Multivariate Time Series Analysis and Applications

3Multivariate time series regression models

Regression analysis is one of the most commonly used statistical methods. It is covered in most undergraduate and graduate statistical courses. However, the method discussed in these courses is the standard multiple regression model with one response variable. In this chapter, we will introduce multivariate time series regression models with several response variables. We will illustrate this method using many examples.

3.1 Introduction

In this chapter, we will discuss several different formulations of multivariate time series regression models. The multiple regression is one of the most commonly used statistical models, so we will start with its multivariate representation in the next section. Other extensions and representations will be introduced in Sections 3.3 and 3.4. They include the representation adapted from the vector autoregressive models, which will be referred to as vector time series regression models. The VARX model is another extension. We will discuss the similarities and differences among these extensions and presentations.

3.2 Multivariate multiple time series regression models

3.2.1 The classical multiple regression model

In a multiple regression model, a response variable Y is related to k predictor variables, X₁, X₂, …, X_k, as follows,

(3.1)

where ξ is assumed to be uncorrelated white noise, often as i.i.d. ...