Learning outcomes

In this chapter, you will learn how to

• highlight the problems that may occur if non-stationary data are used in their levels forms:

• distinguish between types of non-stationarity;

• run unit root and stationarity tests;

• test for cointegration;

• specify error correction models;

• implement the Engle–Granger procedure;

• apply the Johansen technique; and

• forecast with cointegrated variables and error correction models.

Stationarity and unit root testing

Why are tests for non-stationarity necessary?

There are several reasons why the concept of non-stationarity is important and why it is essential that variables that are non-stationary be treated differently from those that are stationary. Two definitions of non-stationarity were presented at the start of chapter 8. For the purpose of the analysis in this chapter, a stationary series can be defined as one with a constant mean, constant variance and constant autocovariances for each given lag. The discussion in this chapter therefore relates to the concept of weak stationarity. An examination of whether a series can be viewed as stationary or not is essential for the following reasons.

• The stationarity or otherwise of a series can strongly influence its behaviour and properties. To offer one illustration, the word ‘shock’ is usually used to denote a change or an unexpected change in a variable, or perhaps simply the value of the error term during a particular time period. For a stationary series, ‘shocks’ to the system will gradually die away. That is, a shock during time t will have a smaller effect in time t + 1, a smaller effect still in time t + 2, and so on.