Co-trending

Abstract

Our basic research strategy is to model the relations among deterministic trends directly without using the parameters of stochastic parts of models. Direct modelling is divided into the parametric approach and the non-parametric approach. The parametric approach is based on a list of parametrically specified functions of time, which will be called trend functions, while the non-parametric approach does not use such functions. We begin with the non-parametric approach in Section 2.1, which will then be followed by the parametric approach in Section 2.2. Section 2.3 will present an example of trend functions that is hoped will be useful for empirical studies of the Japanese economy. Section 2.4 will compare our co-trending with the co-breaking in Hendry and Mizon (1998) and Clements and Hendry (1999). Section 2.5 will briefly survey the history of the direct modelling and the indirect modelling in the time series analyses. We had long seen the indirect modelling only, but Schmidt and Phillips (1992) have advocated the direct modelling.