ARMA AND ARIMA APPROACHES TO THE UNIT ROOT ANALYSIS OF MACRO ECONOMIC VARIABLES

抄録

The extended Nelson-Plosser data on the historical US macro-economic time series is re-analyzed from the view of the Dickey-Fuller type auto-regressive (AR) unit root test as well as from the view of the recently developed moving average (MA) unit root test (Hatanaka and Koto, 1995). The analysis included all MA errors but not breaks in the deterministic trend. An example of the test proposed by Hatanaka and Koto is illustrated when a time series is doubted as to whether it is a stationary ARMA about trend or a non-stationary ARIMA about drift. Search for the best ARMA regressions always includes an MA error term since long lags in the AR process often cause over-differencing phenomena. The adjusted likelihood ratio test is used for arriving at the best ARMA regression. Search for the best ARIMA regressions is carried out in a similar way as that applied for selecting the best ARMA regression. The MA unit root test is calculated for the best ARIMA regression. The AR and MA unit root tests associated with the best ARMA and the best ARIMA regressions, respectively, are compared with each other in order to classify the series into ARMA or ARIMA process as done previously by Hatanaka and Koto. Various lag lengths are examined and overall judgments are drawn.