Market Risk Analysis Volume II: Practical Financial Econometrics

II.5

Time Series Models and Cointegration

II.5.1 INTRODUCTION

This chapter provides a pedagogical introduction to discrete time series models of stationary and integrated processes. A particular example of an integrated process is a random walk. Given enough time, a random walk process could be anywhere, because it has infinite variance, and the best prediction of tomorrow's price is the price today. Hence, there is little point in building a forecasting model of a single random walk. But a stationary process is predictable – not perfectly, of course, but there is some degree of predictability based on its mean-reverting behaviour. Individual asset prices are usually integrated processes, but sometimes the spread between two asset prices can be stationary and in this case we say the prices are cointegrated. Cointegrated prices are ‘tied together’ in the long run. Hence, when two asset prices – or interest rates – are cointegrated, we may not know where each price or rate will be in 10 years' time but we do know that wherever one price or rate is, the other one will be along there with it.

Cointegration is a measure of long term dependency between asset prices. This sets it apart from correlation, whose severe limitations as a dependency measure have been discussed in Chapter II.3, and copulas, which are typically used to construct unconditional joint distributions of asset returns that reflect almost any type of dependence. Although copulas have recently been combined with conditional ...