Hi
This is my first post to this group, so apologies in advance if I get it wrong.
I would like to know how the prediction for arima models works in R. I
have a time series to which I fit an arima model, of varying AR and MA
orders. I then use the predict function to project it forward. I have
also written my own function to perform the prediction, but it gives
different answers to Arima.predict when the MA order is non-zero.
I use the residuals from the arima function in my custom prediction
function. I think this may be my problem. In the arima model:
x{t} = a(1)x{t-1} + a(2)x{t-2} + ... + a(p)x{t-p} + e{t} + b(1)e{t-1}
+ b(2)e{t-2} + ... + b(q)e{t-q}
I am treating the residuals (i.e. arima()$res) as the e{t} terms.
This gives different answers both in the region of the simulation and
in the region of the prediction, so I'm guessing they're not what I
think they are. Indeed, after q intervals in the prediction, the
prediction proceeds as I would expect, presumably because all the
residuals that have an effect are zero by this stage.
Any help greatly appreciated - my code is below.
Thanks
Chris
--
The code to produce the two predictions is as follows:
AR - 5
MA - 3
sim - arima.sim(list(order=c(AR,0,MA), ar=c(.1, .1, .1, .1, .1),
ma=c(.1, .1, .1)), n=100) + 50
fit - arima(sim, order = c(AR, 0, MA))
coefs - fit$coef
series - sim
innov - fit$res
pred - 100
fit.predict - predict(fit, n.ahead = pred)
fit.r - c(sim, fit.predict$pred)
fit.custom - ProjectCentralArima(AR = AR, MA = MA, d = 0, coefs =
coefs, series = sim, innov = innov, pred = pred)$ser
ProjectCentralArima function:
ProjectCentralArima - function(AR, MA, d, coefs, series, innov, pred)
{
if(d==0){
series.diff - series
}
else {
series.diff - diff(series, lag=1, differences=d)
}
intercept - coefs[length(coefs)]
for(i in 1:pred){
temp - intercept
l.s - length(series.diff)
if(AR 0){
for(j in 1:AR){
temp - temp + coefs[j] * (series.diff[l.s - j + 1] -
intercept)
}
}
if(MA 0){
for(j in (1:MA)){
temp - temp + coefs[j + AR] * innov[l.s - j + 1]
}
}
innov - c(innov, 0)
series.diff - c(series.diff, temp)
}
if(d==0){
series.undiff - series.diff
}
else {
series.undiff - diffinv(series.diff, lag=1, differences=d, xi =
series[1:d])
}
return(list(series = series.undiff, innov = innov))
}
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