Multivariate time series

In the previous chapter, we discussed models for univariate time series or a time series of one variable. However, in many modeling situations, it is common to have multiple time-varying variables that are measured together. A time series consisting of multiple time-varying variables is called a multivariate time series. Each variable in the time series is called a covariate. For example, a time series of weather data might include temperature, rain amount, wind speed, and relative humidity. Each of these variables, in the weather dataset, is a univariate time series, and together, a multivariate time series and each pair of variables are covariates.

Mathematically, we typically represent a multivariate time-series as a vector-valued series, as follows:

X = x 0,0 x 0,1 ⋮ , x 1,0 x 1,1 ⋮ , … , x t,0 x t,1 ⋮ 

Here, each X instance consists of multiple...