How to forecast season and trend of data using STL and ARIMA in R

Question

Consider a data series that has a seasonal component, a trend, and an ARIMA part. I want to forecast this series.

data_ts <- ts(data, frequency = 24)
data_deseason <- stl(data_ts, t.window=50, s.window='periodic', robust=TRUE) 
f <- forecast(data_deseason, method='arima', h = N)

By implementing the above code, I am not able to choose the parameters of the ARIMA part, which I would like to.

I tried splitting the data into a season a trend and a remainder part. But then how do I forecast it?

Should I make an ARIMA model for both the trend and the remainder?

trend_arima <- Arima(data_deseason$time.series[,'trend'], order = c(1,1,1))
remainder_arima <- Arima(data_deseason$time.series[,'remainder'], order = c(1,1,1))

and then use forecast() and add the two above components and the season. 

Or is there some way to extract the trend model that STL has found?

Answer 1

You can use the forecast.stl function for the reminder series. It is fast because it need not consider seasonal ARIMA models.

You can select a specific model with specific parameters via the forecast function argument. 

For example, suppose you wanted to use an AR(1) with parameter 0.5, the following code will do it:

data_ts <- ts(data, frequency = 24)
data_deseason <- stl(data_ts, t.window=50, s.window='periodic', robust=TRUE) 
f <- forecast(data_deseason, h=N,
        forecastfunction=function(x,h,level){
        fit <- Arima(x, order=c(1,0,0), fixed=0.5, include.mean=FALSE)
        return(forecast(fit,h=N,level=level))})
plot(f)

If you just want to select the ARIMA order, but not the parameters, then leave out the fixed argument.