Non-regular Time Series Analysis and Econometric Methods

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The main purpose of this project was to re-examine the existing statistical and econometric methods commonly used in analyzing economic time series data and develop some new time series methods. The other purpose of the project was to apply the methods we developed in this project to the economic time series data and financial time series data.There are many empirical evidences on the non-linearity and non-stationarity in economic phenomena. One important aspect of non-linearity in many economic time series and financial time series is the asymmetrical movements of time series in the up-ward phase and the down-word phase. Since it is not possible to describe this aspect by the stationary linear autoregressive moving-average (ARMA) model or the linear autoregressive integrated moving-average (ARIMA) model. N.Kunitomo has proposed the simultaneous switching autoregressive (SSAR) model with the collaboration of S.Sato (Institute of Statistical Mathematics) to describe the asymmetric movem … More ents in two different phases. Kunitomo=Sato (1994), and Sato=Kunitomo (1994) have investigated the various propeties of the stationary SSAR model and applied it to the analysis of some data in agricultural market. The SSAR model is closely related to some disequibrium models in econometrics. Then Kunitomo=Sato (1995) have extended the SSAR model and proposed the non-stationary SSAR (SSIAR) model. They have also applied it to the analysis of financial time series including Nikkei 225 spot and futures indeces.There are some empirical evidnece on the long-memory property in economic time series. One important aspect of the long-memory property can be characterized by the unboundedness of the spectal density of the stationary time series. Yajima (1995) have investigated this possibility and its theoretical outcomes.Also there are many empirical evidences on the non-stationarities in economic time series. One important aspect to non-stationarity in economic time series and financial time series is whether the linear integrated processes such as the autoregressive integrated moving average (ARIMA) model is appropriate or not in data analysis. This problem has been called the unit root testing problem. An important alternative possibility is the existence of structural changes in economic time series. Kunitomo (1995) and Kunitomo=Sato (1995) have investigated this possibility by allowing multiple change points and the number of change points could be unknown (but less than a pre-specified number.) Yajima=Nishino (1995) have investigated the unit root testing problem when some data are missing in economic time series.In conclusion, we have acomplished the most important objectives of this project. Two members participated in this project has written a large number of academic papers and also stimulated a large number of researchers in the related fields. We thank The Ministry of Education, Science and Culture for giving the generous support to our ambitious project. Less