marima (version 2.2)

arma.forecast: arma.forecast

Description

Forecasting of (multivariate) time series of using marima type model.

Usage

arma.forecast(series = NULL, marima = NULL, nstart = NULL, nstep = 1, dif.poly = NULL, check = TRUE)

Arguments

series

matrix holding the kvar-variate timeseries. The series is assumed to have the same format as the timeseries analysed by marima BEFORE differencing (if differencing was used via define.dif) (the length, though, does not need to be the same but can be shorter or longer). Results from estimating the model (for the differenced data, if used) are assumed to be saved in the input-object 'marima' (see 'usage') by marima.

The series is assumed to have the total length=(nstart+nstep) (but it may be longer. In any case the forecasting is starting from nstart continuing to nstart+nstep. Future values already present or initialised, for example, as NAs are overwritten with the forecasted values.)

An example of a series prepared for forcasting is in the marima library: 'data(austr)': (see below, the example).

If future (independent) x-values for the forecasting are to be used these values must be supplied in 'series' at the proper places before calling 'arma.forecast(...)' (that is except the x-value(s) corresponding to the last prediction).

marima

the object holding the marima results to be used for the forecasting, that is an output object created by marima.

If the ar- and/or the ma-model do not include a leading unity matrix this is automatically taken care of in the function (in that case the dimensions of the model arrays used will be, respectively, (kvar, kvar, p+1) and (kvar, kvar, q+1)) after inserting the leading unity matrix (if the object 'marima' was produced by marima, this will automatically be OK.

nstart

starting point for forecasting (1st forecast values will be for time point t = nstart+1).

nstep

length of forecast (forecasts will be for time points nstart+1,...,nstart+nstep).

dif.poly

(most often) output from the function define.dif holding the ar-representation of the differencing polynomial (define.dif$dif.poly). If a differenced timeseries was analysed by marima the forecast-variance/covariance matrices are calculated for the aggregated (original) timeseries if 'dif.poly' is specified. If not, the forecast-variance/covariance matrices are calculated for the differenced time series. If forecasting is wanted for the original (not differenced) time series the 'dif.poly' created by define.dif must be specified.

check

If check=TRUE (default) various checks and printouts are carried out.

Value

forecasts = forecasted values following the nstart first values of the input series (at time points 'nstart+1,...,nstart+nstep'). The forecasted values will be (over-) written in the input series at the proper future positions (if relevant).residuals = corresponding residuals for input series followed by nstep future residuals (all=0).prediction.variances = (kvar, kvar, nstep) array containing prediction covariance matrices corresponding to the nstep forecasts.nstart = starting point for prediction (1st prediction at point nstart+1).nstep = length of forecast

Examples

library(marima)
data(austr)
series<-austr
Model5 <- define.model(kvar=7, ar=1, ma=1, rem.var=1, reg.var=6:7)
Marima5 <- marima(ts(series[1:90, ]), Model5$ar.pattern, Model5$ma.pattern, 
penalty=1)

nstart  <- 90
nstep   <- 10
cat("Calling arma.forecast.\n")
cat("In the example the input series is dim(length,kvar).\n")
cat("and of type ts() (timeseries) for illustration. \n")
Forecasts <- arma.forecast(series=ts(series), marima=Marima5, 
               nstart=nstart, nstep=nstep )
Year<-series[91:100,1]
One.step <- Forecasts$forecasts[, (nstart+1)]
One.step
Predict  <- Forecasts$forecasts[ 2, 91:100]
Predict
stdv<-sqrt(Forecasts$pred.var[2, 2, ])
upper.lim=Predict+stdv*1.645
lower.lim=Predict-stdv*1.645
Out<-rbind(Year, Predict, upper.lim, lower.lim)
print(Out)
# plot results:
plot(series[1:100, 1], Forecasts$forecasts[2, ], type='l', xlab='Year', 
ylab='Rate of armed suicides', main='Prediction of suicides by firearms', 
ylim=c(0.0, 4.1))
lines(series[1:90, 1], series[1:90, 2], type='p')
grid(lty=2, lwd=1, col='black')
Years<-2005:2014
lines(Years, Predict, type='l')
lines(Years, upper.lim, type='l')
lines(Years, lower.lim, type='l')
lines(c(2004.5, 2004.5), c(0.0, 2.0), lty = 2)