You can make predictions based on the estimated ARMA model for both univariate and multivariate time series.

The ARMA model is a general model that includes both the AR and the MA models. You can apply ARMA model-based prediction to AR or MA model-based prediction by converting an AR or MA model to an ARMA model. Use the TSA ARMA Prediction VI to predict the future values of univariate or multivariate time series based on the estimated ARMA or VARMA models.

The following figure shows an example of predicting the monthly temperatures for the following year based on the ARMA model of the monthly temperatures during the previous eleven years:

Figure 84. Forecasting Next Year's Monthly Temperatures Using ARMA Model of Past Eleven Years' Data
Note The data source in the previous figure is from the Time Series Data Library.

In the previous figure, the Original graph contains the monthly average temperatures for twelve consecutive years. Before predicting future values, this example estimates the AR model for the temperature time series of the first eleven years. With the estimated AR model coefficients and by specifying the MA model coefficients to one, this example predicts the monthly temperatures for the twelfth year using the TSA ARMA Prediction VI.

The Prediction Result graph in the previous figure compares the predicted temperatures with the original temperatures of the twelfth year by plotting them together. The prediction may bias from the true values but the true values fall into the estimated confidence range. The Upper Limit and Lower Limit plots in the Prediction Result graph indicate the confidence range of the prediction. You can see in the Confidence Level indicator that the prediction result falls into the estimated confidence range with the confidence level of 99.73% (3σ).