Automatic optimal fitting and prediction of a simple Arima model

Yesterday with R toss a simple time series data Arima automatic fitting and prediction. The process is not complicated, but it is not used much, in order to prevent forgetting, the author records.

Open R and install a package called "Forecast". Each time you turn on R, use the
Library (' forecast ')
Load the package.

Here I use the legendary airline model data. Load data, convert to TS format
Airdata<-read.table (' Airline.dat ')
Airts<-ts (airdata,start=1949,frequency=12)

The

then automatically fits the Arima model with the Auto.arima in the forecast package.  
Arima1<-auto.arima (airts,trace=t)  
Displays the following results:  
Arima (2,0,2) (1,1,1) [] with drift: 974.1468 
Arima (0,0,0) (0,1,0) [n] with drift:1077.823 
ARIMA (1,0,0) (1,1,0) [n] with drift:974.92& nbsp
Arima (0,0,1) (0,1,1) [n] with drift:1022.198 
ARIMA (2,0,2) (0,1,1) [n] with drift:967.1033 
Arim A (2,0,2) (0,1,0) [] with drift:966.755 
Arima (1,0,2) (0,1,0) [n] with drift:964.3004 
ARIMA (1,0,1) ( 0,1,0) [] with drift:963.9208 
ARIMA (1,0,1) (0,1,0) [n]: 971.225 
ARIMA (1,0,1) (1,1,0) [A] with drift:972.4003 
Arima (1,0,1) (0,1,1) [n] with drift:963.9781 
ARIMA (1,0,1) (1,1,1) [n] with drift:97 1.7862 
Arima (0,0,1) (0,1,0) [n] with drift:1022.291 
ARIMA (2,0,1) (0,1,0) [n] with drift:965.183& nbsp
ARIMA (1,0,0) (0,1,0) [] with drift:966.9728

Best Model:arima (1,0,1) (0,1,0) [a] with drift

The result is an AR (1), MA (1), and seasonal differential Arima model. The key to auto-fitting the Arima model is the fixed order, which was previously used by EACF (extended (sample) autocorrelation function) to order, but now it is generally used to order by aic,aicc,bic and other statistics. For example, the above 974.1468 is the AIC of the model

Then you can predict it.
Airfore<-forecast (arima1,h=30,fan=t)
30 months were predicted, and the predicted values of confidence intervals from 50 to 99 were also calculated.
Plot (Airfore)
The final drawing. If you need to get the forecast data, you can get it by using: Airefore$mean.

There is a picture to testify, the prediction effect is good.