Package 'forecast'

Description

Methods and tools for displaying and analysing univariate time series forecasts including exponential smoothing via state space models and automatic ARIMA modelling.

Author(s)

Maintainer: Rob Hyndman [email protected] (ORCID) [copyright holder]

Authors:

• George Athanasopoulos (ORCID)

• Christoph Bergmeir (ORCID)

• Gabriel Caceres (ORCID)

• Leanne Chhay

• Kirill Kuroptev

• Mitchell O'Hara-Wild (ORCID)

• Fotios Petropoulos (ORCID)

• Slava Razbash

• Earo Wang (ORCID)

• Farah Yasmeen (ORCID)

Other contributors:

• Federico Garza [contributor]

• Daniele Girolimetto [contributor]

• Ross Ihaka [contributor, copyright holder]

• R Core Team [contributor, copyright holder]

• Daniel Reid [contributor]

• David Shaub [contributor]

• Yuan Tang (ORCID) [contributor]

• Xiaoqian Wang [contributor]

• Zhenyu Zhou [contributor]

See Also

Useful links:

• https://pkg.robjhyndman.com/forecast/

• https://github.com/robjhyndman/forecast

• Report bugs at https://github.com/robjhyndman/forecast/issues

Description

Returns range of summary measures of the forecast accuracy. If x is provided, the function measures test set forecast accuracy based on x-f. If x is not provided, the function only produces training set accuracy measures of the forecasts based on f["x"]-fitted(f). All measures are defined and discussed in Hyndman and Koehler (2006).

Usage

## Default S3 method:
accuracy(object, x, test = NULL, d = NULL, D = NULL, f = NULL, ...)

Arguments

Details

The measures calculated are:

• ME: Mean Error

• RMSE: Root Mean Squared Error

• MAE: Mean Absolute Error

• MPE: Mean Percentage Error

• MAPE: Mean Absolute Percentage Error

• MASE: Mean Absolute Scaled Error

• ACF1: Autocorrelation of errors at lag 1.

By default, the MASE calculation is scaled using MAE of training set naive forecasts for non-seasonal time series, training set seasonal naive forecasts for seasonal time series and training set mean forecasts for non-time series data. If f is a numerical vector rather than a forecast object, the MASE will not be returned as the training data will not be available.

See Hyndman and Koehler (2006) and Hyndman and Athanasopoulos (2014, Section 2.5) for further details.

Value

Matrix giving forecast accuracy measures.

Author(s)

Rob J Hyndman

References

Hyndman, R.J. and Koehler, A.B. (2006) "Another look at measures of forecast accuracy". International Journal of Forecasting, 22(4), 679-688. Hyndman, R.J. and Athanasopoulos, G. (2018) "Forecasting: principles and practice", 2nd ed., OTexts, Melbourne, Australia. Section 3.4 "Evaluating forecast accuracy". https://otexts.com/fpp2/accuracy.html.

Examples

fit1 <- rwf(EuStockMarkets[1:200, 1], h = 100)
fit2 <- meanf(EuStockMarkets[1:200, 1], h = 100)
accuracy(fit1)
accuracy(fit2)
accuracy(fit1, EuStockMarkets[201:300, 1])
accuracy(fit2, EuStockMarkets[201:300, 1])
plot(fit1)
lines(EuStockMarkets[1:300, 1])

Description

The function Acf computes (and by default plots) an estimate of the autocorrelation function of a (possibly multivariate) time series. Function Pacf computes (and by default plots) an estimate of the partial autocorrelation function of a (possibly multivariate) time series. Function Ccf computes the cross-correlation or cross-covariance of two univariate series.

Usage

Acf(
  x,
  lag.max = NULL,
  type = c("correlation", "covariance", "partial"),
  plot = TRUE,
  na.action = na.contiguous,
  demean = TRUE,
  ...
)

Pacf(
  x,
  lag.max = NULL,
  plot = TRUE,
  na.action = na.contiguous,
  demean = TRUE,
  ...
)

Ccf(
  x,
  y,
  lag.max = NULL,
  type = c("correlation", "covariance"),
  plot = TRUE,
  na.action = na.contiguous,
  ...
)

taperedacf(
  x,
  lag.max = NULL,
  type = c("correlation", "partial"),
  plot = TRUE,
  calc.ci = TRUE,
  level = 95,
  nsim = 100,
  ...
)

taperedpacf(x, ...)

Arguments

Details

The functions improve the acf, pacf and ccf functions. The main differences are that Acf does not plot a spike at lag 0 when type=="correlation" (which is redundant) and the horizontal axes show lags in time units rather than seasonal units.

The tapered versions implement the ACF and PACF estimates and plots described in Hyndman (2015), based on the banded and tapered estimates of autocovariance proposed by McMurry and Politis (2010).

Value

The Acf, Pacf and Ccf functions return objects of class "acf" as described in acf from the stats package. The taperedacf and taperedpacf functions return objects of class "mpacf".

Author(s)

Rob J Hyndman

References

Hyndman, R.J. (2015). Discussion of “High-dimensional autocovariance matrices and optimal linear prediction”. Electronic Journal of Statistics, 9, 792-796.

McMurry, T. L., & Politis, D. N. (2010). Banded and tapered estimates for autocovariance matrices and the linear process bootstrap. Journal of Time Series Analysis, 31(6), 471-482.

See Also

acf, pacf, ccf, tsdisplay

Examples

Acf(wineind)
Pacf(wineind)
## Not run: 
taperedacf(wineind, nsim=50)
taperedpacf(wineind, nsim=50)

## End(Not run)

Description

An ARFIMA(p,d,q) model is selected and estimated automatically using the Hyndman-Khandakar (2008) algorithm to select p and q and the Haslett and Raftery (1989) algorithm to estimate the parameters including d.

Usage

arfima(
  y,
  drange = c(0, 0.5),
  estim = c("mle", "ls"),
  model = NULL,
  lambda = NULL,
  biasadj = FALSE,
  x = y,
  ...
)

Arguments

Details

This function combines fracdiff and auto.arima to automatically select and estimate an ARFIMA model. The fractional differencing parameter is chosen first assuming an ARFIMA(2,d,0) model. Then the data are fractionally differenced using the estimated d and an ARMA model is selected for the resulting time series using auto.arima. Finally, the full ARFIMA(p,d,q) model is re-estimated using fracdiff. If estim=="mle", the ARMA coefficients are refined using arima.

Value

A list object of S3 class "fracdiff", which is described in the fracdiff documentation. A few additional objects are added to the list including x (the original time series), and the residuals and fitted values.

Author(s)

Rob J Hyndman and Farah Yasmeen

References

J. Haslett and A. E. Raftery (1989) Space-time Modelling with Long-memory Dependence: Assessing Ireland's Wind Power Resource (with discussion); Applied Statistics 38, 1-50.

Hyndman, R.J. and Khandakar, Y. (2008) "Automatic time series forecasting: The forecast package for R", Journal of Statistical Software, 26(3).

See Also

fracdiff, auto.arima, forecast.fracdiff.

Examples

library(fracdiff)
x <- fracdiff.sim( 100, ma=-.4, d=.3)$series
fit <- arfima(x)
tsdisplay(residuals(fit))

Description

Largely a wrapper for the arima function in the stats package. The main difference is that this function allows a drift term. It is also possible to take an ARIMA model from a previous call to Arima and re-apply it to the data y.

Usage

Arima(
  y,
  order = c(0, 0, 0),
  seasonal = c(0, 0, 0),
  xreg = NULL,
  include.mean = TRUE,
  include.drift = FALSE,
  include.constant,
  lambda = model$lambda,
  biasadj = FALSE,
  method = c("CSS-ML", "ML", "CSS"),
  model = NULL,
  x = y,
  ...
)

Arguments

Details

See the arima function in the stats package.

Value

See the arima function in the stats package. The additional objects returned are

Author(s)

Rob J Hyndman

See Also

auto.arima, forecast.Arima.

Examples

library(ggplot2)
WWWusage %>%
  Arima(order=c(3,1,0)) %>%
  forecast(h=20) %>%
  autoplot

# Fit model to first few years of AirPassengers data
air.model <- Arima(window(AirPassengers,end=1956+11/12),order=c(0,1,1),
                   seasonal=list(order=c(0,1,1),period=12),lambda=0)
plot(forecast(air.model,h=48))
lines(AirPassengers)

# Apply fitted model to later data
air.model2 <- Arima(window(AirPassengers,start=1957),model=air.model)

# Forecast accuracy measures on the log scale.
# in-sample one-step forecasts.
accuracy(air.model)
# out-of-sample one-step forecasts.
accuracy(air.model2)
# out-of-sample multi-step forecasts
accuracy(forecast(air.model,h=48,lambda=NULL),
         log(window(AirPassengers,start=1957)))

Description

Returns time series of the regression residuals from a fitted ARIMA model.

Usage

arima.errors(object)

Arguments

Details

This is a deprecated function which is identical to residuals.Arima(object, type="regression") Regression residuals are equal to the original data minus the effect of any regression variables. If there are no regression variables, the errors will be identical to the original series (possibly adjusted to have zero mean).

Value

A ts object

Author(s)

Rob J Hyndman

See Also

residuals.Arima.

Description

Returns the order of a univariate ARIMA or ARFIMA model.

Usage

arimaorder(object)

Arguments

Value

A numerical vector giving the values $p$, $d$ and $q$ of the ARIMA or ARFIMA model. For a seasonal ARIMA model, the returned vector contains the values $p$, $d$, $q$, $P$, $D$, $Q$ and $m$, where $m$ is the period of seasonality.

Author(s)

Rob J Hyndman

See Also

ar, auto.arima, Arima, arima, arfima.

Examples

WWWusage %>% auto.arima %>% arimaorder

Description

Returns best ARIMA model according to either AIC, AICc or BIC value. The function conducts a search over possible model within the order constraints provided.

Usage

auto.arima(
  y,
  d = NA,
  D = NA,
  max.p = 5,
  max.q = 5,
  max.P = 2,
  max.Q = 2,
  max.order = 5,
  max.d = 2,
  max.D = 1,
  start.p = 2,
  start.q = 2,
  start.P = 1,
  start.Q = 1,
  stationary = FALSE,
  seasonal = TRUE,
  ic = c("aicc", "aic", "bic"),
  stepwise = TRUE,
  nmodels = 94,
  trace = FALSE,
  approximation = (length(x) > 150 | frequency(x) > 12),
  method = NULL,
  truncate = NULL,
  xreg = NULL,
  test = c("kpss", "adf", "pp"),
  test.args = list(),
  seasonal.test = c("seas", "ocsb", "hegy", "ch"),
  seasonal.test.args = list(),
  allowdrift = TRUE,
  allowmean = TRUE,
  lambda = NULL,
  biasadj = FALSE,
  parallel = FALSE,
  num.cores = 2,
  x = y,
  ...
)

Arguments

Details

The default arguments are designed for rapid estimation of models for many time series. If you are analysing just one time series, and can afford to take some more time, it is recommended that you set stepwise=FALSE and approximation=FALSE.

Non-stepwise selection can be slow, especially for seasonal data. The stepwise algorithm outlined in Hyndman & Khandakar (2008) is used except that the default method for selecting seasonal differences is now based on an estimate of seasonal strength (Wang, Smith & Hyndman, 2006) rather than the Canova-Hansen test. There are also some other minor variations to the algorithm described in Hyndman and Khandakar (2008).

Value

Same as for Arima

Author(s)

Rob J Hyndman

References

Hyndman, RJ and Khandakar, Y (2008) "Automatic time series forecasting: The forecast package for R", Journal of Statistical Software, 26(3).

Wang, X, Smith, KA, Hyndman, RJ (2006) "Characteristic-based clustering for time series data", Data Mining and Knowledge Discovery, 13(3), 335-364.

See Also

Arima

Examples

fit <- auto.arima(WWWusage)
plot(forecast(fit,h=20))

Description

autolayer() uses ggplot2 to draw a particular layer for an object of a particular class in a single command. This defines the S3 generic that other classes and packages can extend.

Usage

autolayer(object, ...)

Arguments

Value

a ggplot layer

See Also

Other plotting automation topics: automatic_plotting, autoplot(), fortify()

Description

autoplot takes an object of type ts or mts and creates a ggplot object suitable for usage with stat_forecast.

Usage

## S3 method for class 'mts'
autolayer(object, colour = TRUE, series = NULL, ...)

## S3 method for class 'msts'
autolayer(object, series = NULL, ...)

## S3 method for class 'ts'
autolayer(object, colour = TRUE, series = NULL, ...)

## S3 method for class 'ts'
autoplot(
  object,
  series = NULL,
  xlab = "Time",
  ylab = deparse(substitute(object)),
  main = NULL,
  ...
)

## S3 method for class 'mts'
autoplot(
  object,
  colour = TRUE,
  facets = FALSE,
  xlab = "Time",
  ylab = deparse(substitute(object)),
  main = NULL,
  ...
)

## S3 method for class 'msts'
autoplot(object, ...)

## S3 method for class 'ts'
fortify(model, data, ...)

Arguments

Details

fortify.ts takes a ts object and converts it into a data frame (for usage with ggplot2).

Value

None. Function produces a ggplot graph.

Author(s)

Mitchell O'Hara-Wild

See Also

plot.ts, fortify

Examples

library(ggplot2)
autoplot(USAccDeaths)

lungDeaths <- cbind(mdeaths, fdeaths)
autoplot(lungDeaths)
autoplot(lungDeaths, facets=TRUE)

Description

Produces a ggplot object of their equivalent Acf, Pacf, Ccf, taperedacf and taperedpacf functions.

Usage

## S3 method for class 'acf'
autoplot(object, ci = 0.95, ...)

ggAcf(
  x,
  lag.max = NULL,
  type = c("correlation", "covariance", "partial"),
  plot = TRUE,
  na.action = na.contiguous,
  demean = TRUE,
  ...
)

ggPacf(
  x,
  lag.max = NULL,
  plot = TRUE,
  na.action = na.contiguous,
  demean = TRUE,
  ...
)

ggCcf(
  x,
  y,
  lag.max = NULL,
  type = c("correlation", "covariance"),
  plot = TRUE,
  na.action = na.contiguous,
  ...
)

## S3 method for class 'mpacf'
autoplot(object, ...)

ggtaperedacf(
  x,
  lag.max = NULL,
  type = c("correlation", "partial"),
  plot = TRUE,
  calc.ci = TRUE,
  level = 95,
  nsim = 100,
  ...
)

ggtaperedpacf(x, ...)

Arguments

Details

If autoplot is given an acf or mpacf object, then an appropriate ggplot object will be created.

ggtaperedpacf

Value

A ggplot object.

Author(s)

Mitchell O'Hara-Wild

See Also

plot.acf, Acf, acf, taperedacf

Examples

library(ggplot2)
ggAcf(wineind)
wineind %>% Acf(plot=FALSE) %>% autoplot
## Not run: 
wineind %>% taperedacf(plot=FALSE) %>% autoplot
ggtaperedacf(wineind)
ggtaperedpacf(wineind)
## End(Not run)
ggCcf(mdeaths, fdeaths)

Description

Produces a ggplot object of seasonally decomposed time series for objects of class “stl” (created with stl), class “seas” (created with seas), or class “decomposed.ts” (created with decompose).

Usage

## S3 method for class 'decomposed.ts'
autoplot(object, labels = NULL, range.bars = NULL, ...)

## S3 method for class 'stl'
autoplot(object, labels = NULL, range.bars = TRUE, ...)

## S3 method for class 'StructTS'
autoplot(object, labels = NULL, range.bars = TRUE, ...)

## S3 method for class 'seas'
autoplot(object, labels = NULL, range.bars = NULL, ...)

## S3 method for class 'mstl'
autoplot(object, ...)

Arguments

Value

Returns an object of class ggplot.

Author(s)

Mitchell O'Hara-Wild

See Also

seas, stl, decompose, StructTS, plot.stl.

Examples

library(ggplot2)
co2 %>%
  decompose() %>%
  autoplot()
nottem %>%
  stl(s.window = "periodic") %>%
  autoplot()
## Not run: 
library(seasonal)
seas(USAccDeaths) %>% autoplot()

## End(Not run)

Description

Plots historical data with multivariate forecasts and prediction intervals.

Usage

## S3 method for class 'mforecast'
autoplot(object, PI = TRUE, facets = TRUE, colour = FALSE, ...)

## S3 method for class 'mforecast'
autolayer(object, series = NULL, PI = TRUE, ...)

## S3 method for class 'mforecast'
plot(x, main = paste("Forecasts from", unique(x$method)), xlab = "time", ...)

Arguments

Details

autoplot will produce an equivalent plot as a ggplot object.

Author(s)

Mitchell O'Hara-Wild

References

Hyndman and Athanasopoulos (2018) Forecasting: principles and practice, 2nd edition, OTexts: Melbourne, Australia. https://otexts.com/fpp2/

See Also

plot.forecast, plot.ts

Examples

library(ggplot2)

lungDeaths <- cbind(mdeaths, fdeaths)
fit <- tslm(lungDeaths ~ trend + season)
fcast <- forecast(fit, h=10)
plot(fcast)
autoplot(fcast)

carPower <- as.matrix(mtcars[,c("qsec","hp")])
carmpg <- mtcars[,"mpg"]
fit <- lm(carPower ~ carmpg)
fcast <- forecast(fit, newdata=data.frame(carmpg=30))
plot(fcast, xlab="Year")
autoplot(fcast, xlab=rep("Year",2))

Description

The bagged model forecasting method.

Usage

baggedModel(y, bootstrapped_series = bld.mbb.bootstrap(y, 100), fn = ets, ...)

baggedETS(y, bootstrapped_series = bld.mbb.bootstrap(y, 100), ...)

Arguments

Details

This function implements the bagged model forecasting method described in Bergmeir et al. By default, the ets function is applied to all bootstrapped series. Base models other than ets can be given by the parameter fn. Using the default parameters, the function bld.mbb.bootstrap is used to calculate the bootstrapped series with the Box-Cox and Loess-based decomposition (BLD) bootstrap. The function forecast.baggedModel can then be used to calculate forecasts.

baggedETS is a wrapper for baggedModel, setting fn to "ets". This function is included for backwards compatibility only, and may be deprecated in the future.

Value

Returns an object of class "baggedModel".

The function print is used to obtain and print a summary of the results.

Author(s)

Christoph Bergmeir, Fotios Petropoulos

References

Bergmeir, C., R. J. Hyndman, and J. M. Benitez (2016). Bagging Exponential Smoothing Methods using STL Decomposition and Box-Cox Transformation. International Journal of Forecasting 32, 303-312.

Examples

fit <- baggedModel(WWWusage)
fcast <- forecast(fit)
plot(fcast)

Description

Fits a BATS model applied to y, as described in De Livera, Hyndman & Snyder (2011). Parallel processing is used by default to speed up the computations.

Usage

bats(
  y,
  use.box.cox = NULL,
  use.trend = NULL,
  use.damped.trend = NULL,
  seasonal.periods = NULL,
  use.arma.errors = TRUE,
  use.parallel = length(y) > 1000,
  num.cores = 2,
  bc.lower = 0,
  bc.upper = 1,
  biasadj = FALSE,
  model = NULL,
  ...
)

Arguments

Value

An object of class "bats". The generic accessor functions fitted.values and residuals extract useful features of the value returned by bats and associated functions. The fitted model is designated BATS(omega, p,q, phi, m1,...mJ) where omega is the Box-Cox parameter and phi is the damping parameter; the error is modelled as an ARMA(p,q) process and m1,...,mJ list the seasonal periods used in the model.

Author(s)

Slava Razbash and Rob J Hyndman

References

De Livera, A.M., Hyndman, R.J., & Snyder, R. D. (2011), Forecasting time series with complex seasonal patterns using exponential smoothing, Journal of the American Statistical Association, 106(496), 1513-1527.

Examples

## Not run: 
fit <- bats(USAccDeaths)
plot(forecast(fit))

taylor.fit <- bats(taylor)
plot(forecast(taylor.fit))

## End(Not run)

Description

Returns number of trading days in each month or quarter of the observed time period in a major financial center.

Usage

bizdays(x, FinCenter = c("New York", "London", "NERC", "Toronto", "Zurich"))

Arguments

Details

Useful for trading days length adjustments. More on how to define "business days", please refer to isBizday.

Value

Time series

Author(s)

Earo Wang

See Also

monthdays

Examples

x <- ts(rnorm(30), start = c(2013, 2), frequency = 12)
bizdays(x, FinCenter = "New York")

Description

Generates bootstrapped versions of a time series using the Box-Cox and Loess-based decomposition bootstrap.

Usage

bld.mbb.bootstrap(x, num, block_size = NULL)

Arguments

Details

The procedure is described in Bergmeir et al. Box-Cox decomposition is applied, together with STL or Loess (for non-seasonal time series), and the remainder is bootstrapped using a moving block bootstrap.

Value

A list with bootstrapped versions of the series. The first series in the list is the original series.

Author(s)

Christoph Bergmeir, Fotios Petropoulos

References

Bergmeir, C., R. J. Hyndman, and J. M. Benitez (2016). Bagging Exponential Smoothing Methods using STL Decomposition and Box-Cox Transformation. International Journal of Forecasting 32, 303-312.

See Also

baggedETS.

Examples

bootstrapped_series <- bld.mbb.bootstrap(WWWusage, 100)

Description

BoxCox() returns a transformation of the input variable using a Box-Cox transformation. InvBoxCox() reverses the transformation.

Usage

BoxCox(x, lambda)

InvBoxCox(x, lambda, biasadj = FALSE, fvar = NULL)

Arguments

Details

The Box-Cox transformation (as given by Bickel & Doksum 1981) is given by

$f_\lambda(x) =(sign(x)|x|^\lambda - 1)/\lambda$

if $\lambda\ne0$. For $\lambda=0$,

$f_0(x)=\log(x)$

.

Value

a numeric vector of the same length as x.

Author(s)

Rob J Hyndman & Mitchell O'Hara-Wild

References

Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations. JRSS B 26 211–246. Bickel, P. J. and Doksum K. A. (1981) An Analysis of Transformations Revisited. JASA 76 296-311.

See Also

BoxCox.lambda

Examples

lambda <- BoxCox.lambda(lynx)
lynx.fit <- ar(BoxCox(lynx,lambda))
plot(forecast(lynx.fit,h=20,lambda=lambda))

Description

If method=="guerrero", Guerrero's (1993) method is used, where lambda minimizes the coefficient of variation for subseries of x.

Usage

BoxCox.lambda(x, method = c("guerrero", "loglik"), lower = -1, upper = 2)

Arguments

Details

If method=="loglik", the value of lambda is chosen to maximize the profile log likelihood of a linear model fitted to x. For non-seasonal data, a linear time trend is fitted while for seasonal data, a linear time trend with seasonal dummy variables is used.

Value

a number indicating the Box-Cox transformation parameter.

Author(s)

Leanne Chhay and Rob J Hyndman

References

Box, G. E. P. and Cox, D. R. (1964) An analysis of transformations. JRSS B 26 211–246.

Guerrero, V.M. (1993) Time-series analysis supported by power transformations. Journal of Forecasting, 12, 37–48.

See Also

BoxCox

Examples

lambda <- BoxCox.lambda(AirPassengers,lower=0)
air.fit <- Arima(AirPassengers, order=c(0,1,1),
                 seasonal=list(order=c(0,1,1),period=12), lambda=lambda)
plot(forecast(air.fit))

Description

If plot=TRUE, produces a time plot of the residuals, the corresponding ACF, and a histogram. If test is not FALSE, the output from either a Ljung-Box test or Breusch-Godfrey test is printed.

Usage

checkresiduals(object, lag, test, plot = TRUE, ...)

Arguments

Value

None

Author(s)

Rob J Hyndman

See Also

ggtsdisplay, Box.test, bgtest

Examples

fit <- ets(WWWusage)
checkresiduals(fit)

Description

Returns forecasts and other information for Croston's forecasts applied to y.

Usage

croston(y, h = 10, alpha = 0.1, x = y)

Arguments

Details

Based on Croston's (1972) method for intermittent demand forecasting, also described in Shenstone and Hyndman (2005). Croston's method involves using simple exponential smoothing (SES) on the non-zero elements of the time series and a separate application of SES to the times between non-zero elements of the time series. The smoothing parameters of the two applications of SES are assumed to be equal and are denoted by alpha.

Note that prediction intervals are not computed as Croston's method has no underlying stochastic model.

Value

An object of class "forecast" is a list containing at least the following elements:

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts.

The generic accessor functions fitted.values and residuals extract useful features of the value returned by croston and associated functions.

Author(s)

Rob J Hyndman

References

Croston, J. (1972) "Forecasting and stock control for intermittent demands", Operational Research Quarterly, 23(3), 289-303.

Shenstone, L., and Hyndman, R.J. (2005) "Stochastic models underlying Croston's method for intermittent demand forecasting". Journal of Forecasting, 24, 389-402.

See Also

ses.

Examples

y <- rpois(20,lambda=.3)
fcast <- croston(y)
plot(fcast)

Description

Computes the leave-one-out cross-validation statistic (the mean of PRESS – prediction residual sum of squares), AIC, corrected AIC, BIC and adjusted R^2 values for a linear model.

Usage

CV(obj)

Arguments

Value

Numerical vector containing CV, AIC, AICc, BIC and AdjR2 values.

Author(s)

Rob J Hyndman

See Also

AIC

Examples

y <- ts(rnorm(120,0,3) + 20*sin(2*pi*(1:120)/12), frequency=12)
fit1 <- tslm(y ~ trend + season)
fit2 <- tslm(y ~ season)
CV(fit1)
CV(fit2)

Description

CVar computes the errors obtained by applying an autoregressive modelling function to subsets of the time series y using k-fold cross-validation as described in Bergmeir, Hyndman and Koo (2015). It also applies a Ljung-Box test to the residuals. If this test is significant (see returned pvalue), there is serial correlation in the residuals and the model can be considered to be underfitting the data. In this case, the cross-validated errors can underestimate the generalization error and should not be used.

Usage

CVar(
  y,
  k = 10,
  FUN = nnetar,
  cvtrace = FALSE,
  blocked = FALSE,
  LBlags = 24,
  ...
)

Arguments

Value

A list containing information about the model and accuracy for each fold, plus other summary information computed across folds.

Author(s)

Gabriel Caceres and Rob J Hyndman

References

Bergmeir, C., Hyndman, R.J., Koo, B. (2018) A note on the validity of cross-validation for evaluating time series prediction. Computational Statistics & Data Analysis, 120, 70-83. https://robjhyndman.com/publications/cv-time-series/.

See Also

CV, tsCV.

Examples

modelcv <- CVar(lynx, k=5, lambda=0.15)
print(modelcv)
print(modelcv$fold1)

library(ggplot2)
autoplot(lynx, series="Data") +
  autolayer(modelcv$testfit, series="Fits") +
  autolayer(modelcv$residuals, series="Residuals")
ggAcf(modelcv$residuals)

Description

The Diebold-Mariano test compares the forecast accuracy of two forecast methods.

Usage

dm.test(
  e1,
  e2,
  alternative = c("two.sided", "less", "greater"),
  h = 1,
  power = 2,
  varestimator = c("acf", "bartlett")
)

Arguments

Details

This function implements the modified test proposed by Harvey, Leybourne and Newbold (1997). The null hypothesis is that the two methods have the same forecast accuracy. For alternative="less", the alternative hypothesis is that method 2 is less accurate than method 1. For alternative="greater", the alternative hypothesis is that method 2 is more accurate than method 1. For alternative="two.sided", the alternative hypothesis is that method 1 and method 2 have different levels of accuracy. The long-run variance estimator can either the auto-correlation estimator varestimator = "acf", or the estimator based on Bartlett weights varestimator = "bartlett" which ensures a positive estimate. Both long-run variance estimators are proposed in Diebold and Mariano (1995).

Value

A list with class "htest" containing the following components:

Author(s)

George Athanasopoulos and Kirill Kuroptev

References

Diebold, F.X. and Mariano, R.S. (1995) Comparing predictive accuracy. Journal of Business and Economic Statistics, 13, 253-263.

Harvey, D., Leybourne, S., & Newbold, P. (1997). Testing the equality of prediction mean squared errors. International Journal of forecasting, 13(2), 281-291.

Examples

# Test on in-sample one-step forecasts
f1 <- ets(WWWusage)
f2 <- auto.arima(WWWusage)
accuracy(f1)
accuracy(f2)
dm.test(residuals(f1), residuals(f2), h = 1)

# Test on out-of-sample one-step forecasts
f1 <- ets(WWWusage[1:80])
f2 <- auto.arima(WWWusage[1:80])
f1.out <- ets(WWWusage[81:100], model = f1)
f2.out <- Arima(WWWusage[81:100], model = f2)
accuracy(f1.out)
accuracy(f2.out)
dm.test(residuals(f1.out), residuals(f2.out), h = 1)

Description

Returns forecasts using Taylor's (2003) Double-Seasonal Holt-Winters method.

Usage

dshw(
  y,
  period1 = NULL,
  period2 = NULL,
  h = 2 * max(period1, period2),
  alpha = NULL,
  beta = NULL,
  gamma = NULL,
  omega = NULL,
  phi = NULL,
  lambda = NULL,
  biasadj = FALSE,
  armethod = TRUE,
  model = NULL
)

Arguments

Details

Taylor's (2003) double-seasonal Holt-Winters method uses additive trend and multiplicative seasonality, where there are two seasonal components which are multiplied together. For example, with a series of half-hourly data, one would set period1=48 for the daily period and period2=336 for the weekly period. The smoothing parameter notation used here is different from that in Taylor (2003); instead it matches that used in Hyndman et al (2008) and that used for the ets function.

Value

An object of class "forecast" which is a list that includes the following elements:

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts.

The generic accessor functions fitted.values and residuals extract useful features of the value returned by dshw.

Author(s)

Rob J Hyndman

References

Taylor, J.W. (2003) Short-term electricity demand forecasting using double seasonal exponential smoothing. Journal of the Operational Research Society, 54, 799-805.

Hyndman, R.J., Koehler, A.B., Ord, J.K., and Snyder, R.D. (2008) Forecasting with exponential smoothing: the state space approach, Springer-Verlag. http://www.exponentialsmoothing.net.

See Also

HoltWinters, ets.

Examples

## Not run: 
fcast <- dshw(taylor)
plot(fcast)

t <- seq(0,5,by=1/20)
x <- exp(sin(2*pi*t) + cos(2*pi*t*4) + rnorm(length(t),0,.1))
fit <- dshw(x,20,5)
plot(fit)

## End(Not run)

Description

Returns a vector of 0's and 1's or fractional results if Easter spans March and April in the observed time period. Easter is defined as the days from Good Friday to Easter Sunday inclusively, plus optionally Easter Monday if easter.mon=TRUE.

Usage

easter(x, easter.mon = FALSE)

Arguments

Details

Useful for adjusting calendar effects.

Value

Time series

Author(s)

Earo Wang

Examples

easter(wineind, easter.mon = TRUE)

Description

Returns ets model applied to y.

Usage

ets(
  y,
  model = "ZZZ",
  damped = NULL,
  alpha = NULL,
  beta = NULL,
  gamma = NULL,
  phi = NULL,
  additive.only = FALSE,
  lambda = NULL,
  biasadj = FALSE,
  lower = c(rep(1e-04, 3), 0.8),
  upper = c(rep(0.9999, 3), 0.98),
  opt.crit = c("lik", "amse", "mse", "sigma", "mae"),
  nmse = 3,
  bounds = c("both", "usual", "admissible"),
  ic = c("aicc", "aic", "bic"),
  restrict = TRUE,
  allow.multiplicative.trend = FALSE,
  use.initial.values = FALSE,
  na.action = c("na.contiguous", "na.interp", "na.fail"),
  ...
)

Arguments

Details

Based on the classification of methods as described in Hyndman et al (2008).

The methodology is fully automatic. The only required argument for ets is the time series. The model is chosen automatically if not specified. This methodology performed extremely well on the M3-competition data. (See Hyndman, et al, 2002, below.)

Value

An object of class "ets".

The generic accessor functions fitted.values and residuals extract useful features of the value returned by ets and associated functions.

Author(s)

Rob J Hyndman

References

Hyndman, R.J., Koehler, A.B., Snyder, R.D., and Grose, S. (2002) "A state space framework for automatic forecasting using exponential smoothing methods", International J. Forecasting, 18(3), 439–454.

Hyndman, R.J., Akram, Md., and Archibald, B. (2008) "The admissible parameter space for exponential smoothing models". Annals of Statistical Mathematics, 60(2), 407–426.

Hyndman, R.J., Koehler, A.B., Ord, J.K., and Snyder, R.D. (2008) Forecasting with exponential smoothing: the state space approach, Springer-Verlag. http://www.exponentialsmoothing.net.

See Also

HoltWinters, rwf, Arima.

Examples

fit <- ets(USAccDeaths)
plot(forecast(fit))

Description

findfrequency returns the period of the dominant frequency of a time series. For seasonal data, it will return the seasonal period. For cyclic data, it will return the average cycle length.

Usage

findfrequency(x)

Arguments

Details

The dominant frequency is determined from a spectral analysis of the time series. First, a linear trend is removed, then the spectral density function is estimated from the best fitting autoregressive model (based on the AIC). If there is a large (possibly local) maximum in the spectral density function at frequency $f$, then the function will return the period $1/f$ (rounded to the nearest integer). If no such dominant frequency can be found, the function will return 1.

Value

an integer value

Author(s)

Rob J Hyndman

Examples

findfrequency(USAccDeaths) # Monthly data
findfrequency(taylor) # Half-hourly data
findfrequency(lynx) # Annual data

Description

Returns h-step forecasts for the data used in fitting the model.

Usage

## S3 method for class 'ARFIMA'
fitted(object, h = 1, ...)

## S3 method for class 'Arima'
fitted(object, h = 1, ...)

## S3 method for class 'ar'
fitted(object, ...)

## S3 method for class 'bats'
fitted(object, h = 1, ...)

## S3 method for class 'ets'
fitted(object, h = 1, ...)

## S3 method for class 'modelAR'
fitted(object, h = 1, ...)

## S3 method for class 'nnetar'
fitted(object, h = 1, ...)

## S3 method for class 'tbats'
fitted(object, h = 1, ...)

Arguments

Value

A time series of the h-step forecasts.

Author(s)

Rob J Hyndman & Mitchell O'Hara-Wild

See Also

forecast.Arima, forecast.bats, forecast.tbats, forecast.ets, forecast.nnetar, residuals.Arima, residuals.bats, residuals.tbats, residuals.ets, residuals.nnetar.

Examples

fit <- ets(WWWusage)
plot(WWWusage)
lines(fitted(fit), col='red')
lines(fitted(fit, h=2), col='green')
lines(fitted(fit, h=3), col='blue')
legend("topleft", legend=paste("h =",1:3), col=2:4, lty=1)

Description

Returns forecasts and other information for bagged models.

Usage

## S3 method for class 'baggedModel'
forecast(
  object,
  h = ifelse(frequency(object$y) > 1, 2 * frequency(object$y), 10),
  ...
)

Arguments

Details

Intervals are calculated as min and max values over the point forecasts from the models in the ensemble. I.e., the intervals are not prediction intervals, but give an indication of how different the forecasts within the ensemble are.

Value

An object of class "forecast".

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts and prediction intervals.

An object of class "forecast" is a list containing at least the following elements:

Author(s)

Christoph Bergmeir, Fotios Petropoulos

References

Bergmeir, C., R. J. Hyndman, and J. M. Benitez (2016). Bagging Exponential Smoothing Methods using STL Decomposition and Box-Cox Transformation. International Journal of Forecasting 32, 303-312.

See Also

baggedModel.

Examples

fit <- baggedModel(WWWusage)
fcast <- forecast(fit)
plot(fcast)

## Not run: 
fit2 <- baggedModel(WWWusage, fn="auto.arima")
fcast2 <- forecast(fit2)
plot(fcast2)
accuracy(fcast2)
## End(Not run)

Description

Forecasts h steps ahead with a BATS model. Prediction intervals are also produced.

Usage

## S3 method for class 'bats'
forecast(object, h, level = c(80, 95), fan = FALSE, biasadj = NULL, ...)

## S3 method for class 'tbats'
forecast(object, h, level = c(80, 95), fan = FALSE, biasadj = NULL, ...)

Arguments

Value

An object of class "forecast".

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts and prediction intervals.

The generic accessor functions fitted.values and residuals extract useful features of the value returned by forecast.bats.

An object of class "forecast" is a list containing at least the following elements:

Author(s)

Slava Razbash and Rob J Hyndman

References

De Livera, A.M., Hyndman, R.J., & Snyder, R. D. (2011), Forecasting time series with complex seasonal patterns using exponential smoothing, Journal of the American Statistical Association, 106(496), 1513-1527.

See Also

bats, tbats,forecast.ets.

Examples

## Not run: 
fit <- bats(USAccDeaths)
plot(forecast(fit))

taylor.fit <- bats(taylor)
plot(forecast(taylor.fit))

## End(Not run)

Description

Returns forecasts and other information for univariate ETS models.

Usage

## S3 method for class 'ets'
forecast(
  object,
  h = ifelse(object$m > 1, 2 * object$m, 10),
  level = c(80, 95),
  fan = FALSE,
  simulate = FALSE,
  bootstrap = FALSE,
  npaths = 5000,
  PI = TRUE,
  lambda = object$lambda,
  biasadj = NULL,
  ...
)

Arguments

Value

An object of class "forecast".

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts and prediction intervals.

The generic accessor functions fitted.values and residuals extract useful features of the value returned by forecast.ets.

An object of class "forecast" is a list containing at least the following elements:

Author(s)

Rob J Hyndman

See Also

ets, ses, holt, hw.

Examples

fit <- ets(USAccDeaths)
plot(forecast(fit,h=48))

Description

Returns forecasts and other information for univariate ARIMA models.

Usage

## S3 method for class 'fracdiff'
forecast(
  object,
  h = 10,
  level = c(80, 95),
  fan = FALSE,
  lambda = object$lambda,
  biasadj = NULL,
  ...
)

## S3 method for class 'Arima'
forecast(
  object,
  h = ifelse(object$arma[5] > 1, 2 * object$arma[5], 10),
  level = c(80, 95),
  fan = FALSE,
  xreg = NULL,
  lambda = object$lambda,
  bootstrap = FALSE,
  npaths = 5000,
  biasadj = NULL,
  ...
)

## S3 method for class 'ar'
forecast(
  object,
  h = 10,
  level = c(80, 95),
  fan = FALSE,
  lambda = NULL,
  bootstrap = FALSE,
  npaths = 5000,
  biasadj = FALSE,
  ...
)

Arguments

Details

For Arima or ar objects, the function calls predict.Arima or predict.ar and constructs an object of class "forecast" from the results. For fracdiff objects, the calculations are all done within forecast.fracdiff using the equations given by Peiris and Perera (1988).

Value

An object of class "forecast".

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts and prediction intervals.

The generic accessor functions fitted.values and residuals extract useful features of the value returned by forecast.Arima.

An object of class "forecast" is a list containing at least the following elements:

Author(s)

Rob J Hyndman

References

Peiris, M. & Perera, B. (1988), On prediction with fractionally differenced ARIMA models, Journal of Time Series Analysis, 9(3), 215-220.

See Also

predict.Arima, predict.ar, auto.arima, Arima, arima, ar, arfima.

Examples

fit <- Arima(WWWusage,c(3,1,0))
plot(forecast(fit))

library(fracdiff)
x <- fracdiff.sim( 100, ma=-.4, d=.3)$series
fit <- arfima(x)
plot(forecast(fit,h=30))

Description

Returns forecasts and other information for univariate Holt-Winters time series models.

Usage

## S3 method for class 'HoltWinters'
forecast(
  object,
  h = ifelse(frequency(object$x) > 1, 2 * frequency(object$x), 10),
  level = c(80, 95),
  fan = FALSE,
  lambda = NULL,
  biasadj = NULL,
  ...
)

Arguments

Details

This function calls predict.HoltWinters and constructs an object of class "forecast" from the results.

It is included for completeness, but the ets is recommended for use instead of HoltWinters.

Value

An object of class "forecast".

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts and prediction intervals.

The generic accessor functions fitted.values and residuals extract useful features of the value returned by forecast.HoltWinters.

An object of class "forecast" is a list containing at least the following elements:

Author(s)

Rob J Hyndman

See Also

predict.HoltWinters, HoltWinters.

Examples

fit <- HoltWinters(WWWusage,gamma=FALSE)
plot(forecast(fit))

Description

forecast.lm is used to predict linear models, especially those involving trend and seasonality components.

Usage

## S3 method for class 'lm'
forecast(
  object,
  newdata,
  h = 10,
  level = c(80, 95),
  fan = FALSE,
  lambda = object$lambda,
  biasadj = NULL,
  ts = TRUE,
  ...
)

Arguments

Details

forecast.lm is largely a wrapper for predict.lm() except that it allows variables "trend" and "season" which are created on the fly from the time series characteristics of the data. Also, the output is reformatted into a forecast object.

Value

An object of class "forecast".

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts and prediction intervals.

The generic accessor functions fitted.values and residuals extract useful features of the value returned by forecast.lm.

An object of class "forecast" is a list containing at least the following elements:

Author(s)

Rob J Hyndman

See Also

tslm, lm.

Examples

y <- ts(rnorm(120,0,3) + 1:120 + 20*sin(2*pi*(1:120)/12), frequency=12)
fit <- tslm(y ~ trend + season)
plot(forecast(fit, h=20))

Description

forecast.mlm is used to predict multiple linear models, especially those involving trend and seasonality components.

Usage

## S3 method for class 'mlm'
forecast(
  object,
  newdata,
  h = 10,
  level = c(80, 95),
  fan = FALSE,
  lambda = object$lambda,
  biasadj = NULL,
  ts = TRUE,
  ...
)

Arguments

Details

forecast.mlm is largely a wrapper for forecast.lm() except that it allows forecasts to be generated on multiple series. Also, the output is reformatted into a mforecast object.

Value

An object of class "mforecast".

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts and prediction intervals.

The generic accessor functions fitted.values and residuals extract useful features of the value returned by forecast.lm.

An object of class "mforecast" is a list containing at least the following elements:

Author(s)

Mitchell O'Hara-Wild

See Also

tslm, forecast.lm, lm.

Examples

lungDeaths <- cbind(mdeaths, fdeaths)
fit <- tslm(lungDeaths ~ trend + season)
fcast <- forecast(fit, h=10)

carPower <- as.matrix(mtcars[,c("qsec","hp")])
carmpg <- mtcars[,"mpg"]
fit <- lm(carPower ~ carmpg)
fcast <- forecast(fit, newdata=data.frame(carmpg=30))

Description

Returns forecasts and other information for user-defined models.

Usage

## S3 method for class 'modelAR'
forecast(
  object,
  h = ifelse(object$m > 1, 2 * object$m, 10),
  PI = FALSE,
  level = c(80, 95),
  fan = FALSE,
  xreg = NULL,
  lambda = object$lambda,
  bootstrap = FALSE,
  npaths = 1000,
  innov = NULL,
  ...
)

Arguments

Details

Prediction intervals are calculated through simulations and can be slow. Note that if the model is too complex and overfits the data, the residuals can be arbitrarily small; if used for prediction interval calculations, they could lead to misleadingly small values.

Value

An object of class "forecast".

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts and prediction intervals.

The generic accessor functions fitted.values and residuals extract useful features of the value returned by forecast.nnetar.

An object of class "forecast" is a list containing at least the following elements:

Author(s)

Rob J Hyndman and Gabriel Caceres

See Also

nnetar.

Description

mforecast is a class of objects for forecasting from multivariate time series or multivariate time series models. The function invokes particular methods which depend on the class of the first argument.

Usage

## S3 method for class 'mts'
forecast(
  object,
  h = ifelse(frequency(object) > 1, 2 * frequency(object), 10),
  level = c(80, 95),
  fan = FALSE,
  robust = FALSE,
  lambda = NULL,
  biasadj = FALSE,
  find.frequency = FALSE,
  allow.multiplicative.trend = FALSE,
  ...
)

Arguments

Details

For example, the function forecast.mlm makes multivariate forecasts based on the results produced by tslm.

Value

An object of class "mforecast".

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the multivariate forecasts and prediction intervals.

The generic accessors functions fitted.values and residuals extract various useful features of the value returned by forecast$model.

An object of class "mforecast" is a list usually containing at least the following elements:

Author(s)

Rob J Hyndman & Mitchell O'Hara-Wild

See Also

Other functions which return objects of class "mforecast" are forecast.mlm, forecast.varest.

Description

Returns forecasts and other information for univariate neural network models.

Usage

## S3 method for class 'nnetar'
forecast(
  object,
  h = ifelse(object$m > 1, 2 * object$m, 10),
  PI = FALSE,
  level = c(80, 95),
  fan = FALSE,
  xreg = NULL,
  lambda = object$lambda,
  bootstrap = FALSE,
  npaths = 1000,
  innov = NULL,
  ...
)

Arguments

Details

Prediction intervals are calculated through simulations and can be slow. Note that if the network is too complex and overfits the data, the residuals can be arbitrarily small; if used for prediction interval calculations, they could lead to misleadingly small values. It is possible to use out-of-sample residuals to ameliorate this, see examples.

Value

An object of class "forecast".

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts and prediction intervals.

The generic accessor functions fitted.values and residuals extract useful features of the value returned by forecast.nnetar.

An object of class "forecast" is a list containing at least the following elements:

Author(s)

Rob J Hyndman and Gabriel Caceres

See Also

nnetar.

Examples

## Fit & forecast model
fit <- nnetar(USAccDeaths, size=2)
fcast <- forecast(fit, h=20)
plot(fcast)

## Not run: 
## Include prediction intervals in forecast
fcast2 <- forecast(fit, h=20, PI=TRUE, npaths=100)
plot(fcast2)

## Set up out-of-sample innovations using cross-validation
fit_cv <- CVar(USAccDeaths,  size=2)
res_sd <- sd(fit_cv$residuals, na.rm=TRUE)
myinnovs <- rnorm(20*100, mean=0, sd=res_sd)
## Forecast using new innovations
fcast3 <- forecast(fit, h=20, PI=TRUE, npaths=100, innov=myinnovs)
plot(fcast3)

## End(Not run)

Description

Forecasts of STL objects are obtained by applying a non-seasonal forecasting method to the seasonally adjusted data and re-seasonalizing using the last year of the seasonal component.

Usage

## S3 method for class 'stl'
forecast(
  object,
  method = c("ets", "arima", "naive", "rwdrift"),
  etsmodel = "ZZN",
  forecastfunction = NULL,
  h = frequency(object$time.series) * 2,
  level = c(80, 95),
  fan = FALSE,
  lambda = NULL,
  biasadj = NULL,
  xreg = NULL,
  newxreg = NULL,
  allow.multiplicative.trend = FALSE,
  ...
)

stlm(
  y,
  s.window = 7 + 4 * seq(6),
  robust = FALSE,
  method = c("ets", "arima"),
  modelfunction = NULL,
  model = NULL,
  etsmodel = "ZZN",
  lambda = NULL,
  biasadj = FALSE,
  xreg = NULL,
  allow.multiplicative.trend = FALSE,
  x = y,
  ...
)

## S3 method for class 'stlm'
forecast(
  object,
  h = 2 * object$m,
  level = c(80, 95),
  fan = FALSE,
  lambda = object$lambda,
  biasadj = NULL,
  newxreg = NULL,
  allow.multiplicative.trend = FALSE,
  ...
)

stlf(
  y,
  h = frequency(x) * 2,
  s.window = 7 + 4 * seq(6),
  t.window = NULL,
  robust = FALSE,
  lambda = NULL,
  biasadj = FALSE,
  x = y,
  ...
)

Arguments

Details

stlm takes a time series y, applies an STL decomposition, and models the seasonally adjusted data using the model passed as modelfunction or specified using method. It returns an object that includes the original STL decomposition and a time series model fitted to the seasonally adjusted data. This object can be passed to the forecast.stlm for forecasting.

forecast.stlm forecasts the seasonally adjusted data, then re-seasonalizes the results by adding back the last year of the estimated seasonal component.

stlf combines stlm and forecast.stlm. It takes a ts argument, applies an STL decomposition, models the seasonally adjusted data, reseasonalizes, and returns the forecasts. However, it allows more general forecasting methods to be specified via forecastfunction.

forecast.stl is similar to stlf except that it takes the STL decomposition as the first argument, instead of the time series.

Note that the prediction intervals ignore the uncertainty associated with the seasonal component. They are computed using the prediction intervals from the seasonally adjusted series, which are then reseasonalized using the last year of the seasonal component. The uncertainty in the seasonal component is ignored.

The time series model for the seasonally adjusted data can be specified in stlm using either method or modelfunction. The method argument provides a shorthand way of specifying modelfunction for a few special cases. More generally, modelfunction can be any function with first argument a ts object, that returns an object that can be passed to forecast. For example, forecastfunction=ar uses the ar function for modelling the seasonally adjusted series.

The forecasting method for the seasonally adjusted data can be specified in stlf and forecast.stl using either method or forecastfunction. The method argument provides a shorthand way of specifying forecastfunction for a few special cases. More generally, forecastfunction can be any function with first argument a ts object, and other h and level, which returns an object of class forecast. For example, forecastfunction=thetaf uses the thetaf function for forecasting the seasonally adjusted series.

Value

stlm returns an object of class stlm. The other functions return objects of class forecast.

There are many methods for working with forecast objects including summary to obtain and print a summary of the results, while plot produces a plot of the forecasts and prediction intervals. The generic accessor functions fitted.values and residuals extract useful features.

Author(s)

Rob J Hyndman

See Also

stl, forecast.ets, forecast.Arima.

Examples

tsmod <- stlm(USAccDeaths, modelfunction = ar)
plot(forecast(tsmod, h = 36))

decomp <- stl(USAccDeaths, s.window = "periodic")
plot(forecast(decomp))

plot(stlf(AirPassengers, lambda = 0))

Description

Returns forecasts and other information for univariate structural time series models.

Usage

## S3 method for class 'StructTS'
forecast(
  object,
  h = ifelse(object$coef["epsilon"] > 1e-10, 2 * object$xtsp[3], 10),
  level = c(80, 95),
  fan = FALSE,
  lambda = NULL,
  biasadj = NULL,
  ...
)

Arguments

Details

This function calls predict.StructTS and constructs an object of class "forecast" from the results.

Value

An object of class "forecast".

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts and prediction intervals.

The generic accessor functions fitted.values and residuals extract useful features of the value returned by forecast.StructTS.

An object of class "forecast" is a list containing at least the following elements:

Author(s)

Rob J Hyndman

See Also

StructTS.

Examples

fit <- StructTS(WWWusage,"level")
plot(forecast(fit))

Description

forecast is a generic function for forecasting from time series or time series models. The function invokes particular methods which depend on the class of the first argument.

Usage

## S3 method for class 'ts'
forecast(
  object,
  h = ifelse(frequency(object) > 1, 2 * frequency(object), 10),
  level = c(80, 95),
  fan = FALSE,
  robust = FALSE,
  lambda = NULL,
  biasadj = FALSE,
  find.frequency = FALSE,
  allow.multiplicative.trend = FALSE,
  model = NULL,
  ...
)

## Default S3 method:
forecast(object, ...)

## S3 method for class 'forecast'
print(x, ...)

Arguments

Details

For example, the function forecast.Arima makes forecasts based on the results produced by arima.

If model=NULL,the function forecast.ts makes forecasts using ets models (if the data are non-seasonal or the seasonal period is 12 or less) or stlf (if the seasonal period is 13 or more).

If model is not NULL, forecast.ts will apply the model to the object time series, and then generate forecasts accordingly.

Value

An object of class "forecast".

The function summary is used to obtain and print a summary of the results, while the function plot produces a plot of the forecasts and prediction intervals.

The generic accessors functions fitted.values and residuals extract various useful features of the value returned by forecast$model.

An object of class "forecast" is a list usually containing at least the following elements:

Author(s)

Rob J Hyndman

See Also

Other functions which return objects of class "forecast" are forecast.ets, forecast.Arima, forecast.HoltWinters, forecast.StructTS, meanf, rwf, splinef, thetaf, croston, ses, holt, hw.

Examples

WWWusage %>% forecast %>% plot
fit <- ets(window(WWWusage, end=60))
fc <- forecast(WWWusage, model=fit)

Description

fourier returns a matrix containing terms from a Fourier series, up to order K, suitable for use in Arima, auto.arima, or tslm.

Usage

fourier(x, K, h = NULL)

fourierf(x, K, h)

Arguments

Details

fourierf is deprecated, instead use the h argument in fourier.

The period of the Fourier terms is determined from the time series characteristics of x. When h is missing, the length of x also determines the number of rows for the matrix returned by fourier. Otherwise, the value of h determines the number of rows for the matrix returned by fourier, typically used for forecasting. The values within x are not used.

Typical use would omit h when generating Fourier terms for training a model and include h when generating Fourier terms for forecasting.

When x is a ts object, the value of K should be an integer and specifies the number of sine and cosine terms to return. Thus, the matrix returned has 2*K columns.

When x is a msts object, then K should be a vector of integers specifying the number of sine and cosine terms for each of the seasonal periods. Then the matrix returned will have 2*sum(K) columns.

Value

Numerical matrix.

Author(s)

Rob J Hyndman

See Also

seasonaldummy

Examples

library(ggplot2)

# Using Fourier series for a "ts" object
# K is chosen to minimize the AICc
deaths.model  <- auto.arima(USAccDeaths, xreg=fourier(USAccDeaths,K=5), seasonal=FALSE)
deaths.fcast <- forecast(deaths.model, xreg=fourier(USAccDeaths, K=5, h=36))
autoplot(deaths.fcast) + xlab("Year")

# Using Fourier series for a "msts" object
taylor.lm <- tslm(taylor ~ fourier(taylor, K = c(3, 3)))
taylor.fcast <- forecast(taylor.lm,
    data.frame(fourier(taylor, K = c(3, 3), h = 270)))
autoplot(taylor.fcast)

Description

Australian monthly gas production: 1956–1995.

Usage

gas

Format

Time series data

Source

Australian Bureau of Statistics.

Examples

plot(gas)
seasonplot(gas)
tsdisplay(gas)

Description

getResponse is a generic function for extracting the historical data from a time series model (including Arima, ets, ar, fracdiff), a linear model of class lm, or a forecast object. The function invokes particular methods which depend on the class of the first argument.