Cyclical common factors in cointegrated systems

When working with vectors of time series which fluctuate regularly we may possibly want to consider the presence of common factors characterized by cyclical or seasonal behavior as well as trend. For example, Deaton89 provides a hint of a theoretical model where cointegration at the annual frequency may exist between consumption and income in addition to the usual secular cointegration. It is well known that a non-cyclical system cointegrated at frequency zero has a common trend (CT) representation Stock-Watson: 88. In this paper we show that a time series vector that is cointegrated at one or several frequencies simultaneously (e.g. seasonal data) has a common factors (CF) representation which belongs to a class of common factor models that encompasses many cointegrating situations found in the literature. We study these issues and extend the method proposed by Gonzalo-Granger: 95 to the estimation and testing of common factors which may combine trend as well as cyclical or seasonal characteristics. Two illustrative applications are also provided. JEL Classification: C10, C32, C50 Javier Fernández-Macho: Financial support from research group grant 9/UPV00038.321-13503/2001 of UPV/EHU is gratefully acknowledged by both authors and from research project BEC2003-02028 of Ministerio de Ciencia y Tecnología by the first author. We are also indebted to two anonymous referees for their helpful comments.