In the previous session you have studied about two Auto Regressive Models- AR and MA. In this segment you will learn about an Auto Regressive Model consisting of both ‘AR’ and ‘MA’ components called Auto Regressive Moving Average (ARMA).

A time series that exhibits the characteristics of an AR(p) and/or an MA(q) process can be modelled using an ARMA(p,q) model.

ARMA (1,1) equation: For p = 1 and q=1 —

$$//$\gamma ={\beta}_{0}+{\beta}_{1}{\mathrm{S}}_{\mathrm{t}\u20131}+{\mathrm{\varphi}}_{1}{\mathrm{\epsilon}}_{\mathrm{t}\u20131}$//$$

Here, ^y is forecasted value.

**To determine the parameters ‘p’ and ‘q’ —**

- Plot autocorrelation function (ACF) and partial autocorrelation function (PACF).

- If you check the plot for PACF, you will see that you need to select p = 1 as the highest lag where partial autocorrelation is significantly high.

- Similarly from the ACF plot, select q = 2 as the highest lag beyond which autocorrelation dies down.

- So, we would select an ARMA (1, 2) model in this example.

You can solve an optional model building assessment on ARMA here.

In this segment, you have learnt how to build an ARMA model. In the next segment, you will learn another Auto-Regressive model called Auto-Regressive Integrated Moving Average (ARIMA).