Non-regular Time Series Analysis and Econometric Methods

本项目的主要目的是重新审查分析经济时间序列数据常用的现有统计和计量经济学方法，并开发一些新的时间序列方法。本项目的另一个目的是将我们在本项目中开发的方法应用于经济时间序列数据和金融时间序列数据。经济现象中的非线性和非平稳性有许多经验证据。在许多经济时间序列和金融时间序列中，非线性的一个重要方面是时间序列在上升阶段和下降阶段的不对称运动。由于平稳线性自回归滑动平均（阿尔马）模型或线性自回归积分滑动平均（ARIMA）模型无法描述这方面的情况。N.Kunitomo与S.Sato（统计数学研究所）合作提出了同步开关自回归（SSAR）模型来描述非对称运动， ...更多信息 在两个不同的阶段。Kunitomo=Sato（1994）和Sato=Kunitomo（1994）研究了平稳SSAR模型的各种性质，并将其应用于农业市场的一些数据分析。SSAR模型与计量经济学中的一些非均衡模型密切相关。随后Kunitomo=Sato（1995）对SSAR模型进行了扩展，提出了非平稳SSAR（SSIAR）模型。并将其应用于日经225指数、期货指数和现货指数等金融时间序列的分析中，对经济时间序列的长记忆性进行了实证研究。长记忆特性的一个重要方面可以通过平稳时间序列的谱密度的无界性来表征。Yajima（1995）对这一可能性进行了研究，并取得了一些理论成果，同时也有许多实证证据表明经济时间序列具有非平稳性。经济时间序列和金融时间序列非平稳性的一个重要方面是自回归积分移动平均（ARIMA）模型等线性积分过程在数据分析中是否合适。这个问题被称为单位根测试问题。另一种重要的可能性是经济时间序列中存在结构性变化。Kunitomo（1995）和Kunitomo=Sato（1995）通过允许多个变化点和变化点的数量可以是未知的（但小于预先指定的数量）来研究这种可能性。Yajima=Nishino（1995）研究了经济时间序列中某些数据缺失情况下的单位根检验问题，结论是我们完成了这个项目的主要目标。两名成员参与了这个项目，撰写了大量的学术论文，也激发了一大批相关领域的研究者。我们感谢教育、科学和文化部对我们雄心勃勃的项目给予的慷慨支持。少

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