5 Modeling an autoregressive process
This chapter covers
- Defining an autoregressive process
- Defining the PACF
- Using the PACF plot to determine the order of an autoregressive process
- Forecasting a time series using the autoregressive model
In the previous chapter, we covered the moving average process, also denoted as MA(q), where q is the order. We learned that in a moving average process, the present value is linearly dependent on current and past error terms. Therefore, if we predict more than q steps ahead, the prediction will fall flat and will return only the mean of the series because the error terms are not observed in the data and must be recursively estimated. Finally, we saw that we can determine the order of a stationary MA(q) process by studying the ACF plot; the autocorrelation coefficients will be significant up until lag q. In the case where the autocorrelation coefficients slowly decay or exhibit a sinusoidal pattern, then we are possibly in the presence of an autoregressive process.
In this chapter, we will first define the autoregressive process. Then, we will define the partial autocorrelation function and use it to find the order of the underlying autoregressive process of our dataset. Finally, we will use the AR(p) model to produce forecasts.