After running my auto.arima model I'm getting coefficients ar1, ar2 & sar1. What do these coefficients mean?
Solved – What do coefficients of auto.arima mean
arimar
Related Solutions
The sum of the AR coefficients is close to 1 which shows that the parameters are near the edge of the stationarity region. That will cause difficulties in trying to compute the standard errors. However, there is nothing wrong with the estimates, so if all you need is the value of $L_0$, you've got it.
auto.arima() takes a few short-cuts to try to speed up the computation, and when it gives a model that looks suspect, it is a good idea to turn those short-cuts off and see what you get. In this case:
> n.auto <- auto.arima(log(L),xreg=year,stepwise=FALSE,approx=FALSE)
>
> n.auto
Series: log(L)
ARIMA(2,0,0) with non-zero mean
Coefficients:
ar1 ar2 intercept year
1.8544 -0.9061 11.0776 0.0081
s.e. 0.0721 0.0714 0.0102 0.0008
sigma^2 estimated as 1.594e-06: log likelihood=107.19
AIC=-204.38 AICc=-200.38 BIC=-199.15
This model is a little better (a smaller AIC for example).
Seasonality is probably not very strong. Different algorithms will give different results, unless seasonality is glaringly obvious.
The best measure is always to compare forecast accuracy on a holdout set: hold back the last $n$ observations, fit your models to all other observations, forecast into the last $n$ time periods with both models, then compare forecast accuracy using your error measure of choice (see 5 below).
Yes, this is a common complaint. I don't think there is an easy way to get the in-sample fit. But you can get the residuals:
auto.arima(WWWusage)$residuals. Best to look into the code ofauto.arima()to see whether you need to add or subtract them from the original series to get the fit. I'd say you have to subtract ("actuals=model+residuals"), but better check.I recommend a good forecasting textbook. This is a very good start. Otherwise, read through the help pages.
The appropriate error measure will depend on your personal loss function. Is your pain symmetric, and will it increase more strongly with larger errors? Then use MSE. Is your pain proportional to absolute errors? Then use MAE. Best to look at multiple error measures.
One tip: averaging forecasts will usually improve accuracy. Consider taking the average of your two models' forecasts per future time bucket.
auto.arima()apparently fits no drift, even if you allow it.
Best Answer
The ar1 and ar2 coefficients are autoregressive coefficients of orders 1 and 2. The sar1 coefficient is a seasonal autoregressive coefficient of order 1.
You can read all about seasonal ARIMA models in this section of this excellent free online forecasting textbook. If you are not familiar with nonseasonal ARIMA, it would make sense to read the entire chapter on ARIMA models.