indicating whether the short or long version of the truncation lag parameter is used. |
The general regression equation which incorporates a constant and a
linear trend is used and the Z(alpha) or Z(t_alpha)
statistic for a first order autoregressive coefficient equals one are
computed. To estimate sigma^2 the Newey-West estimator is
used. If lshort is TRUE, then the truncation lag
parameter is set to trunc(4*(n/100)^0.25), otherwise
trunc(12*(n/100)^0.25) is used. The p-values are interpolated
from Table 4.1 and 4.2, p. 103 of Banerjee et al. (1993). If the
computed statistic is outside the table of critical values, then a
warning message is generated.
Missing values are not handled.
A list with class "htest" containing the following components:
statistic |
the value of the test statistic. |
parameter |
the truncation lag parameter. |
p.value |
the p-value of the test. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name of the data. |
alternative |
a character string describing the alternative hypothesis. |
A. Trapletti
A. Banerjee, J. J. Dolado, J. W. Galbraith, and D. F. Hendry (1993): Cointegration, Error Correction, and the Econometric Analysis of Non-Stationary Data, Oxford University Press, Oxford.
P. Perron (1988): Trends and Random Walks in Macroeconomic Time Series. Journal of Economic Dynamics and Control 12, 297–332.
x <- rnorm(1000) # no unit-root pp.test(x) y <- cumsum(x) # has unit root pp.test(y)x <- rnorm(1000) # no unit-root pp.test(x) y <- cumsum(x) # has unit root pp.test(y)
Computes the quadratic map simulation.
quadmap(xi = 0.2, a = 4.0, n = 1000)quadmap(xi = 0.2, a = 4.0, n = 1000)
xi |
the initial value for the iteration. |
a |
the quadratic map parameter. |
n |
the length of the simulated series. |
A vector containing the simulated series.
A. Trapletti
x <- quadmap() acf(x, 10)x <- quadmap() acf(x, 10)
Reads a matrix data file.
read.matrix(file, header = FALSE, sep = "", skip = 0)read.matrix(file, header = FALSE, sep = "", skip = 0)
file |
the name of the file which the data are to be read from. |
header |
a logical value indicating whether the file contains the names of the columns as its first line. |
sep |
the field separator character. Values on each line of the file are separated by this character. |
skip |
the number of lines of the data file to skip before beginning to read data. |
Usually each row of the file represents an observation and each column contains a variable. The first row possibly contains the names of the variables (columns).
read.matrix might be more efficient than
read.table for very large data sets.
A. Trapletti
x <- matrix(0, 10, 10) write(x, "test", ncolumns=10) x <- read.matrix("test") x unlink("test")x <- matrix(0, 10, 10) write(x, "test", ncolumns=10) x <- read.matrix("test") x unlink("test")
Reads a time series file.
read.ts(file, header = FALSE, sep = "", skip = 0, ...)read.ts(file, header = FALSE, sep = "", skip = 0, ...)
file |
the name of the file which the data are to be read from. Each line of the file contains one observation of the variables. |
header |
a logical value indicating whether the file contains the names of the variables as its first line. |
sep |
the field separator character. Values on each line of the file are separated by this character. |
skip |
the number of lines of the data file to skip before beginning to read data. |
... |
Additional arguments for |
Each row of the file represents an observation and each column contains a variable. The first row possibly contains the names of the variables.
A. Trapletti
ts.
data(sunspots) st <- start(sunspots) fr <- frequency(sunspots) write(sunspots, "sunspots", ncolumns=1) x <- read.ts("sunspots", start=st, frequency=fr) plot(x) unlink("sunspots")data(sunspots) st <- start(sunspots) fr <- frequency(sunspots) write(sunspots, "sunspots", ncolumns=1) x <- read.ts("sunspots", start=st, frequency=fr) plot(x) unlink("sunspots")
Computes the runs test for randomness of the dichotomous (binary) data
series x.
runs.test(x, alternative = c("two.sided", "less", "greater"))runs.test(x, alternative = c("two.sided", "less", "greater"))
x |
a dichotomous factor. |
alternative |
indicates the alternative hypothesis and must be
one of |
This test searches for randomness in the observed data series
x by examining the frequency of runs. A "run" is defined as a
series of similar responses.
Note, that by using the alternative "less" the null of
randomness is tested against some kind of "under-mixing"
("trend"). By using the alternative "greater" the null of
randomness is tested against some kind of "over-mixing"
("mean-reversion").
Missing values are not allowed.
A list with class "htest" containing the following components:
statistic |
the value of the test statistic. |
p.value |
the p-value of the test. |
method |
a character string indicating what type of test was performed. |
data.name |
a character string giving the name of the data. |
alternative |
a character string describing the alternative hypothesis. |
A. Trapletti
S. Siegel (1956): Nonparametric Statistics for the Behavioural Sciences, McGraw-Hill, New York.
S. Siegel and N. J. Castellan (1988): Nonparametric Statistics for the Behavioural Sciences, 2nd edn, McGraw-Hill, New York.
x <- factor(sign(rnorm(100))) # randomness runs.test(x) x <- factor(rep(c(-1,1),50)) # over-mixing runs.test(x)x <- factor(sign(rnorm(100))) # randomness runs.test(x) x <- factor(rep(c(-1,1),50)) # over-mixing runs.test(x)
Plot two time series on the same plot frame.
seqplot.ts(x, y, colx = "black", coly = "red", typex = "l", typey = "l", pchx = 1, pchy = 1, ltyx = "solid", ltyy = "solid", oma = c(6, 0, 5, 0), ann = par("ann"), xlab = "Time", ylab = deparse(substitute(x)), main = NULL)seqplot.ts(x, y, colx = "black", coly = "red", typex = "l", typey = "l", pchx = 1, pchy = 1, ltyx = "solid", ltyy = "solid", oma = c(6, 0, 5, 0), ann = par("ann"), xlab = "Time", ylab = deparse(substitute(x)), main = NULL)
x, y
|
the time series. |
colx, coly
|
color code or name for the |
typex, typey
|
what type of plot should be drawn for the |
pchx, pchy
|
character or integer code for kind of points/lines
for the |
ltyx, ltyy
|
line type code for the |
oma |
a vector giving the size of the outer margins in lines of
text, see |
ann |
annotate the plots? See |
xlab, ylab
|
titles for the x and y axis. |
main |
an overall title for the plot. |
Unlike plot.ts the series can have different time bases,
but they should have the same frequency. Unlike ts.plot
the series can be plotted in different styles and for multivariate
x and y the common variables are plotted together in a
separate array element.
None.
A. Trapletti
data(USeconomic) x <- ts.union(log(M1), log(GNP), rs, rl) m.ar <- ar(x, method = "ols", order.max = 5) y <- predict(m.ar, x, n.ahead = 200, se.fit = FALSE) seqplot.ts(x, y)data(USeconomic) x <- ts.union(log(M1), log(GNP), rs, rl) m.ar <- ar(x, method = "ols", order.max = 5) y <- predict(m.ar, x, n.ahead = 200, se.fit = FALSE) seqplot.ts(x, y)
This function computes the Sharpe ratio of the univariate time series
(or vector) x.
sharpe(x, r = 0, scale = sqrt(250))sharpe(x, r = 0, scale = sqrt(250))
x |
a numeric vector or univariate time series corresponding to a portfolio's cumulated returns. |
r |
the risk free rate. Default corresponds to using portfolio returns not in excess of the riskless return. |
scale |
a scale factor. Default corresponds to an annualization when working with daily financial time series data. |
The Sharpe ratio is defined as a portfolio's mean return in excess of the riskless return divided by the portfolio's standard deviation. In finance the Sharpe Ratio represents a measure of the portfolio's risk-adjusted (excess) return.
a double representing the Sharpe ratio.
A. Trapletti
data(EuStockMarkets) dax <- log(EuStockMarkets[,"DAX"]) ftse <- log(EuStockMarkets[,"FTSE"]) sharpe(dax) sharpe(ftse)data(EuStockMarkets) dax <- log(EuStockMarkets[,"DAX"]) ftse <- log(EuStockMarkets[,"FTSE"]) sharpe(dax) sharpe(ftse)
This function computes the Sterling ratio of the univariate time series
(or vector) x.
sterling(x)sterling(x)
x |
a numeric vector or univariate time series corresponding to a portfolio's cumulated returns. |
The Sterling ratio is defined as a portfolio's overall return divided
by the portfolio's maxdrawdown statistic. In finance the
Sterling Ratio represents a measure of the portfolio's risk-adjusted
return.
a double representing the Sterling ratio.
A. Trapletti
data(EuStockMarkets) dax <- log(EuStockMarkets[,"DAX"]) ftse <- log(EuStockMarkets[,"FTSE"]) sterling(dax) sterling(ftse)data(EuStockMarkets) dax <- log(EuStockMarkets[,"DAX"]) ftse <- log(EuStockMarkets[,"FTSE"]) sterling(dax) sterling(ftse)
Methods for creating and printing summaries of ARMA model fits.
## S3 method for class 'arma' summary(object, ...) ## S3 method for class 'summary.arma' print(x, digits = max(3, getOption("digits") - 3), signif.stars = getOption("show.signif.stars"), ...)## S3 method for class 'arma' summary(object, ...) ## S3 method for class 'summary.arma' print(x, digits = max(3, getOption("digits") - 3), signif.stars = getOption("show.signif.stars"), ...)
object |
an object of class |
x |
an object of class |
digits, signif.stars
|
see |
... |
further arguments passed to or from other methods. |
The summary method computes the asymptotic standard errors of the coefficient estimates from the numerically differentiated Hessian matrix approximation. The AIC is computed from the conditional sum-of-squared errors and not from the true maximum likelihood function. That may be problematic.
A list of class "summary.arma".
Methods for creating and printing summaries of GARCH model fits.
## S3 method for class 'garch' summary(object, ...) ## S3 method for class 'summary.garch' print(x, digits = max(3, getOption("digits") - 3), signif.stars = getOption("show.signif.stars"), ...)## S3 method for class 'garch' summary(object, ...) ## S3 method for class 'summary.garch' print(x, digits = max(3, getOption("digits") - 3), signif.stars = getOption("show.signif.stars"), ...)
object |
an object of class |
x |
an object of class |
digits, signif.stars
|
see |
... |
further arguments passed to or from other methods. |
summary computes the asymptotic standard errors of the
coefficient estimates from an outer-product approximation of the
Hessian evaluated at the estimates, see Bollerslev (1986). It
furthermore tests the residuals for normality and remaining ARCH
effects, see jarque.bera.test and
Box.test.
A list of class "summary.garch".
T. Bollerslev (1986): Generalized Autoregressive Conditional Heteroscedasticity. Journal of Econometrics 31, 307–327.
Generates ns surrogate samples from the original data x
and computes the standard error and the bias of statistic as in
a bootstrap setup, if statistic is given.
surrogate(x, ns = 1, fft = FALSE, amplitude = FALSE, statistic = NULL, ...)surrogate(x, ns = 1, fft = FALSE, amplitude = FALSE, statistic = NULL, ...)
x |
a numeric vector or time series. |
ns |
the number of surrogate series to compute. |
fft |
a logical indicating whether phase randomized surrogate data is generated. |
amplitude |
a logical indicating whether amplitude-adjusted surrogate data is computed. |
statistic |
a function which when applied to a time series returns a vector containing the statistic(s) of interest. |
... |
Additional arguments for |
If fft is FALSE, then x is mixed in temporal
order, so that all temporal dependencies are eliminated, but the
histogram of the original data is preserved. If fft is
TRUE, then surrogate data with the same spectrum as x is
computed by randomizing the phases of the Fourier coefficients of
x. If in addition amplitude is TRUE, then also
the amplitude distribution of the original series is preserved.
Note, that the interpretation of the computed standard error and bias is different than in a bootstrap setup.
To compute the phase randomized surrogate and the amplitude adjusted data algorithm 1 and 2 from Theiler et al. (1992), pp. 183, 184 are used.
Missing values are not allowed.
If statistic is NULL, then it returns a matrix or time
series with ns columns and length(x) rows containing the
surrogate data. Each column contains one surrogate sample.
If statistic is given, then a list of class
"resample.statistic" with the following elements is returned:
statistic |
the results of applying |
orig.statistic |
the results of applying |
bias |
the bias of the statistics computed as in a bootstrap setup. |
se |
the standard error of the statistics computed as in a bootstrap setup. |
call |
the original call of |
A. Trapletti
J. Theiler, B. Galdrikian, A. Longtin, S. Eubank, and J. D. Farmer (1992): Using Surrogate Data to Detect Nonlinearity in Time Series, in Nonlinear Modelling and Forecasting, Eds. M. Casdagli and S. Eubank, Santa Fe Institute, Addison Wesley, 163–188.
x <- 1:10 # Simple example surrogate(x) n <- 500 # Generate AR(1) process e <- rnorm(n) x <- double(n) x[1] <- rnorm(1) for(i in 2:n) { x[i] <- 0.4 * x[i-1] + e[i] } x <- ts(x) theta <- function(x) # Autocorrelations up to lag 10 return(acf(x, plot=FALSE)$acf[2:11]) surrogate(x, ns=50, fft=TRUE, statistic=theta)x <- 1:10 # Simple example surrogate(x) n <- 500 # Generate AR(1) process e <- rnorm(n) x <- double(n) x[1] <- rnorm(1) for(i in 2:n) { x[i] <- 0.4 * x[i-1] + e[i] } x <- ts(x) theta <- function(x) # Autocorrelations up to lag 10 return(acf(x, plot=FALSE)$acf[2:11]) surrogate(x, ns=50, fft=TRUE, statistic=theta)
This data set contains monthly 1 year, 3 year, 5 year, and 10 year yields on treasury securities at constant, fixed maturity.
data(tcm)data(tcm)
4 univariate time series tcm1y, tcm3y, tcm5y, and
tcm10y and the joint series tcm.
The yields at constant fixed maturity have been constructed by the Treasury Department, based on the most actively traded marketable treasury securities.
U.S. Fed https://www.federalreserve.gov/Releases/H15/data.htm
This data set contains daily 1 year, 3 year, 5 year, and 10 year yields on treasury securities at constant, fixed maturity.
data(tcmd)data(tcmd)
4 univariate time series tcm1yd, tcm3yd, tcm5yd,
and tcm10yd and the joint series tcmd.
The yields at constant fixed maturity have been constructed by the Treasury Department, based on the most actively traded marketable treasury securities.
Daily refers to business days, i.e., weekends and holidays are eliminated.
U.S. Fed https://www.federalreserve.gov/Releases/H15/data.htm
Generically computes Teraesvirta's neural network test for neglected
nonlinearity either for the time series x or the regression
y~x.
## S3 method for class 'ts' terasvirta.test(x, lag = 1, type = c("Chisq","F"), scale = TRUE, ...) ## Default S3 method: terasvirta.test(x, y, type = c("Chisq","F"), scale = TRUE, ...)## S3 method for class 'ts' terasvirta.test(x, lag = 1, type = c("Chisq","F"), scale = TRUE, ...) ## Default S3 method: terasvirta.test(x, y, type = c("Chisq","F"), scale = TRUE, ...)
x |
a numeric vector, matrix, or time series. |
y |
a numeric vector. |
lag |
an integer which specifies the model order in terms of lags. |
type |
a string indicating whether the Chi-Squared test or the
F-test is computed. Valid types are |
scale |
a logical indicating whether the data should be scaled
before computing the test statistic. The default arguments to
|
... |
further arguments to be passed from or to methods. |
The null is the hypotheses of linearity in
“mean”. This test uses a Taylor series expansion of the activation
function to arrive at a suitable test statistic. If type equals
"F", then the F-statistic instead of the Chi-Squared statistic
is used in analogy to the classical linear regression.
Missing values are not allowed.
A list with class "htest" containing the following components:
statistic |
the value of the test statistic. |
p.value |
the p-value of the test. |
method |
a character string indicating what type of test was performed. |
parameter |
a list containing the additional parameters used to compute the test statistic. |
data.name |
a character string giving the name of the data. |
arguments |
additional arguments used to compute the test statistic. |
A. Trapletti
T. Teraesvirta, C. F. Lin, and C. W. J. Granger (1993): Power of the Neural Network Linearity Test. Journal of Time Series Analysis 14, 209-220.
n <- 1000 x <- runif(1000, -1, 1) # Non-linear in ``mean'' regression y <- x^2 - x^3 + 0.1*rnorm(x) terasvirta.test(x, y) ## Is the polynomial of order 2 misspecified? terasvirta.test(cbind(x,x^2,x^3), y) ## Generate time series which is nonlinear in ``mean'' x[1] <- 0.0 for(i in (2:n)) { x[i] <- 0.4*x[i-1] + tanh(x[i-1]) + rnorm(1, sd=0.5) } x <- as.ts(x) plot(x) terasvirta.test(x)n <- 1000 x <- runif(1000, -1, 1) # Non-linear in ``mean'' regression y <- x^2 - x^3 + 0.1*rnorm(x) terasvirta.test(x, y) ## Is the polynomial of order 2 misspecified? terasvirta.test(cbind(x,x^2,x^3), y) ## Generate time series which is nonlinear in ``mean'' x[1] <- 0.0 for(i in (2:n)) { x[i] <- 0.4*x[i-1] + tanh(x[i-1]) + rnorm(1, sd=0.5) } x <- as.ts(x) plot(x) terasvirta.test(x)
tsbootstrap generates bootstrap samples for general stationary
data and computes the bootstrap estimate of standard error and bias
if a statistic is given.
tsbootstrap(x, nb = 1, statistic = NULL, m = 1, b = NULL, type = c("stationary","block"), ...)tsbootstrap(x, nb = 1, statistic = NULL, m = 1, b = NULL, type = c("stationary","block"), ...)
x |
a numeric vector or time series giving the original data. |
nb |
the number of bootstrap series to compute. |
statistic |
a function which when applied to a time series returns a vector containing the statistic(s) of interest. |
m |
the length of the basic blocks in the block of blocks bootstrap. |
b |
if |
type |
the type of bootstrap to generate the simulated time
series. The possible input values are |
... |
additional arguments for |
If type is "stationary", then the stationary
bootstrap scheme with mean block length b according to Politis
and Romano (1994) is computed. For type equals "block",
the blockwise bootstrap with block length b according to
Kuensch (1989) is used.
If m > 1, then the block of blocks bootstrap is computed
(see Kuensch, 1989). The basic sampling scheme is the same as for
the case m = 1, except that the bootstrap is applied to a series
y containing blocks of length m, where each block of y is
defined as . Therefore, for the block
of blocks bootstrap the first argument of statistic is given by
a n x m matrix yb, where each row of yb contains one
bootstrapped basic block observation (n is the number of
observations in x).
Note, that for statistics which are functions of the empirical
m-dimensional marginal (m > 1) only this procedure
yields asymptotically valid bootstrap estimates. The
case m = 1 may only be used for symmetric statistics (i.e., for
statistics which are invariant under permutations of x).
tsboot does not implement the block of blocks
bootstrap, and, therefore, the first example in tsboot
yields inconsistent estimates.
For consistency, the (mean) block length b should grow with
n at an appropriate rate. If b is not given, then a
default growth rate of const * n^(1/3) is used. This rate is
"optimal" under certain conditions (see the references for more
details). However, in general the growth rate depends on the specific
properties of the data generation process. A default value for
const has been determined by a Monte Carlo simulation using a
Gaussian AR(1) process (AR(1)-parameter of 0.5, 500
observations). const has been chosen such that the mean square
error for the bootstrap estimate of the variance of the empirical mean
is minimized.
Note, that the computationally intensive parts are fully implemented
in C which makes tsbootstrap about 10 to 30 times faster
than tsboot.
Missing values are not allowed.
There is a special print method for objects of class
"resample.statistic" which by default uses
max(3, getOption("digits") - 3) digits to format real numbers.
If statistic is NULL, then it returns a matrix or time
series with nb columns and length(x) rows containing the
bootstrap data. Each column contains one bootstrap sample.
If statistic is given, then a list of class
"resample.statistic" with the following elements is returned:
statistic |
the results of applying |
orig.statistic |
the results of applying |
bias |
the bootstrap estimate of the bias of |
se |
the bootstrap estimate of the standard error of |
call |
the original call of |
A. Trapletti
H. R. Kuensch (1989): The Jackknife and the Bootstrap for General Stationary Observations. The Annals of Statistics 17, 1217–1241.
D. N. Politis and J. P. Romano (1994): The Stationary Bootstrap. Journal of the American Statistical Association 89, 1303–1313.
n <- 500 # Generate AR(1) process a <- 0.6 e <- rnorm(n+100) x <- double(n+100) x[1] <- rnorm(1) for(i in 2:(n+100)) { x[i] <- a * x[i-1] + e[i] } x <- ts(x[-(1:100)]) tsbootstrap(x, nb=500, statistic=mean) # Asymptotic formula for the std. error of the mean sqrt(1/(n*(1-a)^2)) acflag1 <- function(x) { xo <- c(x[,1], x[1,2]) xm <- mean(xo) return(mean((x[,1]-xm)*(x[,2]-xm))/mean((xo-xm)^2)) } tsbootstrap(x, nb=500, statistic=acflag1, m=2) # Asymptotic formula for the std. error of the acf at lag one sqrt(((1+a^2)-2*a^2)/n)n <- 500 # Generate AR(1) process a <- 0.6 e <- rnorm(n+100) x <- double(n+100) x[1] <- rnorm(1) for(i in 2:(n+100)) { x[i] <- a * x[i-1] + e[i] } x <- ts(x[-(1:100)]) tsbootstrap(x, nb=500, statistic=mean) # Asymptotic formula for the std. error of the mean sqrt(1/(n*(1-a)^2)) acflag1 <- function(x) { xo <- c(x[,1], x[1,2]) xm <- mean(xo) return(mean((x[,1]-xm)*(x[,2]-xm))/mean((xo-xm)^2)) } tsbootstrap(x, nb=500, statistic=acflag1, m=2) # Asymptotic formula for the std. error of the acf at lag one sqrt(((1+a^2)-2*a^2)/n)
This is the E.3 example data set of Luetkepohl (1991).
data(USeconomic)data(USeconomic)
4 univariate time series M1, GNP, rs, and
rl and the joint series USeconomic containing the
logarithm of M1, the logarithm of GNP, rs, and
rl.
It contains seasonally adjusted real U.S. money M1 and GNP in
1982 Dollars; discount rate on 91-Day treasury bills rs and
yield on long-term treasury bonds rl.
Luetkepohl, H. (1991): Introduction to Multiple Time Series Analysis. Springer Verlag, NY, 500–503.
Generically computes the White neural network test for neglected
nonlinearity either for the time series x or the regression
y~x.
## S3 method for class 'ts' white.test(x, lag = 1, qstar = 2, q = 10, range = 4, type = c("Chisq","F"), scale = TRUE, ...) ## Default S3 method: white.test(x, y, qstar = 2, q = 10, range = 4, type = c("Chisq","F"), scale = TRUE, ...)## S3 method for class 'ts' white.test(x, lag = 1, qstar = 2, q = 10, range = 4, type = c("Chisq","F"), scale = TRUE, ...) ## Default S3 method: white.test(x, y, qstar = 2, q = 10, range = 4, type = c("Chisq","F"), scale = TRUE, ...)
x |
a numeric vector, matrix, or time series. |
y |
a numeric vector. |
lag |
an integer which specifies the model order in terms of lags. |
q |
an integer representing the number of phantom hidden units used to compute the test statistic. |
qstar |
the test is conducted using |
range |
the input to hidden unit weights are initialized uniformly over [-range/2, range/2]. |
type |
a string indicating whether the Chi-Squared test or the
F-test is computed. Valid types are |
scale |
a logical indicating whether the data should be scaled
before computing the test statistic. The default arguments to
|
... |
further arguments to be passed from or to methods. |
The null is the hypotheses of linearity in “mean”. This
type of test is consistent against arbitrary nonlinearity
in mean. If type equals "F", then the F-statistic
instead of the Chi-Squared statistic is used in analogy to the
classical linear regression.
Missing values are not allowed.
A list with class "htest" containing the following components:
statistic |
the value of the test statistic. |
p.value |
the p-value of the test. |
method |
a character string indicating what type of test was performed. |
parameter |
a list containing the additional parameters used to compute the test statistic. |
data.name |
a character string giving the name of the data. |
arguments |
additional arguments used to compute the test statistic. |
A. Trapletti
T. H. Lee, H. White, and C. W. J. Granger (1993): Testing for neglected nonlinearity in time series models. Journal of Econometrics 56, 269-290.
n <- 1000 x <- runif(1000, -1, 1) # Non-linear in ``mean'' regression y <- x^2 - x^3 + 0.1*rnorm(x) white.test(x, y) ## Is the polynomial of order 2 misspecified? white.test(cbind(x,x^2,x^3), y) ## Generate time series which is nonlinear in ``mean'' x[1] <- 0.0 for(i in (2:n)) { x[i] <- 0.4*x[i-1] + tanh(x[i-1]) + rnorm(1, sd=0.5) } x <- as.ts(x) plot(x) white.test(x)n <- 1000 x <- runif(1000, -1, 1) # Non-linear in ``mean'' regression y <- x^2 - x^3 + 0.1*rnorm(x) white.test(x, y) ## Is the polynomial of order 2 misspecified? white.test(cbind(x,x^2,x^3), y) ## Generate time series which is nonlinear in ``mean'' x[1] <- 0.0 for(i in (2:n)) { x[i] <- 0.4*x[i-1] + tanh(x[i-1]) + rnorm(1, sd=0.5) } x <- as.ts(x) plot(x) white.test(x)