[R-SIG-Finance] Seasonal time-series.

[rkevinburton at charter.net]

I have a general question that although I will speak in specifics, what I am really after is a process.

I have a time series that I have removed the trend and seasonality from using the 'R' method 'stl. What remains is the "remainder" and that is the subject of this question. 

First I looked at the ACF and PACF of the series and it plot seem to die down. The ACF seems to die down in more or less a linear fashion. The PACF oscilates but seems to die down at what looks like an exponential rate.

Based on this information I tried fitting an ARIMA model with p = 1, d = 1, and q = 1. The residuals of this fit and a Box-Ljung test indicated that this didn't fit properly. I looked again at the PACF and noticed that the first lag that was below 0.05 was at lag 10 so I set p = 10 and it still didn't seem to fit (based on the tests of the residuals and the Box-Ljung test). I am not sure where to proceed from here. I have dabbled a little in ARCH models and I have run what Tsay in his book "Analysis of Financial Time Series" says are ARCH effect tests. These tests seem to indicate that there is an ARCH effect in this "remainder" data. I would rather not go there if I can help it a) I don't have alot of experience with ARCH models b) there isn't alot of data (examples) that I have seen on developing those models with 'R'. The other possibility that I have not tried is to not use 'stl' to remove the seasonality and instead let the ARIMA model incorporate it into the fitted model. 

My eventual goal would be to combine all of this into a model that I could use for forecast. Using stl it seems that I am almost there. The trend fits to an ARMA model readily, of course the seasonal component can be readily added to a forcast model. The only thing that remains is the pesky "remainder".

Thoughts?

Thank you.

Kevin