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

[Adams, Zeno]

Temperature data is not my field but I noticed one thing that appears odd:

You use three times differencing on the seasonal part which suggests some extreme form of nonstationarity in the seasonality. Normally, differencing once for the seasonality should be sufficient. You may want to check the optimal parameter, differencing, and lag setting by running several model specifications. The lowest AIC should tell you which specification to use. The following code (see more in "Applied Econometrics with R", Kleiber & Zeileis (2008)) should help:

optimal_par <- expand.grid(ar = 0:2, diff = 1, ma = 0:2, sar = 0:3, sdiff = 0:3, sma = 0:3)
opt_aic <- rep(0, nrow(optimal_par))
for(i in seq(along = opt_aic)) opt_aic[i] <- AIC(arima(temp,
unlist(optimal_par[i, 1:3]), unlist(optimal_par[i, 4:6])),
k = log(length(temp)))
optimal_par[which.min(opt_aic),]


Zeno




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Gesendet: Freitag, 31. Juli 2009 16:19
An: r-sig-finance at stat.math.ethz.ch
Betreff: [R-SIG-Finance] Question about seasonal parameters in ARIMA model.

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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