Stock price volatility: tests for linear and non-linear cointegration in the present value model of stock prices

Abstract

Since the publication of Shiller's (1981a) work, variance bounds tests have been the focus of controversy in the literature. Recently a considerable amount of dissatisfaction with non-model-based volatility tests has been expressed. This study aims to offer an alternative approach based on a cointegrating regression model for the present value (PV) relation. The novelty of this study lies in its distinction between linear and nonlinear cointegration. It is demonstrated that Campbell and Shiller's linear cointegration between stock prices and dividends (Campbell, J. Y. and Shiller, R. J. 1987. Cointegration and tests of present value models, Journal of Political Economy, 95, 1062-1088) is not appropriate for investigating stock price volatility and a non-linear representation of cointegration is developed. The two types of cointegration are tested for the US stock market using monthly data from 1959.1 to 1992.6. Little evidence is found for linear cointegration, but the evidence of non-linear cointegration...