The forecasting Package - Uni Bayreuthftp.uni-bayreuth.de/math/statlib/R/CRAN/doc/packages/...Largely a wrapper for the arima function in the stats package. The main difference is

The forecasting PackageJuly 28, 2007

Contains forecast fma Mcomp

Version 1.07

Date 2007-07-25

Depends R (>= 2.0.0), graphics, stats, tseries

LazyData yes

LazyLoad yes

Author Rob J Hyndman <[email protected]>

Maintainer Rob J Hyndman <[email protected]>

License GPL (version 2 or later).

URL http://www.robhyndman.info/Rlibrary/forecast/

Contents

Package ‘forecast’ 1BoxCox . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1arima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2arima.errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4best.arima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5croston . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6ets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8fitted.Arima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10forecast.Arima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10forecast.HoltWinters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13forecast.StructTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14forecasterrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16forecast.ets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17plot.forecast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19gof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20gold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21meanf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21monthdays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23na.interp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23ndiffs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24plot.ets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25rwf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26seasadj . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27seasonaldummy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28seasonplot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29ses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30simulate.ets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31sindexf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32splinef . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33thetaf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35tsdisplay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36wineind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37woolyrnq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

i

ii CONTENTS

Package ‘fma’ 39advert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39advsales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40airpass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40auto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42beer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42bicoal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43books . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43boston . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44bricksq . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45canadian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46cement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46chicken . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47condmilk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48copper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48copper1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49copper2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49copper3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50cowtemp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50cpimel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51dexter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51dj . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52dole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53dowjones . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53econsumption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54eggs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54eknives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55elco . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55elec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56expenditure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56fancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57french . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57housing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58hsales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59hsales2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59huron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60ibm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60ibmclose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62internet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62invent15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63jcars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63kkong . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64labour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65lynx . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65milk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

CONTENTS iii

mink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67mortal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67motel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68nail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69oilprice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70olympic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70ozone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71paris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71pcv . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72petrol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73pigs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74pollution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74productC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75pulpprice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76qelec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76qsales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77running . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77sales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78schizo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78shampoo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79sheep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80ship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80shipex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81strikes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81telephone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82texasgas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82ukdeaths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83usdeaths . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84uselec . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84ustreas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85wagesuk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85wheat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86wn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86wnoise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87writing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Package ‘Mcomp’ 89M1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89plot.Mdata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90subset.Mcomp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

Index 93

iv CONTENTS

Package ‘forecast’

Title Forecasting functions for time series

Description Various functions to aid in univariate time series forecasting including exponentialsmoothing via state space models, arima models, and many more.

BoxCox Box Cox Transformation

Description

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

Usage

BoxCox(x,lambda)InvBoxCox(x,lambda)

Arguments

x a numeric vector or time series

lambda transformation parameter

Details

The Box-Cox transformation is given by

fλ(x) =xλ − 1

λ

if λ 6= 0. For λ = 0,f0(x) = log(x)

.

Value

a numeric vector of the same length as x.

1

2 arima

Author(s)

Rob J Hyndman

References

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

Examples

lynx.sqrt <- BoxCox(lynx,0.5)lynx.fit <- ar(lynx.sqrt)plot(forecast(lynx.fit,h=20),lambda=0.5)

arima Fit ARIMA model to univariate time series

Description

Largely a wrapper for the arima function in the stats package. The main difference is that thisfunction returns some additional information that is required by the forecast.Arima function.Also, it is possible to take an ARIMA model from a previous call to arima and re-apply it to thedata x.

Usage

arima(x, order = c(0, 0, 0), seasonal = list(order = c(0, 0, 0), period = NA),xreg = NULL, include.mean = TRUE, include.drift = FALSE,transform.pars = TRUE, fixed = NULL, init = NULL,method = c("CSS-ML", "ML", "CSS"), n.cond,optim.control = list(), kappa = 1e6, model=NULL)

Arguments

x a univariate time series

order A specification of the non-seasonal part of the ARIMA model: the three com-ponents (p, d, q) are the AR order, the degree of differencing, and the MA order.

seasonal A specification of the seasonal part of the ARIMA model, plus the period (whichdefaults to frequency(x)). This should be a list with components order and pe-riod, but a specification of just a numeric vector of length 3 will be turned into asuitable list with the specification as the order.

xreg Optionally, a vector or matrix of external regressors, which must have the samenumber of rows as x.

include.mean Should the ARIMA model include a mean term? The default is TRUE for un-differenced series, FALSE for differenced ones (where a mean would not affectthe fit nor predictions).

arima 3

include.driftShould the ARIMA model include a linear drift term? (i.e., a linear regressionwith ARIMA errors is fitted.) The default is FALSE.

transform.parsLogical. If true, the AR parameters are transformed to ensure that they remainin the region of stationarity. Not used for method = "CSS".

fixed optional numeric vector of the same length as the total number of parameters.If supplied, only NA entries in fixed will be varied. transform.pars = TRUEwill be overridden (with a warning) if any AR parameters are fixed. It may bewise to set transform.pars = FALSE when fixing MA parameters, especially nearnon-invertibility.

init optional numeric vector of initial parameter values. Missing values will be filledin, by zeroes except for regression coefficients. Values already specified in fixedwill be ignored.

method Fitting method: maximum likelihood or minimize conditional sum-of-squares.The default (unless there are missing values) is to use conditional-sum-of-squaresto find starting values, then maximum likelihood.

n.cond Only used if fitting by conditional-sum-of-squares: the number of initial obser-vations to ignore. It will be ignored if less than the maximum lag of an ARterm.

optim.controlList of control parameters for optim.

kappa the prior variance (as a multiple of the innovations variance) for the past obser-vations in a differenced model. Do not reduce this.

model Output from a previous call to arima. If model is passed, this same model isfitted to x without re-estimating any parameters.

Details

See the arima function in the stats package.

Value

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

x The time series data

xreg The regressors used in fitting (when relevant).

Author(s)

Rob J Hyndman

See Also

arima

4 arima.errors

Examples

fit <- arima(WWWusage,order=c(3,1,0))plot(forecast(fit,h=20))

air.model <- arima(AirPassengers[1:100],c(0,1,1))air.model2 <- arima(AirPassengers,model=air.model)outofsample <- ts(fitted(air.model2)[-c(1:100)],s=1957+4/12,f=12)

arima.errors ARIMA errors

Description

Returns original time series after adjusting for regression variables. These are not the same as theresiduals. If there are no regression variables in the ARIMA model, then the errors will be identicalto the original series. If there are regression variables in the ARIMA model, then the errors willbe equal to the original series minus the effect of the regression variables, but leaving in the serialcorrelation that is modelled with the AR and MA terms. If you want the "residuals", then useresiduals(z)..

Usage

arima.errors(z)

Arguments

z Fitted ARIMA model from arima

Value

A time series containing the "errors".

Author(s)

Rob J Hyndman

See Also

arima, residuals

Examples

ukdeaths.fit <- arima(UKDriverDeaths,c(1,0,1),c(0,1,1),xreg=Seatbelts[,"law"])ukdeaths.errors <- arima.errors(ukdeaths.fit)par(mfrow=c(2,1))plot(UKDriverDeaths)plot(ukdeaths.errors)

best.arima 5

best.arima Fit best ARIMA model to univariate time series

Description

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

Usage

auto.arima(x, d = NA, D = NA, max.p = 5, max.q = 5,max.P = 2, max.Q = 2, max.order = 5,start.p=2, start.q=2, start.P=1, start.Q=1,

stationary = FALSE, ic = c("aic","aicc", "bic"),stepwise=TRUE, trace=FALSE)

Arguments

x a univariate time series

d Order of first-differencing. If missing, will choose a value based on KPSS test.

D Order of seasonal-differencing. If missing, will choose a value based on CHtest.

max.p Maximum value of p

max.q Maximum value of q

max.P Maximum value of P

max.Q Maximum value of Q

max.order Maximum value of p+q+P+Q if model selection is not stepwise.

start.p Starting value of p in stepwise procedure.

start.q Starting value of q in stepwise procedure.

start.P Starting value of P in stepwise procedure.

start.Q Starting value of Q in stepwise procedure.

stationary If TRUE, restricts search to stationary models.

ic Information criterion to be used in model selection.

stepwise If TRUE, will do stepwise selection (faster). Otherwise, it searches over all mod-els. Non-stepwise selection can be very slow, especially for seasonal models.

trace If TRUE, the list of ARIMA models considered will be reported.

Details

Non-stepwise selection can be slow, especially for seasonal data. Non-seasonal differences chosenusing kpss.test. Seasonal differences chosen using a variation on the Canova-Hansen test.Stepwise algorithm outlined in Hyndman and Khandakar (2007).

6 croston

Value

Same as for arima

Author(s)

Rob J Hyndman

References

Hyndman, R.J. and Khandakar, Y. (2007) "Automatic time series forecasting: The forecast packagefor R", Journal of Statistical Software, to appear.

See Also

arima

Examples

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

croston Forecasts for intermittent demand using Croston’s method

Description

Returns forecasts and other information for Croston’s forecasts applied to x.

Usage

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

Arguments


h Number of periods for forecasting.

alpha Value of alpha. Default value is 0.1.

Details

Based on Croston’s (1972) method for intermittent demand forecasting, also described in Shenstoneand Hyndman (2005). Croston’s method involves using simple exponential smoothing (SES) on thenon-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 areassumed to be equal and are denoted by alpha.

Note that prediction intervals are not computed as Croston’s method has no underlying stochasticmodel.

croston 7

Value

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

model A list containing information about the fitted model

method The name of the forecasting method as a character string

mean Point forecasts as a time series

x The original time series (either object itself or the time series used to createthe model stored as object).

residuals Residuals from the fitted model. That is x minus fitted values.

fitted Fitted values (one-step forecasts)

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

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

Author(s)

Rob J Hyndman

References

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

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

See Also

ses.

Examples

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

8 ets

ets Exponential smoothing state space model

Description

Returns ets model applied to x.

Usage

ets(y, model="ZZZ", damped=NULL, alpha=NULL, beta=NULL, gamma=NULL, phi=NULL,additive.only=FALSE, lower=c(rep(0.01,3), 0.8), upper=c(rep(0.99,3),0.98),opt.crit=c("lik","amse","mse","sigma"), nmse=3,bounds=c("both","usual","admissible"), ic=c("aic","aicc","bic"))

Arguments

y a numeric vector or time series

model Usually a three-character string identifying method using the framework termi-nology of Hyndman et al. (2002) and Hyndman et al. (2008). The first letterdenotes the error type ("A", "M" or "Z"); the second letter denotes the trend type("N","A","M" or "Z"); and the third letter denotes the season type ("N","A","M"or "Z"). In all cases, "N"=none, "A"=additive, "M"=multiplicative and "Z"=automaticallyselected. So, for example, "ANN" is simple exponential smoothing with addi-tive errors, "MAM" is multiplicative Holt-Winters’ method with multiplicativeerrors, and so on. It is also possible for the model to be equal to the outputfrom a previous call to ets. In this case, the same model is fitted to y withoutre-estimating any parameters.

damped If TRUE, use a damped trend (either additive or multiplicative). If NULL, bothdamped and non-damped trends will be tried and the best model (according tothe information criterion ic) returned.

alpha Value of alpha. If NULL, it is estimated.

beta Value of beta. If NULL, it is estimated.

gamma Value of gamma. If NULL, it is estimated.

phi Value of phi. If NULL, it is estimated.additive.only

If TRUE, will only consider additive models. Default is FALSE.

lower Lower bounds for the parameters (alpha, beta, gamma, phi)

upper Upper bounds for the parameters (alpha, beta, gamma, phi)

opt.crit Optimization criterion. One of "mse" (Mean Square Error), "amse" (AverageMSE over first nmse forecast horizons), "sigma" (Standard deviation of residu-als), or "lik" (Log-likelihood, the default).

nmse Number of steps for average multistep MSE (1<=nmse<=10).

ets 9

bounds Type of parameter space to impose: "usual" indicates all parameters mustlie between specified lower and upper bounds; "admissible" indicates pa-rameters must lie in the admissible space; "both" (default) takes the intersec-tion of these regions.

ic Information criterion to be used in model selection.

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. Themodel is chosen automatically if not specified. This methodology performed extremely well on theM3-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 thevalue 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 forautomatic forecasting using exponential smoothing methods", International J. Forecasting, 18(3),439–454.

Hyndman, R.J., Akram, Md., and Archibald, B. (2007) "The admissible parameter space for expo-nential smoothing models". Annals of Statistical Mathematics, to appear.

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

See Also

HoltWinters, rwf, arima.

Examples

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

http://www.robhyndman.info/expsmooth

http://www.robhyndman.info/expsmooth

10 forecast.Arima

fitted.Arima One-step in-sample forecasts using ARIMA models

Description

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

Usage

fitted.Arima(object,...)

Arguments

object An object of class "Arima". Usually the result of a call to arima.... Other arguments.

Value

An time series of the one-step forecasts.

Author(s)

Rob J Hyndman

See Also

forecast.Arima.

Examples

fit <- arima(WWWusage,c(3,1,0))plot(WWWusage)lines(fitted(fit),col=2)

forecast.Arima Forecasting using ARIMA models

Description

Returns forecasts and other information for univariate ARIMA models.

Usage

## S3 method for class 'Arima':forecast(object, h=ifelse(object$arma[5]>1,2*object$arma[5],10),

conf=c(80,95), fan=FALSE, xreg=NULL,...)## S3 method for class 'ar':forecast(object, h=10, conf=c(80,95), fan=FALSE, ...)

forecast.Arima 11

Arguments

object An object of class "Arima" or "ar". Usually the result of a call to arima orar.

h Number of periods for forecastingconf Confidence level for prediction intervals.fan If TRUE, conf is set to seq(50,99,by=1). This is suitable for fan plots.xreg Future values of an regression variables (for class Arima objects only).... Other arguments.

Details

This function calls predict.arima or predict.ar 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 functionplot produces a plot of the forecasts and prediction intervals.

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


model A list containing information about the fitted modelmethod The name of the forecasting method as a character stringmean Point forecasts as a time serieslower Lower limits for prediction intervalsupper Upper limits for prediction intervalsconf The confidence values associated with the prediction intervalsx The original time series (either object itself or the time series used to create

the model stored as object).residuals Residuals from the fitted model. That is x minus fitted values.fitted Fitted values (one-step forecasts)

Author(s)

Rob J Hyndman

See Also

predict.arima, predict.ar, rwf, arima.

Examples

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

12 forecast.HoltWinters

forecast.HoltWintersForecasting using Holt-Winters objects

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),

conf=c(80,95),fan=FALSE,...)

Arguments

object An object of class "HoltWinters". Usually the result of a call to HoltWinters.

h Number of periods for forecasting

conf Confidence level for prediction intervals.

fan If TRUE, conf is set to seq(50,99,by=1). This is suitable for fan plots.

... Other 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



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





lower Lower limits for prediction intervals

upper Upper limits for prediction intervals

conf The confidence values associated with the prediction intervals

forecast 13




Author(s)

Rob J Hyndman

See Also

predict.HoltWinters, HoltWinters.

Examples

fit <- HoltWinters(WWWusage,gamma=0)plot(forecast(fit))

forecast Forecasting time series

Description

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

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

The function forecast.ts makes forecasts using exponential smoothing state space models.

Usage

forecast(...)## S3 method for class 'ts':forecast(x, h, conf=c(80,95), fan=FALSE, ...)

Arguments

x a time series or time series model for which forecasts are required




... Additional arguments affecting the forecasts produced. forecast.ts passesthese to forecast.ets

14 forecast.StructTS

Details

The default behaviour is to use a model estimated using ets.

Value



The generic accessor functions fitted.values and residuals extract various useful featuresof the value returned by forecast$model.











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.

forecast.StructTS Forecasting using Structural Time Series models

Description

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

Usage

## S3 method for class 'StructTS':forecast(object, h=ifelse(object$call$type=="BSM",2*object$xtsp[3],10),

conf=c(80,95), fan=FALSE, ...)

forecast.StructTS 15

Arguments

object An object of class "StructTS". Usually the result of a call to StructTS.





Details

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

Value



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











Author(s)

Rob J Hyndman

See Also

predict.StructTS, StructTS.

Examples

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

16 forecasterrors

forecasterrors Forecast errors

Description

Returns range of summary measures of the error x-f. These are (usually) out-of-sample forecasterrors. Compare gof which provides a summary of in-sample forecast errors. All measures aredefined and discussed in Hyndman and Koehler (2006).

Usage

forecasterrors(f, x, test=1:length(x))

Arguments

f Vector of univariate forecasts or object of class code"forecast".

x Vector of actual values of the same length as f.

test Indicator of which elements of x and f to test.

Value

Vector giving forecast error measures.

Author(s)

Rob J Hyndman

References

Hyndman, R.J. and Koehler, A.B. (2006) "Another look at measures of forecast accuracy". Inter-national Journal of Forecasting, 22(4).

See Also

gof

Examples

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

forecast.ets 17

forecast.ets Forecasting using ETS models

Description

Returns forecasts and other information for univariate ETS models.

Usage

## S3 method for class 'ets':forecast(obj, h=ifelse(obj$m>1, 2*obj$m, 10), conf=c(80,95),

fan=FALSE, simulate=FALSE, bootstrap=FALSE, npaths=5000,...)

Arguments

obj An object of class "ets". Usually the result of a call to ets.h Number of periods for forecastingconf Confidence level for prediction intervals.fan If TRUE, conf is set to seq(50,99,by=1). This is suitable for fan plots.simulate If TRUE, prediction intervals produced by simulation rather than using analytic

formulae.bootstrap If TRUE, simulation uses resampled errors rather than normally distributed er-

rors.npaths Number of sample paths used in computing simulated prediction intervals.... Other arguments.

Value



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


model A list containing information about the fitted modelmethod The name of the forecasting method as a character stringmean Point forecasts as a time serieslower Lower limits for prediction intervalsupper Upper limits for prediction intervalsconf The confidence values associated with the prediction intervalsx The original time series (either object itself or the time series used to create

the model stored as object).residuals Residuals from the fitted model. That is x minus fitted values.fitted Fitted values (one-step forecasts)

18 plot.forecast

Author(s)

Rob J Hyndman

See Also

ets, ses, holt, hw.

Examples

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

plot.forecast Forecast plot

Description

Plots a time series with forecasts and prediction intervals.

Usage

## S3 method for class 'forecast':plot(x, include, plot.conf = TRUE, shaded = TRUE, shadecols

= switch(1 + (length(x$conf) > 1), 7, length(x$conf):1),shadepalette=heat.colors(length(x$conf)+1)[-1], lambda = NULL,

col = 1, fcol = 4, ylim = NULL, main = NULL, ylab = "", xlab = "", ...)## S3 method for class 'splineforecast':plot(x,fitcol=2,...)

Arguments

x Forecast object produced by forecast.

include number of values from time series to include in plot

plot.conf Logical flag indicating whether to plot prediction intervals.

shaded Logical flag indicating whether prediction intervals should be shaded (TRUE)or lines (FALSE)

shadecols Colors for shaded prediction intervals

shadepalette Palette for shaded prediction intervals

lambda Box-Cox parameter. If present, function backtransforms data and forecasts us-ing InvBoxCox.

col the colour for the data line.

fcol the colour for the forecast line.

ylim Limits on y-axis

main Main title

gas 19

ylab Y-axis label

xlab X-axis label

fitcol Line colour for fitted values.

... additional arguments to plot.

Value

None.

Author(s)

Rob J Hyndman

References

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, Wiley:New York.

See Also

plot.ts

Examples

deaths.fit <- hw(USAccDeaths,h=48)plot(deaths.fit)

gas Australian monthly gas production

Description

Australian monthly gas production: 1956–1995.

Usage

gas

Format

Time series data

Source

Australian Bureau of Statistics.

20 gof

Examples

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

gof Goodness-of-fit for forecast model

Description

Returns range of summary measures of the in-sample errors. Compare forecasterrors whichprovides a summary of out-of-sample forecast errors. All measures are defined and discussed inHyndman and Koehler (2006).

Usage

gof(object)

Arguments

object An object of class "forecast"

Value

Vector giving in-sample error measures.

Author(s)

Rob J Hyndman

References

Hyndman, R.J. and Koehler, A.B. (2006) "Another look at measures of forecast accuracy". Inter-national Journal of Forecasting, 22(4).

Examples

fit1 <- rwf(Nile)fit2 <- meanf(Nile)gof(fit1)gof(fit2)

gold 21

gold Daily morning gold prices

Description

Daily morning gold prices in US dollars. 1 January 1985 – 31 March 1989.

Usage

data(gold)

Format

Time series data

Source

Time Series Data Library. http://www-personal.buseco.monash.edu.au/~hyndman/TSDL/

Examples

tsdisplay(gold)

meanf Mean Forecast

Description

Returns forecasts and prediction intervals for an iid model applied to x.

Usage

meanf(x, h=10, conf=c(80,95), fan=FALSE)

Arguments



conf Confidence levels for prediction intervals.


http://www-personal.buseco.monash.edu.au/~hyndman/TSDL/


22 meanf

Details

The iid model isYt = µ + Zt

where Zt is a normal iid error. Forecasts are given by

Yn(h) = µ

where µ is estimated by the sample mean.

Value



The generic accessor functions fitted.values and residuals extract useful features of thevalue returned by meanf.











Author(s)

Rob J Hyndman

See Also

rwf

Examples

nile.fcast <- meanf(Nile, h=10)plot(nile.fcast)

monthdays 23

monthdays Number of days in each season

Description

Returns number of days in each month or quarter of the observed time period.

Usage

monthdays(x)

Arguments

x time series

Details

Useful for month length adjustments

Value

Time series

Author(s)

Rob J Hyndman

Examples

par(mfrow=c(2,1))plot(ldeaths,xlab="Year",ylab="pounds",

main="Monthly deaths from lung disease (UK)")ldeaths.adj <- ldeaths/monthdays(ldeaths)*365.25/12plot(ldeaths.adj,xlab="Year",ylab="pounds",

main="Adjusted monthly deaths from lung disease (UK)")

na.interp Interpolate missing values in a time series

Description

Uses linear interpolation to replace missing values.

Usage

na.interp(x)

24 ndiffs

Arguments

x time series

Details

Value

Time series

Author(s)

Rob J Hyndman

Examples

data(gold)plot(na.interp(gold))

ndiffs Number of differences

Description

Uses a KPSS test for the null hypothesis that x has a stationary root against a unit-root alternative.Returns the least number of differences required to pass the test at the level alpha.

Usage

ndiffs(x,alpha=0.05)

Arguments

x A univariate time series

alpha Level of the test

Value

An integer.

Author(s)

Rob J Hyndman

See Also

kpss.test

plot.ets 25

Examples

ndiffs(WWWusage)

plot.ets Plot components from ETS model

Description

Produces a plot of the level, slope and seasonal components from an ETS model.

Usage

## S3 method for class 'ets':plot(x, ...)

Arguments

x Object of class “ets”.

... Other plotting parameters passed to par.

Value

None. Function produces a plot

Author(s)

Rob J Hyndman

See Also

ets

Examples

fit <- ets(USAccDeaths)plot(fit)plot(fit,plot.type="single",ylab="",col=1:3)

26 rwf

rwf Random Walk Forecast

Description

Returns forecasts and prediction intervals for a random walk with drift model applied to x.

Usage

rwf(x, h=10, drift=FALSE, conf=c(80,95), fan=FALSE)

Arguments



drift Logical flag. If TRUE, fits a random walk with drift model.



Details

The random walk with drift model is

Yt = c + Yt−1 + Zt

where Zt is a normal iid error. Forecasts are given by

Yn(h) = ch + Yn

. If there is no drift, the drift parameter c=0. Forecast standard errors allow for uncertainty inestimating the drift parameter.

Value



The generic accessor functions fitted.values and residuals extract useful features of thevalue returned by rwf.






seasadj 27






Author(s)

Rob J Hyndman

See Also

arima, meanf

Examples

gold.fcast <- rwf(gold[1:60],h=50)plot(gold.fcast)

seasadj Seasonal adjustment

Description

Returns seasonally adjusted data constructed by removing the seasonal component.

Usage

seasadj(object)

Arguments

object Object created by decompose or stl.

Value

Univariate time series.

Author(s)

Rob J Hyndman

See Also

stl, decompose

28 seasonaldummy

Examples

plot(AirPassengers)lines(seasadj(decompose(AirPassengers,"multiplicative")),col=4)

seasonaldummy Seasonal dummy variables

Description

Returns matrix of dummy variables suitable for use in arima, lm or arima.predict. The lastseason is omitted and used as the control.

Usage

seasonaldummy(x)seasonaldummyf(x,h)

Arguments

x Seasonal time series

h Number of periods ahead to forecast

Value

Numerical matrix with number of rows equal to the length(x) and number of columns equal tofrequency(x)-1.

Author(s)

Rob J Hyndman

Examples

plot(ldeaths)plot(ldeaths)month <- seasonaldummy(ldeaths)deaths.lm <- lm(ldeaths ~ month)tsdisplay(residuals(deaths.lm))ldeaths.fcast <- predict(deaths.lm,

data.frame(month=I(seasonaldummyf(ldeaths,36))),se.fit=TRUE)

seasonplot 29

seasonplot Seasonal plot

Description

Plots a seasonal plot as described in Makridakis, Wheelwright and Hyndman (1998, chapter 2).

Usage

seasonplot(x, s, season.labels = NULL, year.labels = FALSE,year.labels.left = FALSE, type = "o", main, ylab = "",xlab = NULL, col = 1, ...)

Arguments

x a numeric vector or time series.

s seasonal frequency of xseason.labels

Labels for each season in the "year"

year.labels Logical flag indicating whether labels for each year of data should be plotted onthe right.

year.labels.leftLogical flag indicating whether labels for each year of data should be plotted onthe left.

type plot type (as for plot)

main Main title.

ylab Y-axis label

xlab X-axis label

col Colour

... additional arguments to plot.

Value

None.

Author(s)

Rob J Hyndman

References


30 ses

See Also

monthplot

Examples

seasonplot(AirPassengers)

ses Exponential smoothing forecasts

Description

Returns forecasts and other information for exponential smoothing forecasts applied to x.

Usage

ses(x, h=10, conf=c(80,95), fan=FALSE, ...)

holt(x, h=10, damped=FALSE, conf=c(80,95), fan=FALSE, ...)

hw(x, h=2*frequency(x), seasonal="additive", damped=FALSE, conf=c(80,95), fan=FALSE, ...)

Arguments


h Number of periods for forecasting.

damped If TRUE, use a damped trend.

seasonal Type of seasonality in hw model. "additive" or "multiplicative"



... Other arguments passed to ets.

Details

ses, holt and hw are simply convenient wrapper functions for forecast(ets(...)).

Value



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


simulate.ets 31










Author(s)

Rob J Hyndman

References

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

Hyndman, R.J., Akram, Md., and Archibald, B. (2003) "The admissible parameter space for expo-nential smoothing models". Working paper, Department of Econometrics and Business Statistics,Monash University.

See Also

ets, HoltWinters, rwf, arima.

Examples

fcast <- holt(airmiles)plot(fcast)deaths.fcast <- hw(USAccDeaths,h=48)plot(deaths.fcast)

simulate.ets Simulation from an ETS model

Description

Returns a time series based on the model object object.

Usage

simulate.ets(object, nsim=length(object$x), seed=NULL, initstate=object$state[1,], bootstrap=TRUE, ...)

32 sindexf

Arguments

object An object of class "ets". Usually the result of a call to ets.

nsim Number of periods for the simulated series

seed Either NULL or an integer that will be used in a call to set.seed beforesimulating the time seriers. The default, NULL will not change the randomgenerator state.

initstate State at time 0.

bootstrap If TRUE, simulation uses resampled errors rather than normally distributed er-rors.


Value

An object of class "ts".

Author(s)

Rob J Hyndman

See Also

ets

Examples

fit <- ets(USAccDeaths)plot(simulate(fit, 100))

sindexf Forecast seasonal index

Description

Returns vector containing the seasonal index for h future periods. If the seasonal index is non-periodic, it uses the last values of the index.

Usage

sindexf(object, h)

Arguments

object Output from decompose or stl.

h Number of periods ahead to forecast

splinef 33

Value

Time series

Author(s)

Rob J Hyndman

Examples

uk.stl <- stl(UKDriverDeaths,"periodic")uk.sa <- seasadj(uk.stl)uk.fcast <- holt(uk.sa,36)seasf <- sindexf(uk.stl,36)uk.fcast$mean <- uk.fcast$mean + seasfuk.fcast$lower <- uk.fcast$lower + cbind(seasf,seasf)uk.fcast$upper <- uk.fcast$upper + cbind(seasf,seasf)uk.fcast$x <- UKDriverDeathsplot(uk.fcast,main="Forecasts from Holt's method with seasonal adjustment")

splinef Cubic Spline Forecast

Description

Returns local linear forecasts and prediction intervals using cubic smoothing splines.

Usage

splinef(x, h=10, conf=c(80,95), fan=FALSE)

Arguments





Details

The cubic smoothing spline model is equivalent to an ARIMA(0,2,2) model but with a restrictedparameter space. The advantage of the spline model over the full ARIMA model is that it providesa smooth historical trend as well as a linear forecast function. Hyndman, King, Pitrun, and Bil-lah (2002) show that the forecast performance of the method is hardly affected by the restrictedparameter space.

34 splinef

Value



The generic accessor functions fitted.values and residuals extract useful features of thevalue returned by meanf.











Author(s)

Rob J Hyndman

References

Hyndman, King, Pitrun and Billah (2002) Local linear forecasts using cubic smoothing splines.Working paper available at http://www-personal.buseco.monash.edu.au/~hyndman/papers/splinefcast.htm.

See Also

smooth.spline, arima, holt.

Examples

fcast <- splinef(uspop,h=5)plot(fcast)summary(fcast)

http://www-personal.buseco.monash.edu.au/~hyndman/papers/splinefcast.htm

http://www-personal.buseco.monash.edu.au/~hyndman/papers/splinefcast.htm

thetaf 35

thetaf Theta method forecast

Description

Returns forecasts and prediction intervals for a theta method forecast.

Usage

thetaf(x, h=10, conf=c(80,95), fan=FALSE)

Arguments





Details

The theta method of Assimakopoulos and Nikolopoulos (2000) is equivalent to simple exponentialsmoothing with drift. This is demonstrated in Hyndman and Billah (2003). Prediction intervals arecomputed using the underlying state space model.

Value



The generic accessor functions fitted.values and residuals extract useful features of thevalue returned by rwf.











36 tsdisplay

Author(s)

Rob J Hyndman

References

Assimakopoulos, V. and Nikolopoulos, K. (2000). The theta model: a decomposition approach toforecasting. International Journal of Forecasting 16, 521-530.

Hyndman, R.J., and Billah, B. (2003) Unmasking the Theta method. International J. Forecasting,19, 287-290.

See Also

arima, meanf, rwf, ses

Examples

nile.fcast <- thetaf(Nile)plot(nile.fcast)

tsdisplay Time series display

Description

Plots a time series along with its acf and either its pacf, lagged scatterplot or spectrum.

Usage

tsdisplay(x, plot.type = "partial", points = TRUE, ci.type ="white", lag.max = round(10 * log10(length(x))),na.action = na.interp, main = NULL, ylab = "", xlab ="", pch = 1, cex = 0.5, ...)

Arguments

x a numeric vector or time series.

plot.type type of plot to include in lower right corner. Possible values are "partial", "scat-ter" or "spectrum".

points logical flag indicating whether to show the individual points or not in the timeplot.

ci.type type of confidence limits for ACF. Possible values are as for acf.

lag.max the maximum lag to plot for the acf and pacf.

na.action how to handle missing values. Default is to use linear interpolation.

main Main title.

ylab Y-axis label

wineind 37

xlab X-axis labelpch Plotting charactercex Character size... additional arguments to acf.

Value

None.

Author(s)

Rob J Hyndman

References


See Also

plot.ts, acf

Examples

tsdisplay(diff(WWWusage))

wineind Australian total wine sales

Description

Australian total wine sales by wine makers in bottles <= 1 litre. Jan 1980 – Aug 1994.

Usage

wineind

Format

Time series data

Source


Examples

tsdisplay(wineind)



38 woolyrnq

woolyrnq Quarterly production of woollen yarn in Australia

Description

Quarterly production of woollen yarn in Australia: tonnes. Mar 1965 – Sep 1994.

Usage

woolyrnq

Format

Time series data

Source


Examples

tsdisplay(woolyrnq)



Package ‘fma’

Title Data sets from “Forecasting: methods and applications” by Makridakis, Wheelwright &Hyndman (1998)

Description All data sets from “Forecasting: methods and applications” by Makridakis, Wheelwright& Hyndman (Wiley, 3rd ed., 1998).

advert Sales and advertising expenditure

Description

Monthly sales and advertising expenditure for an automotive parts company.

Usage

advert

Format

Data frame containing the following columns:

advert Monthly Advertising expenditure

sales Monthly sales volume

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Exercise 6.7. Exercise 8.1.

Examples

plot(sales ~ advert, data=advert)

39

40 airpass

advsales Sales volume and advertising expenditure

Description

Sales volume and advertising expenditure for a dietary weight control product.

Usage

advsales

Format

Time series data

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Chapter 8.

References

Blattberg and Jeuland (1981).

Examples

plot(advsales)

airpass Monthly Airline Passenger Numbers 1949-1960

Description

The classic Box & Jenkins airline data. Monthly totals of international airline passengers (1949–1956).

Usage

airpass

Format

A monthly time series, in thousands.

auto 41

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Exercise 2.4, Chapter 3, Exercise 4.7.

References

Box, Jenkins and Reinsell (1994) Time series analysis: forecasting and control, 3rd edition, Holden-Day: San Francisco. Series G.

Examples

plot(airpass)seasonplot(airpass)tsdisplay(airpass)

auto Attributes of some US and Japanese automobiles

Description

Price, mileage, age and country of origin for 45 automobiles.

Usage

auto

Format

This data frame contains the following columns:

Model Name of modelCountry Country of manufactureMileage Mileage per gallonPrice Price of car at time of measurement

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, Wiley:New York. Chapter 2.

References

Consumer Reports, April 1990, pp.235-255.

Examples

plot(Price ~ Mileage, data=auto,pch=19,col=2)points(auto$Mileage[auto$Country=="USA"],auto$Price[auto$Country=="USA"],pch=19,col=4)legend(30,25000,legend=c("USA","Japan"),pch=19,col=c(4,2))

42 beer

bank Mutual savings bank deposits

Description

Deposits in a mutual savings bank in a large metropolitan area.

Usage

bank

Format


EOM End of month balance

AAA Composite AAA bond rates

threefour US Government 3-4 year bonds

Source


Examples

plot(bank)

beer Monthly beer production

Description

Monthly Australian beer production: Jan 1991 – Aug 1995.

Usage

beer

Format

Time series data

Source


bicoal 43

Examples

plot(beer)seasonplot(beer)tsdisplay(beer)

bicoal Annual bituminous coal production

Description

Annual bituminous coal production in the USA: 1920–1968.

Usage

bicoal

Format

Time series data

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Exercise 7.7.

Examples

tsdisplay(bicoal)

books Sales of paperback and hardcover books

Description

Daily sales of paperback and hardcover books at the same store.

Usage

books

Format

Bivariate time series containing the following columns:

Paperback Number of paperback sales each day

Hardcover Number of hardcover sales each day

44 boston

Source


Examples

plot(books)

boston Monthly dollar volume of sales

Description

Monthly dollar volume of sales on Boston stock exchange and combined New York and Americanstock exchange. January 1967 – November 1969.

Usage

boston

Format


nyase New York and American Stock Exchange dollar volume

bse Boston Stock Exchange dollar volume

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Exercise 6.5

References

McGee and Carleton (1970) Piecewise regression, Journal of the American Statistical Association,65, 1109–1124.

Examples

plot(boston)

bricksq 45

bricksq Quarterly clay brick production

Description

Australian quarterly clay brick production: 1956–1994.

Usage

bricksq

Format

Time series data

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Chapter 1 and Exercise 2.3.

Examples

plot(bricksq)seasonplot(bricksq)tsdisplay(bricksq)

canadian Canadian unemployment rate

Description

Canadian unemployment rate as a percentage of the civilian labor force between 1974 and the thirdquarter of 1975.

Usage

canadian

Format

Time series data

Source


46 cement

Examples

plot(canadian)

capital Quarterly capital expenditure and appropriations

Description

Seasonally adjusted quarterly capital expenditure and appropriations in U.S. manufacturing: 1953–1974.

Usage

capital

Format


capital Quarterly capital expenditure for US manufacturing.

appropriations Quarterly capital appropriations for US manufacturing.

Source


Examples

plot(capital)

cement Cement composition and heat data

Description

Cement composition and heat data.

Usage

cement

chicken 47

Format


pc1 Percentage by weight of component 1



heat Heat emitted in calories per gram of cement.

Source


Examples

plot(cement)

chicken Price of chicken

Description

Price of chicken in US (constant dollars): 1924–1993.

Usage

chicken

Format

Time series data

Source


Examples

plot(chicken)

48 copper

condmilk Condensed milk

Description

Manufacturer’s Stocks of evaporated and sweetened condensed milk.

Usage

condmilk

Format

Time series data

Source


Examples

plot(condmilk)seasonplot(condmilk)tsdisplay(condmilk)

copper Copper price

Description

Yearly copper prices, 1800–1997 (in constant 1997 dollars).

Usage

copper

Format

Time series data

Source


Examples

plot(copper)

copper1 49

copper1 Copper prices

Description

Monthly copper prices for 28 consecutive months (in constant 1997 dollars).

Usage

copper1

Format

Time series data

Source


Examples

plot(copper1)


Description

Yearly copper prices for 14 consecutive years (in constant 1997 dollars).

Usage

copper2

Format

Time series data

Source


Examples

plot(copper2)

50 cowtemp


Description

Yearly copper prices for 43 consecutive years (in constant 1997 dollars).

Usage

copper3

Format

Time series data

Source


Examples

plot(copper3)

cowtemp Temperature of a cow

Description

Daily morning temperature of a cow. Measure at 6.30am for 75 consecutive mornings by countingchirps from a telemetric thermometer implanted in the cow. Data are chirps per 5-minute intervalminus 800.

Usage

cowtemp

Format

Time series data

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Exercises 2.3 and 2.4.

cpimel 51

References

Velleman, Paul. (1981) The ABC of EDA, Duxbury Press.

Examples

plot(cowtemp)tsdisplay(cowtemp)

cpimel Consumer price index

Description

Quarterly CPI (consumer price index) for Victoria: Q1 1980 to Q2 1995.

Usage

cpimel

Format

Time series data

Source


Examples

tsdisplay(cpimel)

dexter Dexterity test and production ratings

Description

Scores on manual dexterity test and production ratings for 20 workers.

Usage

dexter

52 dj

Format


score Test score for manual dexterity

production Production rating

Source


Examples

plot(production~score,data=dexter,pch=19,col=3)

dj Dow-Jones index

Description

Dow-Jones index on 251 trading days ending 26 Aug 1994.

Usage

dj

Format

Time series data

Source


References

Brockwell and Davis (1996)

Examples

tsdisplay(dj)

dole 53

dole Unemployment benefits in Australia

Description

Monthly total of people on unemployment benefits in Australia (Jan 1965 – Jul 1992).

Usage

dole

Format

Time series data

Source


Examples

plot(dole)tsdisplay(dole)

dowjones Dow-Jones index

Description

Dow-Jones index, 28 Aug - 18 Dec 1972.

Usage

dowjones

Format

Time series data

Source


Examples

tsdisplay(dowjones)

54 eggs

econsumption Electricity consumption and temperature

Description

Electricity consumption and maximum temperature for 12 randomly chosen days.

Usage

temperature

Format


Mwh Daily electricity consumption (megawatt-hours)

temp Daily maximum temperature (degrees Celsius)

Source


Examples

plot(Mwh ~ temp, data=econsumption,pch=19,col=4)

eggs Price of eggs

Description

Price of dozen eggs in US, 1900–1993, in constant dollars.

Usage

eggs

Format

Time series data

Source


eknives 55

Examples

plot(eggs)

eknives Sales of electric knives

Description

Sales of electric knives: Jan 1991 - April 1992.

Usage

eknives

Format

Time series data

Source


Examples

plot(eknives)

elco Sales of Elco’s laser printers

Description

Sales of Elco’s laser printers: 1992–1998.

Usage

elco

Format

Time series data

Source


56 expenditure

Examples

plot(elco)

elec Electricity production

Description

Australian monthly electricity production: Jan 1956 – Aug 1995.

Usage

elec

Format

Time series data

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Chapters 1–2, 7.

Examples

plot(elec)seasonplot(elec)tsdisplay(elec)

expenditure Expenditure

Description

Expenditure for 12 supermarket customers.

Usage

expenditure

Format

Time series data

fancy 57

Source


Examples

hist(expenditure)

fancy Sales for a souvenir shop

Description

Monthly sales for a souvenir shop on the wharf at a beach resort town in Queensland, Australia.

Usage

fancy

Format

Time series data

Source


Examples

plot(fancy)seasonplot(fancy)

french Industry index

Description

French index of industry.

Usage

french

Format

Time series data

58 housing

Source


Examples

plot(french)

housing Housing data

Description

Monthly housing starts, construction contracts and average new home mortgage rates (Jan 1983 -Oct 1989).

Usage

housing

Format

Trivariate time series containing the following columns:

hstarts Monthly housing starts (thousands of units)

construction Construction contracts (millions of dollars)

interest Average new home mortgage rates

Source


References

Survey of current business, US Department of Commerce, 1990.

Examples

plot(housing)

hsales 59

hsales Sales of one-family houses

Description

Monthly sales of new one-family houses sold in the USA since 1973.

Usage

hsales

Format

Time series data

Source


References

US Census Bureau, Manufacturing and Construction Division

Examples

plot(hsales)plot(stl(hsales,"periodic"),main="Sales of new one-family houses, USA")

hsales2 Sales of new one-family houses

Description

Sales of new one-family houses in the USA (Jan 1987 – Nov 1995).

Usage

hsales2

Format

Time series data

60 ibm

Source


Examples

plot(hsales2)seasonplot(hsales2)tsdisplay(hsales2)

huron Level of Lake Huron

Description

Level of Lake Huron in feet (reduced by 570 feet): 1875–1972.

Usage

huron

Format

Time series data

Source


Examples

plot(huron)

ibm IBM sales and profit

Description

IBM sales and profit (1954-1984) and forecasts.

Usage

ibm

ibmclose 61

Format

Time series data

Sales IBM annual sales

Profit IBM annual profit

FSales Forecast of IBM sales made in 1984

FProfit Forecast of IBM profits made in 1984

Source


Examples

par(mfrow=c(2,1))plot(ibm[,1],xlim=c(1954,2000),ylim=c(0,200),

ylab="Sales (billions of $)",xlab="Year",type="o")lines(ibm[,3],col=2,type="o")plot(ibm[,2],xlim=c(1954,2000),ylim=c(-10,30),

ylab="Profits (billions of $)",xlab="Year",type="o")lines(ibm[,4],col=2,type="o")

ibmclose Closing IBM stock price

Description

Daily closing IBM stock price.

Usage

ibmclose

Format

Time series data

Source


References

Box, Jenkins and Reinsell (1994) Time series analysis: forecasting and control, 3rd edition, Holden-Day: San Francisco.

62 internet

Examples

tsdisplay(ibmclose)

input Input series

Description

Input series for exercise 8.6.

Usage

input

Format

Time series data

Source


Examples

plot(input)

internet Number of internet users

Description

Number of users logged on to an internet server each minute over a 100-minute period.

Usage

internet

Format

Time series data

Source


invent15 63

Examples

tsdisplay(internet)

invent15 Inventory demand

Description

Inventory demand for product E15.

Usage

invent15

Format

Time series data

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Exercise 2.6. Also Chapter 4.

Examples

plot(invent15)

jcars Motor vehicle production

Description

Japanese motor vehicle production in thousand (1947–1989).

Usage

jcars

Format

Time series data

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Exercise 2.8. Chapter 8.

64 kkong

References

World motor vehicle data, Motor Vehicle Manufacturers of US Inc, Detroit, 1991.

Examples

plot(jcars)log.jcars <- BoxCox(jcars,0)jcars.f <- holt(log.jcars)plot(jcars.f)

kkong King Kong data

Description

King Kong data.

Usage

kkong

Format

Data frame consisting of following columns

weight Weights of 21 gorillas

height Heights of 21 gorillas

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Chapter 5. Exercise 5.6.

Examples

plot(weight~height,data=kkong,pch=19,col=2)

labour 65

labour Civilian labour force

Description

Number of persons in the civilian labour force in Australia each month (Feb 1978 - Aug 1995).

Usage

labour

Format

Time series data

Source


Examples

plot(labour)labour.stl <- stl(labour,10)plot(labour.stl)monthplot(labour.stl$time.series[,1],type="h")

lynx Annual Canadian Lynx trappings 1821–1934

Description

Annual number of lynx trapped in McKenzie river district of northwest Canada: 1821–1934.

Usage

lynx

Format

Time series data

Source


66 milk

References

Campbell, M. J.and A. M. Walker (1977). A Survey of statistical work on the Mackenzie Riverseries of annual Canadian lynx trappings for the years 1821–1934 and a new analysis. Journal ofthe Royal Statistical Society series A, 140, 411–431.

Examples

plot(lynx)tsdisplay(lynx)

milk Monthly milk production per cow

Description

Average monthly milk production per cow over 14 years.

Usage

milk

Format

Time series data

Source


References

Cryer (1986) Time series analysis, Duxbury Press: Belmont.

Examples

par(mfrow=c(2,1))plot(milk,xlab="Year",ylab="pounds",

main="Monthly milk production per cow")milk.adj <- milk/monthdays(milk)*365.25/12plot(milk.adj,xlab="Year",ylab="pounds",

main="Adjusted monthly milk production per cow")

mink 67

mink Number of minks trapped

Description

Annual number of minks trapped in McKenzie river district of northwest Canada: 1848–1911.

Usage

mink

Format

Time series data

Source


Examples

tsdisplay(mink)

mortal Mortality

Description

Bird mortality for 156 poultry farms, Aug 1995 - Jul 1996.

Usage

mortal

Format


typeA Percentage of Type A birds for each farm.

mortality Percentage mortality of all birds for each farm.

Source


68 motion

Examples

plot(mortality~typeA,data=mortal)

motel Total accommodation at hotel, motel and guest house

Description

Total room nights occupied and total monthly takings from accommodation at hotel, motel andguest house in Victoria, Australia: Jan 1980 - June 1995.

Usage

motel

Format

Trivariate time series containing the following columns:

Roomnights Total room nights

Takings Total monthly takings (thousands of dollars)

CPI Quarterly CPI values

Source


Examples

plot(motel[,2],motel[,1], xlab="Room nights", ylab="Takings",pch=19,col=4)

motion Employment figures in the motion picture industry

Description

Monthly employment figures for the motion picture industry (SIC Code 78): Jan 1955 – Dec 1970.

Usage

motion

Format

Time series data

nail 69

Source


References

"Employment and earnings, US 1909–1978", Department of Labor, 1979.

Examples

plot(motion)seasonplot(motion)tsdisplay(motion)

nail Nail prices

Description

Nail prices, 1800–1996 in constant dollars.

Usage

nail

Format

Time series data

Source


Examples

plot(nail)

70 olympic

oilprice Oil prices

Description

Oil prices in constant 1997 dollars: 1870–1997.

Usage

oilprice

Format

Time series data

Source


Examples

plot(oilprice)

olympic Men’s 400 m final winning times in each Olympic Games

Description

Winning times for the men’s 400 m final in each Olympic Games: 1896–1996.

Usage

olympic

Format


Year Year of Olympics

time Winning time in 400m final

Source


ozone 71

Examples

plot(time~Year,data=olympic,pch=19,col=3)

ozone Ozone depletion and melanoma rates

Description

Ozone depletion and melanoma rates in various locations.

Usage

ozone

Format


ozonedep Ozone depletion rates as percentages

melanoma Melanoma rates as percentages

Source


Examples

plot(ozonedep~melanoma,data=ozone,pch=19,col=2)

paris Average temperature

Description

Average monthly temperature in Paris.

Usage

paris

Format

Time series data

72 pcv

Source


Examples

plot(paris)seasonplot(paris)tsdisplay(paris)

pcv GDP

Description

GDP for Western Europe and PCV industry sales.

Usage

pcv

Format

Bivariate time series consisting of the following columns

GDP GDP Western Europe

PCV PCV Industry sales

Source


Examples

plot(PCV~GDP,data=pcv,pch=20,col=2)

petrol 73

petrol Sales of petroleum and related product

Description

US monthly sales of petroleum and related product: Jan 1971 - Dec 1991.

Usage

petrol

Format

Multivariate time series data:

Chemicals Sales of chemicals and allied products

Coal Sales of Bituminous coal products

Petrol Sales of petroleum and coal products

Vehicles Sales of motor vehicles and parts

Source


Examples

plot(petrol)

pigs Number of pigs slaughtered

Description

Monthly total number of pigs slaughtered in Victoria, Australia (Jan 1980 – Aug 1995).

Usage

pigs

Format

Time series data

74 pollution

Source


Examples

tsdisplay(pigs)

plastics Sales of plastic product

Description

Monthly sales of product A for a plastics manufacturer.

Usage

plastics

Format

Time series data

Source


Examples

plot(plastics)seasonplot(plastics)plot(stl(plastics,"periodic"))

pollution Shipment of pollution equipment

Description

Monthly shipments of pollution equipment (in thousands of French francs), Jan 1986 – Oct 1996.

Usage

pollution

productC 75

Format

Time series data

Source


Examples

tsdisplay(pollution)

productC Sales of product C

Description

Sales of product C (a lubricant sold in large containers).

Usage

productC

Format

Time series data

Source


Examples

plot(productC)

76 qelec

pulpprice Pulp price and shipments

Description

World pulp price and shipments.

Usage

pulpprice

Format

Data frame consisting of following columns

shipments World pulp shipments

price World pulp price

Source


Examples

plot(shipments~price,data=pulpprice)

qelec Electricity production

Description

Quarterly electricity production.

Usage

qelec

Format

Time series data

Source


qsales 77

Examples

plot(decompose(qelec))

qsales Sales data

Description

Quarterly exports of a French company in thousands of francs.

Usage

qsales

Format

Time series data

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Exercise 3.7 and Table 4-7.

Examples

plot(qsales)

running Running times and maximal aerobic capacity

Description

Running times and maximal aerobic capacity for 14 female runners.

Usage

running

Format

Time series data

Source


78 schizo

References

Conley, Krahenbuhl, Burkett and Millar (1981) Physiological correlates of female road racing per-formance, Research Quarterly Exercise Sport, 52, 441–448.

Examples

plot(times~capacity,data=running,pch=19,col=2)

sales Sales data

Description

Sales data over 10 time periods.

Usage

sales

Format

Time series data

Source


Examples

plot(sales,type="p")abline(lsfit(1:10,sales))

schizo Perceptual speed scores

Description

Daily perceptual speed scores for a schizophrenic patient. The patient began receiving a powerfultranquilizer (chlorpromzaine) on the 61st day and continued receiving the drug for the remainder ofthe sample period. It is expected that this drug would reduce perceptual speed.

Usage

schizo

shampoo 79

Format

Time series data

Source


References

McCleary and Hay (1980).

Examples

plot(schizo)

shampoo Sales of shampoo

Description

Sales of shampoo over a three year period.

Usage

shampoo

Format

Time series data

Source


Examples

plot(shampoo)

80 ship

sheep Sheep population

Description

Sheep population (in millions) of England and Wales: 1867–1939.

Usage

sheep

Format

Time series data

Source


References

Kendall (1976).

Examples

tsdisplay(sheep)

ship Electric can opener shipments

Description

Electric can opener shipments.

Usage

ship

Format

Time series data

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Chapter 4. Exercise 4.6.

shipex 81

Examples

plot(ship)

shipex Shipments

Description

Shipments

Usage

shipex

Format

Time series data

Source


Examples

plot(shipex)

strikes Number of strikes

Description

Number of strikes in the US from 1951 to 1980.

Usage

strikes

Format

Time series data

Source


82 texasgas

References

Brockwell and Davis (1991)

Examples

tsdisplay(strikes)

telephone Telephone cost

Description

Telephone cost in San Francisco, New York: 1915–1996.

Usage

telephone

Format

Time series data

Source


Examples

plot(telephone)

texasgas Price and consumption of natural gas

Description

Price and per capita consumption of natural gas in 20 towns in Texas.

Usage

texasgas

Format


price Average price in cents per thousand cubic feetconsumption Consumption per customer in thousand cubic feet.

ukdeaths 83

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Exercise 5.10. Exercise 6.2.

Examples

plot(consumption ~ price, data=texasgas)

ukdeaths Total deaths and serious injuries

Description

Monthly total deaths and serious injuries on UK roads: Jan 1975 – Dec 1984. In February 1983,new legislation came into force requiring seat belts to be worn.

Usage

ukdeaths

Format

Time series data

Source


References

Harvey (1989)

Examples

plot(ukdeaths)seasonplot(ukdeaths)tsdisplay(ukdeaths)

84 uselec

usdeaths Accidental deaths in USA

Description

Monthly accidental deaths in USA.

Usage

usdeaths

Format

Time series data

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Exercises 2.3 and 2.4.

Examples

plot(usdeaths)seasonplot(usdeaths)tsdisplay(usdeaths)

uselec Total generation of electricity

Description

Monthly total generation of electricity by the U.S. electric industry (Jan 1985 - Oct 1996.

Usage

uselec

Format

Time series data

Source


ustreas 85

Examples

plot(uselec)seasonplot(uselec)tsdisplay(uselec)

ustreas Treasury bill contracts

Description

US treasury bill contracts on the Chicago market for 100 consecutive trading days in 1981.

Usage

ustreas

Format

Time series data

Source


Examples

plot(ustreas)tsdisplay(ustreas)

wagesuk Real daily wages

Description

Real daily wages in pound, England: 1260–1994.

Usage

wagesuk

Format

Time series data

86 wn

Source


Examples

plot(wagesuk)

wheat Wheat prices

Description

Wheat prices in constant 1996 pounds: 1264–1996.

Usage

wheat

Format

Time series data

Source


Examples

plot(wheat)

wn White noise series

Description

White noise series.

Usage

wn

Format

Time series data

wnoise 87

Source


Examples

tsdisplay(wn)

wnoise White noise time series

Description

White noise time series with 36 values.

Usage

wnoise

Format

Time series data

Source

Makridakis, Wheelwright and Hyndman (1998) Forecasting: methods and applications, John Wiley& Sons: New York. Chpater 7.

Examples

tsdisplay(wnoise)

writing Sales of printing and writing paper

Description

Industry sales for printing and writing paper (in thousands of French francs): Jan 1963 – Dec 1972.

Usage

writing

Format

Time series data

88 writing

Source


Examples

tsdisplay(writing)seasonplot(writing)

Package ‘Mcomp’

Title Data from the M-competitions

Description The 1001 time series from the M-competition (Makridakis et al. 1982) and the 3003 timeseries from the IJF-M3 competition (Makridakis and Hibon, 2000).

M1 M-Competition data

Description

The time series from the M1 and M3 forecasting competitions.

Usage

data(M1)data(M3)

Format

M1 is a list of 1001 series and M3 is a list of 3003 series. Each list is of class Mcomp. Each serieswithin M1 and M3 is of class Mdata with the following structure:

sn Name of the series

st Series number and period. For example "Y1" denotes first yearly series, "Q20" denotes 20thquarterly series and so on.

n The number of observations in the time series

h The number of required forecasts

period Interval of the time series. Possible values are "YEARLY", "QUARTERLY", "MONTHLY"& "OTHER".

type The type of series. Possible values for M1 are "DEMOGR", "INDUST", "MACRO1", "MACRO2","MICRO1", "MICRO2" & "MICRO3". Possible values for M3 are "DEMOGRAPHIC", "FI-NANCE", "INDUSTRY", "MACRO", "MICRO", "OTHER".

description A short description of the time series

x A time series of length n (the historical data)

xx A time series of length h (the future data)

89

90 plot.Mdata

Author(s)

Muhammad Akram and Rob Hyndman

Source

http://www.forecasters.org/data/tsdata.htm.

Detailed results from M3 competition at http://www-marketing.wharton.upenn.edu/forecast/m3-competition.html.

References

Makridakis, S., A. Andersen, R. Carbone, R. Fildes, M. Hibon, R. Lewandowski, J. Newton, E.Parzen, and R. Winkler (1982) The accuracy of extrapolation (time series) methods: results of aforecasting competition. Journal of Forecasting, 1, 111–153.

Makridakis and Hibon (2000) The M3-competition: results, conclusions and implications. Interna-tional Journal of Forecasting, 16, 451-476.

See Also

subset.Mcomp, plot.Mdata

Examples

M1plot(M1$YAF2)subset(M1,"monthly")

plot.Mdata Plotting M Competition data

Description

plot.Mdata plots a time series from the M competition data sets.

Usage

plot.Mdata(x, xlim=c(start(x$x)[1],end(x$xx)[1]), ylim=range(x$x,x$xx),main=x$sn, xlab="", ylab="", ...)

Arguments

x A series of M-competition data

xlim Limits on x-axis

ylim Limits on y-axis

main Main title

http://www.forecasters.org/data/tsdata.htm

http://www-marketing.wharton.upenn.edu/forecast/m3-competition.html

http://www-marketing.wharton.upenn.edu/forecast/m3-competition.html

subset.Mcomp 91

xlab Label on x-axis

ylab Label on y-axis

... Other plotting arguments

Value

None. The function produces a time series plot of the selected series.

Author(s)


See Also

M1

Examples

plot(M1[[1]])plot(M1$YAF3)plot(M3$N0647)

subset.Mcomp Subset of time series from the M Competitions

Description

subset.Mcomp returns a subset of the time series data from the M Competitions. Subsets can befor specific periods, or specific types of data or both.

Usage

## S3 method for class 'Mcomp':subset(x, cond1, cond2, ...)

Arguments

x M-competition data or a subset of M-competition data

cond1 Type or period of the data. Type is a character variable and period could becharacter or numeric.

cond2 Optional second condition specifying type or period of the data, depending oncond1. If cond1 denotes type then cond2would denote period, but if cond1denotes period then cond2 would denote type.


92 subset.Mcomp

Details

Possible values for cond1 and cond2 denoting period are 1, 4, 12, "yearly", "quarterly", "monthly"and "other".

Possible values for cond1 and cond2 denoting type are "macro", "micro", "industry", "finance","demographic", "allother", "macro1", "macro2", "micro1", "micro2", "micro3". These correspondto the descriptions used in the competitions. See the references for details.

Partial matching used for both conditions.

Value

An object of class Mcomp consisting of the selected series.

Author(s)


References

Makridakis, S., A. Andersen, R. Carbone, R. Fildes, M. Hibon, R. Lewandowski, J. Newton, E.Parzen, and R. Winkler (1982) The accuracy of extrapolation (time series) methods: results of aforecasting competition. Journal of Forecasting, 1, 111–153.

Makridakis and Hibon (2000) The M3-competition: results, conclusions and implications. Interna-tional Journal of Forecasting, 16, 451-476.

See Also

M1

Examples

M3.quarterly <- subset(M3,4)M1.yearly.industry <- subset(M1,1,"industry")

Index

∗Topic datasetsadvert, 39advsales, 40airpass, 40auto, 41bank, 42beer, 42bicoal, 43books, 43boston, 44bricksq, 45canadian, 45capital, 46cement, 46chicken, 47condmilk, 48copper, 48copper1, 49copper2, 49copper3, 50cowtemp, 50cpimel, 51dexter, 51dj, 52dole, 53dowjones, 53econsumption, 54eggs, 54eknives, 55elco, 55elec, 56expenditure, 56fancy, 57french, 57gas, 19gold, 21housing, 58hsales, 59hsales2, 59

huron, 60ibm, 60ibmclose, 61input, 62internet, 62invent15, 63jcars, 63kkong, 64labour, 65lynx, 65M1, 89milk, 66mink, 67mortal, 67motel, 68motion, 68nail, 69oilprice, 70olympic, 70ozone, 71paris, 71pcv, 72petrol, 73pigs, 73plastics, 74pollution, 74productC, 75pulpprice, 76qelec, 76qsales, 77running, 77sales, 78schizo, 78shampoo, 79sheep, 80ship, 80shipex, 81strikes, 81telephone, 82

93

94 INDEX

texasgas, 82ukdeaths, 83usdeaths, 84uselec, 84ustreas, 85wagesuk, 85wheat, 86wineind, 37wn, 86wnoise, 87woolyrnq, 38writing, 87

∗Topic datasubset.Mcomp, 91

∗Topic hplotplot.ets, 25plot.Mdata, 90

∗Topic tsarima, 2arima.errors, 4best.arima, 5BoxCox, 1croston, 6ets, 8fitted.Arima, 10forecast, 13forecast.Arima, 10forecast.ets, 17forecast.HoltWinters, 12forecast.StructTS, 14forecasterrors, 16gof, 20meanf, 21monthdays, 23na.interp, 23ndiffs, 24plot.forecast, 18rwf, 26seasadj, 27seasonaldummy, 28seasonplot, 29ses, 30simulate.ets, 31sindexf, 32splinef, 33thetaf, 35tsdisplay, 36

acf, 36, 37

advert, 39advsales, 40airpass, 40ar, 11arima, 2, 2–4, 6, 9–11, 13, 27, 28, 31, 34, 36arima.errors, 4arima.predict, 28auto, 41auto.arima (best.arima), 5

bank, 42beer, 42best.arima, 5bicoal, 43books, 43boston, 44BoxCox, 1bricksq, 45

canadian, 45capital, 46cement, 46chicken, 47condmilk, 48copper, 48copper1, 49copper2, 49copper3, 50cowtemp, 50cpimel, 51croston, 6, 14

decompose, 27, 32dexter, 51dj, 52dole, 53dowjones, 53

econsumption, 54eggs, 54eknives, 55elco, 55elec, 56ets, 8, 12, 14, 17, 18, 25, 31, 32expenditure, 56

fancy, 57fitted.Arima, 10forecast, 13, 18

INDEX 95

forecast.ar (forecast.Arima), 10forecast.Arima, 2, 10, 10, 13, 14forecast.ets, 13, 14, 17forecast.HoltWinters, 12, 14forecast.StructTS, 14, 14forecast.ts, 13forecasterrors, 16, 20french, 57

gas, 19gof, 16, 20gold, 21

holt, 14, 34holt (ses), 30HoltWinters, 9, 12, 13, 31housing, 58hsales, 59hsales2, 59huron, 60hw, 14hw (ses), 30

ibm, 60ibmclose, 61input, 62internet, 62InvBoxCox, 18InvBoxCox (BoxCox), 1invent15, 63

jcars, 63

kkong, 64kpss.test, 5, 24

labour, 65lm, 28lynx, 65

M1, 89, 91, 92M3 (M1), 89meanf, 14, 21, 27, 36milk, 66mink, 67monthdays, 23monthplot, 30mortal, 67motel, 68motion, 68

na.interp, 23nail, 69ndiffs, 24

oilprice, 70olympic, 70ozone, 71

par, 25paris, 71pcv, 72petrol, 73pigs, 73plastics, 74plot, 19, 29plot.ets, 25plot.forecast, 18plot.Mdata, 90, 90plot.splineforecast

(plot.forecast), 18plot.ts, 19, 37pollution, 74predict.ar, 11predict.arima, 11predict.HoltWinters, 12, 13predict.StructTS, 15print.ets (ets), 8print.forecast (forecast), 13productC, 75pulpprice, 76

qelec, 76qsales, 77

residuals, 4running, 77rwf, 9, 11, 14, 22, 26, 31, 36

sales, 78schizo, 78seasadj, 27seasonaldummy, 28seasonaldummyf (seasonaldummy), 28seasonplot, 29ses, 7, 14, 30, 36set.seed, 32shampoo, 79sheep, 80ship, 80

96 INDEX

shipex, 81simulate.ets, 31sindexf, 32smooth.spline, 34splinef, 14, 33stl, 27, 32strikes, 81StructTS, 15subset.Mcomp, 90, 91summary.forecast (forecast), 13

telephone, 82texasgas, 82thetaf, 14, 35tsdisplay, 36

ukdeaths, 83usdeaths, 84uselec, 84ustreas, 85

wagesuk, 85wheat, 86wineind, 37wn, 86wnoise, 87woolyrnq, 38writing, 87

Documents

The forecasting Package - Uni Bayreuthftp.uni-bayreuth.de/math/statlib/R/CRAN/doc/packages/...Largely a wrapper for the arima function in the stats package. The main difference is