State -space vs. VAR representations of cointegration in international macroeconomic variables
The objective of this dissertation is to provide tools to analyze the long-run persistence of the economic time series data which have commonly been observed to be nonstationary. Based on the cointegration concept, the empirical distribution and the out-of-sample forecasting performance of Aoki's two-step procedure of nonstationary state space model are compared with those of Johansen and of Engle and Granger methods of ARMA model via Monte Carlo simulations.^ Aoki's state space method provides better estimates of cointegrating vectors for non-normally distributed errors or for the smaller number of observations, while Johansen's method performs better for normally distributed errors or for larger sample. And it has been advocated to use Aoki's method for the long-run forecasts.^ Using Aoki's procedure we find the real variables (GNP, investment, consumption, and government spending) of national income account and the monetary variables (price and money stock) in five advanced countries (Australia, Canada, Sweden, U.K., and U.S.) are cointegrated with one common trend. The results imply that there have been forces that keep the macroeconomic variables in different countries from drifting too far apart since the end of last century. Furthermore, mean square errors and nonparametric test of direction for the model from out-of-sample forecasts for 10 years confirm the model specification and the parameter estimation.^ We also showed that if the series are long-memory stationary with finite variance, the estimator based on the stationary stochastic process produces the most consistent and efficient estimates of cointegrating vectors through Monte Carlo simulations. Furthermore, Engle and Granger's two-step procedure is the best for short-run forecast while Aoki's nonstationary state space procedure is for long-run. ^
Hong, Eun Pyo, "State -space vs. VAR representations of cointegration in international macroeconomic variables" (1993). ETD Collection for Fordham University. AAI9416669.