Here is my problem:
Autoregressive models are very interesting in forecasting consumptions (eg water, gas etc).

Generally time series of this type have a long history with relatively simple patterns and can be useful to add external regressors for calendar events (holydays, vacations etc).

arima() is a very powerful function but kalman filter is very slow (and I foun difficulties of estimation) while ar() is too simple but fast (but do not have a method for forecasting I think)

Is there something like arima() but entirely implemented in C and efficient like ar() ???
Is there something like step() for ARIMAX? It would be very useful for external regressors.

Try the code below (imagine daily data for some years):

x <- rep(c(15,20,20,20,20,12,10), 5*52)
set.seed(1234)
x <- x + rnorm(length(x))

#plot(as.ts(x[1:21]))

#slow
arima(x, c(1,0,1), list(order = c(2,0,0), period = 7))
arima(x, c(2,0,0), list(order = c(3,0,0), period = 7))
#slower
arima(x, c(2,0,1), list(order = c(3,0,0), period = 7))
# do not converge
arima(x, c(2,0,0), list(order = c(3,0,1), period = 7))

#fast but not enough sophisticated
ar(x)

Thanks in advance
Daniele



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