The ARMA model

Up until now, we have seen how the applications of AR and MA are processed separately. However, in some cases, combining the two allows us to handle more complex time series data. The ARMA model is a combination of the AR(p) and MA(q) processes and can be written as follows:

The following terms are used in the preceding equation:

• ARMA(p,q) defines an ARMA process with a p-order AR process and q-order moving average process
• Y_t represents the series itself
• c represents a constant (or drift)
• p defines the number of lags to regress against Y_t
• is the coefficient of the i lag of the series
• Y_t-1 is the i lag of the series
• q defines the number of past error terms to be used in the equation
• is the corresponding coefficient of
• are white noise error terms
• represents the error term, which is white noise

For instance, an ARMA(3,2) model is defined by the following equation...