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. 

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