Statistical Inference on Multivariate Nonlinear Time Series Models : Simulation Based Approach

研究了可能具有非线性特征的时间序列的线性模型和非线性模型的联合预测。预测结果采用常系数回归法和时变法进行组合。时变方法允许局部（非线性）线性模型。这些方法应用于两类学科的数据：来自自然科学的加拿大猞猁和太阳黑子系列，以及来自经济学的Nelson-Plosser的美国系列。结果表明，组合预测效果较好，特别是时变系数的组合预测效果较好。这一结果适用于太阳黑子和加拿大猞猁数量序列的样本外表现，但不适用于经济时间序列。此外，本项目还考虑了一个测试连续时间非线性商业周期模型的框架，该框架通过“局部线性化（L.L.）”方法的时间离散化使用离散观测。我们用贝叶斯推理的方法对模型作为经济周期模型有效的条件进行了推导，这些条件用一些参数函数的不等式的形式表示。针对该问题提出了一种计算效率高的蒙特卡罗积分算法，并应用于美国和日本的数据。最后，为了分析多变量市场份额时间序列，我利用贝叶斯VAR模型提出了一个具有“逻辑一致性”的动态市场份额模型。提出的方法不仅可以预测自身的市场份额值，还可以预测不同品牌或公司之间的各种动态市场份额关系。

Combined forecasts from a linear and a nonlinear model are investigated for time series with possibly nonlinear characteristics. The forecasts are combined by a constant coefficient regression method as well as a time varying method. The time varying method allows for a locally (non)linear model. The methods are applied to data from two kinds of disciplines : the Canadian lynx and sunspot series from the natural sciences, and Nelson-Plosser's U.S. series from economics. It is shown that the combined forecasts perform well, especially with time varying coefficients. This result holds for out of sample performance for the sunspot and Canadian lynx number series, but it does not uniformly hold for economic time series.Further this project considered a framework of testing continuous time nonlinear business cycle models by using discrete observations through time discretization in terms of "Local Linearization(L.L.)" method. We employ a Bayesian inference on the conditions for the models to be valid as business cycle models, which are represented in the form of inequality of some function of parameters. A computationally efficient algorithm of Monte Carlo integration for that problem is proposed and applied to data of the U.S. and Japan.Finally, for analyzing multivariate market share time series, I proposed a dynamic market share model with "logical consistency" by using Bayesian VAR model. The proposed method makes it possible to forecast not only the values of market share by themselves, but also various dynamic market share relations across different brands or companies.