Statistical modeling of economic time series based on the tests of multivariate Gaussianity and linearity

基于高斯随机变量经Hermitian多项式变换后的正交性特征，本文提出了一种多元平稳时间序列的高斯性检验方法，其中Terui和Imano（2003）提出的多元高斯性检验，本文在多元高斯性检验和线性检验的基础上，对经济时间序列的统计建模进行了如下研究：1.提高了统计模型的收敛速度，2.将Terui和货车Dijk（2002）提出的线性和非线性时间序列的组合预测方法推广到多元时间序列; 3.作为非高斯时间序列的统计建模，研究了计数型数据的时间序列模型，如多项式和毒药变量。研究了基于状态空间表示的动态贝叶斯线性建模及其MCMC算法。我表明，这种模型可以用于销售预测的产品销售数量，其中市场的扩张和收缩可以纳入模型。4.我给了一个动态预测模型，适应不对称的市场反应的营销组合可变价格促销的阈值模型。作为一个阈值变量，以产生不同的市场反应的机制，我们使用对应的价格阈值的概念，适用于一个代表性的消费者在商店。贝叶斯方法被用于统计建模，因为它提供了超过估计和预测的优势。该模型包含了价格变量的滞后效应。因此，无数的定价策略可以在时间范围内实施。它们的有效性可以使用预测密度来评估。我们打算提高传统的线性时间序列模型的预测性能。

Based on a characterization of orthogonality of Gaussian random variates after Hermitian polynomials transformation, we develop a Gaussianity test for multivariate stationary time series, where amultivariate Gaussianity test proposed by Terui and Imano(2003), I conducted the research on the statistical modeling of economic time series based on the tests of multivariate Gaussianity and linearity as follows.1.The improvement of speed of convergence of test statistics for multivariate Gaussinaity was conducted by using Bootstrap.2.I conducted the research that generalizes the combined forecasts between linear nad some nonlinear time series forecasts by Terui and van Dijk(2002) for univariate time series to multivariate series.3.As a statistical modeling of non-Gaussian time series, I did the research of time series models for count data, such as multinomial and poison variables. The dynamic Bayesian linear modeling by using state space representation and their MCMC algorithm was investigated. I showed that this modeling could be useful for sale forecasting of number of sales of product, where the market expansion and shrink can be incorporated in the model.4.I gave a dynamic forecasting model that accommodates asymmetric market responses to marketing mix variable - price promotion - by threshold models. As a threshold variable to generate a mechanism for different market responses, we use the counterpart to the concept of a price threshold applied to a representative consumer in a store. A Bayesian approach is taken for statistical modeling because of advantages that it offers over estimation and forecasting. The proposed model incorporates the lagged effects of a price variable. Thereby, myriad pricing strategies can be implemented in the time horizon. Their effectiveness can be evaluated using the predictive density. We intend to improve the forecasting performance over conventional linear time series models.