Conditional Heteroscedasticity and Unit Root Tests

Abstract

The two types of model introduced in this chapter are linked by the theme of (conditional) heteroscedasticity. The first model relates to the development of AR models to allow for random rather than fixed coefficients, where the particular focus is on a stochastic unit root (StUR) in contrast to the deterministic unit root of the conventional approach. A number of economic models can be viewed as generating a StUR; for example, a model of efficient markets can generate a root that is stochastic and differs from a unit root by the expected return on a financial asset (see LeRoy, 1982, and Leybourne, McCabe and Mills, 1996); another example is based on the permanent income hypothesis, which leads to an equation for consumption with a stochastic root that differs from unity by the ratio of the difference between the rate of inter-temporal time preference and the real rate of interest to the rate of interest (see Granger and Swanson, 1997).