Abstract
In this paper, the Johansen and Schaumburg method for seasonal cointegration has been tried to be applied for testing an a priori hypothesized cointegrating money demand variable space. We aim to provide a comprehensive discussion of the significance of the variables in the long-run context as stationary relationships for both zero and bi-annual frequencies. For this purpose, several restrictions have been used to impose for identification purposes of the relevant vectors. We also touch upon the possibility that most time series data have been subject to the stochastic seasonality as opposed to the general acceptance in empirical papers. Our results employing data from the Turkish economy show that it is not possible to estimate only a single theory-accepted money demand relationship in the long-run variable space for both zero and bi-annual frequences, but we are able to identify different vectors somewhat consistent with theoretical arguments for the annual frequency.
Highlights
The analysis of unit roots and co-integration at zero frequency has recently been extended to the seasonal frequencies in the co-integration literature
Permitting seasonal frequencies in a co-integration analysis has been of a special importance especially when the researchers choose their main issue of interest as carrying out an analysis of the money demand relationship
We touch upon the possibility that most time series data have been subject to the stochastic seasonality, but this issue in general has been ignored for that the seasonality of co-integrating relationships tends to be modelled
Summary
The analysis of unit roots and co-integration at zero frequency has recently been extended to the seasonal frequencies in the co-integration literature. Permitting seasonal frequencies in a co-integration analysis has been of a special importance especially when the researchers choose their main issue of interest as carrying out an analysis of the money demand relationship On this subject, Lee (1992) tries to develop a seasonal cointegration approach using reduced rank regression (RR) procedure, the method suggested for this purpose has a limitation of applying only to synchronous co-integration at annual frequency. Johansen and Schaumburg (1999) succeed in developing a maximum likelihood inference for seasonal series and introduce a general asymptotic theory For this purpose, they consider a polynomial (non-synchronous) cointegration approach in an error-correction modelling (ECM) framework with complex valued coefficient matrices and apply to an iterative procedure for estimating co-integration relations at annual frequency.
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