ARIMAX

In the previous chapter, we discussed the ARIMA family of models and demonstrated how to model univariate time-series data. However, as we mentioned in the previous section, many time series are multivariate, such as stock data, weather data, or economic data. In this section, we will discuss how we can incorporate information from covariate variables when modeling time-series data.

When we model a multivariate time series, we typically have a variable we are interested in forecasting. This variable is commonly called the endogenous variable. The other covariates in the multivariate time series are called exogenous variables. Recall from Chapter 11, ARIMA Models, the equation representing the ARIMA model:

y′ t = c + ϕ 1 y′ t−1 + … + ϕ p  y ′  t−p + ϵ t + θ 1 ϵ t−1 + … + ϕ q ϵ t−q

Here, y′ ...