Statistical Theory and Application of Nonstationary and Noninvertible Time Series Model

目前的研究有三个主要结果。第一个是建设一个统一的方法与非平稳时间序列模型的统计渐近理论。对于非平稳时间序列模型，我们提出了一种精确计算随机变量二次型和双线性型之比统计量极限分布的一般方法。基于不变性原理的传统方法无法做到这一点。我们只需要依赖于模拟，而本方法克服了这种模糊性。其次，我们研究了不可逆移动平均模型的极大似然估计的渐近性质。与自回归模型相比，移动平均模型的分析难度更大。我们试图推导出最大似然估计量的极限分布，但在静脉。另一方面，我们提出了移动平均单位根的检验方法，得到了一些有趣的结果。第三，发展了协整的渐近理论。协整是非平稳时间序列分析领域的重要研究内容。我们导出了协整向量的最小二乘估计的渐近分布。直到最近，我才注意到协整与移动平均模型的不可逆性密切相关。我还意识到，协整可以用移动平均模型的可逆性来检验，这将是未来研究的一个主题。

There are three major results of the present research. The first is the construction of a unified approach to the asymptotic theory of statistics associated with nonstationary time series models. For nonstationary time series models we suggested a general approach to computing accurately the limiting distribution of the statistic of a ratio of quadratic and bilinear forms in random variables. The traditional approach based on invariance principles is unable to do this. One just has to rely on simulations, while the present approach approach overcame that ambiguity.Second we explored asymptotic properties of the maximum likelihood estimator for the noninvertible moving average model. In comparison with autoregressive models the analysis in much harder with moving average models. We attempted to derive the limiting distribution of the maximum likelihood estimator, but in vein. On the other hand we suggested testing for a moving average unit root, which contains some interesting results.Third an asymptotic theory of cointegration has been developed. Cointegration is now the most important topic in the area of nonstationary time series analysis. We derived the asymptotic distribution of the least squares estimator of the cointegrating vector. It is only recently that I noticed that cointegration is closely connected with noninvertibility of moving average models. I also realized that cointegration can be tested in terms of invertibility of the moving average model, which will be a topic for future research.