Analysis of Financial Data

Chapter 11. Regression with time series variables with several equations

Chapters 8–10 developed several different regression models for time series variables. For many cases, knowledge of these models and the relevant techniques (e.g. cointegration tests) is enough to allow you to write a report and gain a good basic understanding of the properties of the data. However, in some cases, a knowledge of slightly more sophisticated methods is necessary. Fortunately, many such cases can be shown to be simple extensions of the methods learned in earlier chapters. In this chapter and the next we discuss two important such extensions. In the present chapter, we discuss methods which involve more than one equation. In the next, we discuss financial volatility. To motivate why multiple equation methods are important, we begin by discussing Granger causality before discussing the most popular class of multiple-equation models: so-called Vector Autoregressive (VAR)^[73] models. VARs can be used to investigate Granger causality, but are also useful for many other things in finance. Using financial examples, we will show their importance. Furthermore, an extension of a VAR related to the concepts of cointegration and error correction is discussed in this chapter. This is called the Vector Error Correction Model (VECM) and it allows us to introduce another popular test for cointegration called the Johansen test. In Appendix 11.2, we informally introduce the concept of a variance decomposition