Does the absence of cointegration explain the typical findings in long horizon regressions

Abstract

One of the stylized facts in financial and international economics is that of increasing predictabilityofvariables such as exchange rates and stock returns at longer horizons. This fact is based upon applications of long horizon regressions, from which the typical findings are that the point estimates of the regression parameter, the associated t-statistic, and the regression R² all tend to increase as the horizon increases. Such long horizon regression analyses implicitly assume the existence of cointegration between the variables involved. In this paper, we investigate the consequences of dropping this assumption. In particular, we look upon the long horizon regression as a conditional error-correction model and interpret the test for long horizon predictabilityas a single equation test for cointegration. We derive the asymptotic distributions of the estimator of the regression parameter and its t-statistic for arbitrary horizons, under the null hypothesis of no cointegration. It i...