Integrated modified OLS and fixed-b inference for seasonally cointegrated processes

Abstract

Many economic time series exhibit persistent seasonal patterns. One approach to model this phenomenon is given by models including seasonal unit roots and, if several time series are considered jointly, seasonal cointegration. For quarterly time series, e.g., unit roots may be present at frequencies =2 and , in addition to the “standard unit root” at frequency zero. Gregoir (2010) has extended the fully modified OLS estimator of Phillips and Hansen (1990) from the cointegrating regression to the seasonally cointegrating regression case. In this paper, we have a similar agenda, in that we undertake the corresponding extension for the IM-OLS estimator of Vogelsang and Wagner (2014). The benefit of the seasonal IMOLS estimator, or SIM-OLS estimator, is that it forms the basis not only for asymptotic standard inference but also allows for fixed-b inference. The paper furthermore proposes a test for seasonal cointegration at all unit root frequencies. Note here that the cointegrating spaces in general differ across frequencies and have to be estimated separately for each frequency. The theoretical analysis is complemented by a simulation study.