A Condition for Independence of Permanent and Transitory Components of a Series

Abstract

Abstract This article derives a necessary condition for the independence of permanent and transitory components of a series when the permanent component is any weighted average of past, present and future values of the observed series and the transitory component is the difference between the contemporaneous observed and permanent values of the series. This restrictive necessary condition is derived assuming a most elementary stochastic specification of the observed series. A specific example of the restrictiveness of this condition is afforded if the permanent component of a series is generated by the Koyck or exponentially-weighted expectations model. For this leading example it is possible to derive the theoretical correlation between the permanent and transitory components of the series as a positive valued function of the coefficient of expectations adjustment. Finally, we discuss the importance of these results to Friedman's [3] permanent income theory and suggest a modification of that theory.