Guide to Autoregressive Models

AR(1) is stationary only if |φ| < 1 or −1 <φ< 1. This is a non-stationary explosive process.

As a result of combining all the inequalities, we can find a region bounded by the lines φ2 =1+ φ1; φ2 = 1 − φ1; φ2 = −1. This is the region where the AR(2) process is stationary.

Therefore, AR, MA, and ARMA are either stationary or non-stationary depending on the parameters

AR and MA models differ primarily in how they correlate time series objects at different points in time. MA models have zero covariance between x(t) and x(t-n).

In the AR model, however, the correlation between x(t) and x(t-n) gradually declines as n increases. It means that the moving average(MA) model uses the errors from past forecasts rather than past forecasts to predict future values.

On the other hand, an autoregressive model(AR) uses past forecasts for future predictions.

The autoregressive model predicts the future based on the past data. A lot of technical analysts use them to predict future security prices. In autoregressive models, the future gets implicitly considered to be similar to the past.