非定常ベクトル時系列分析

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We firstly specify the uni-variate ARMA models of the money, income, GNP deflator, and the rate of interest using the Dickey and Fuller (DF) or the augmented DF (ADF) tests. Two diagnostic tests are applied to each selected ARMA regression. One is the residual DF test, and the other is the MA unit root test of residuals. After the ARMA model selection, the VAR regression is estimated with co-integrated relation using Johansen's maximum likelihood method. In this estimation, the lag length of each variable is taken to be different. It is found out that the income is causing money but not the opposite. Further analyses of the causality are performed using various lag lengths in VAR but keeping the same lag length for all variables. The income to money causality is found again.The causality is examined for the shorter sample periods which are used by Oritani (1979). There, the money is found to be non-stationary but the income is stationary. The Granger test is modified to the VAR which includes both stationary and non-stationary variables. The Granger test resulted in the income to money causality, not in the money to income causality. Comments follow on the filter used by Sims (1972).