Seasonal Cointegration Approach on Expenditure Based Gross Domestic Product and Its Some Sub-Components for Turkey

In this study, it has been aimed to investigate the existence of co-integration relationship between quarterly gross domestic product (GDP), final consumption expenditures of resident households (CONS), exports of goods and services (EXP), government final consumption expenditures (GOV) and private sector machinery-equipment (PRIEQ) series for the period 1998Q1-2014Q4 for Turkey. Since, Engle and Granger (1987) cointegration test does not take unit roots at seasonal frequencies into account; seasonal cointegration approach proposed by Engle, Granger, Hylleberg and Lee (EGHL) (1993) has been conducted in order to be able to detect the long-run equilibrium relationship among variables which are integrated at the same seasonal frequency. With the aim of determining the stationarity order of series, HEGY seasonal unit root test has been applied. Consequently, there has been found a cointegrating relationship only between GDP and GOV series at quarterly frequencies for only the auxiliary regression including constant term and seasonal dummies.

FULLY MODIFIED ESTIMATION OF SEASONALLY COINTEGRATED PROCESSES

We extend the framework of the fully modified, ordinary least squares (OLS) estimator introduced by Phillips and Hansen (1990) to the case of seasonally cointegrated processes at a given frequency. First we extend a weak convergence result of sample covariance matrices (Phillips, 1988) to the case of seasonal unit roots. Using a complex number framework, we then show that we can take into account the constraints that exist in a situation of seasonal cointegration as illustrated in Gregoir (1999a) and derive estimates of the cointegration vectors that allow for asymptotic normal inference. This allows us to propose a test whose null hypothesis is the existence of seasonal cointegration. A Monte Carlo exercise investigates the finite sample properties of this test procedure. The paper closes with the analysis of situations in which there exist more than one frequency at which seasonal cointegration can be observed.

Seasonal co-integration: An extention of the Johansen and Schaumburg approach with an exclusion test

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.