4 Modeling a moving average process
This chapter covers
- Defining a moving average process
- Using the ACF to identify the order of a moving average process
- Forecasting a time series using the moving average model
In the previous chapter, we learned how to identify and forecast a random walk process. We defined a random walk process as a series whose first difference is stationary with no autocorrelation. This means that plotting its ACF will show no significant coefficients after lag 0. However, it is possible that a stationary process still exhibits autocorrelation. In this case, we have a time series that can be approximated by a moving average model MA(q), an autoregressive model AR(p), or an autoregressive moving average model ARMA(p,q). In this chapter, we will first focus on identifying and modeling using the moving average model.
Suppose that you want to forecast the volume of sales of widgets from the XYZ Widget Company. By predicting futures sales, the company can better manage its production of widgets to avoid producing too much or too little. In the case where not enough widgets are produced, the company would not be able to meet the client’s demand, leaving customers unhappy. On the other hand, producing too many widgets will increase inventory. The widgets might become obsolete or lose their value, which will increase the business’s liabilities ultimately making shareholders unhappy.