[R-SIG-Finance] Question about seasonal parameters in ARIMA model.

[Brian G. Peterson]

This message belongs on r-help, not r-sig-finance, as it is not finance
related that I can see.

Regards,

    - Brian

On Fri, 2009-07-31 at 10:18 -0400, englishinparis at aim.com wrote:
> Hi all.
>  
> I am playing with monthly temperature data collected in Seattle from 1931 through 2009 in order to learn about the modeling and analysis of time series. I am using an ARIMA procedure. Beforehand, I ran a Partial Autocorrelation Function analysis and found the obvious winter/summer seasonality of termperatures.

> I am getting 

> Call: 
>  arima(x = temp, order = c(1, 1, 1), seasonal = list(order = c(1, 3, 
>  3), period = 1), 
>  ? ? include.mean = 1) 
>  
> 
> Coefficients: 
>  ? ? ? ? ? ar1 ? ? ?ma1 ? ? sar1 ? ?sma1 ? ? sma2 ? ?sma3 
>  ? ? ? -0.6912 ?-1.0000 ?-0.6912 ?0.0567 ?-0.8644 ?-0.192 
>  s.e. ? ? ?NaN ? 0.0029 ? 0.0069 ? ? NaN ? 0.0070 ? ? NaN 

> So I seem to have a very significant (negative) seasonal auto regressive (SAR1) effect. I would like to know how to interpret this coefficient in layman's terms. Is this is a statement about the temperatures of 2 consecutive months, or 2 nonconsecutive months? What is the difference between SAR1 and SAR2 in an ARIMA?
> 
> I greatly appreciate your help.