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

多元非线性时间序列模型的统计推断：基于仿真的方法

• 批准号: 10630020
• 负责人: TERUI Nobuhiko
• 金额: $ 1.09万
• 依托单位: TOHOKU UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10630020/
• 关键词: Combined forecast; Threshold Model; Exp AR Model; Time Varying Model; Predictive Density; 閾値自己回帰モデル; 結合予測量

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.

针对可能具有非线性特征的时间序列，研究了线性模型和非线性模型的组合预测问题。预测采用常系数回归法和时变法相结合。时变方法允许局部(非线性)线性模型。这些方法被应用于两种学科的数据：来自自然科学的加拿大山猫和太阳黑子系列，以及来自经济学的纳尔逊-普洛瑟的美国系列。结果表明，组合预测效果较好，特别是在系数随时间变化的情况下。这一结果对太阳黑子和加拿大山猫数序列的样本外表现是成立的，但对经济时间序列并不一致。此外，本项目考虑了一个框架，通过时间离散化利用离散观测来检验连续时间的非线性经济周期模型。方法。我们利用贝叶斯推理对模型作为经济周期模型有效的条件进行推断，这些条件以参数的某个函数的不等式的形式表示。最后，为了分析多元市场份额时间序列，利用贝叶斯VAR模型建立了一个具有“逻辑一致性”的动态市场份额模型。该方法不仅可以预测市场占有率的价值，还可以预测不同品牌或公司之间的各种动态市场占有率关系。

项目成果

Nobuhiko Terui and Herman van Pijk: "Composite Forecasts of Linear and Nonlinear Time Series Models"Working paper, Institute of Economic Research, Kyoto Univ. A-49. (1998)

Nobuhiko Terui 和 Herman van Pijk：“线性和非线性时间序列模型的复合预测”工作论文，京都大学经济研究所。

Nobuhiko Terui, Herman van Dijk: "Composite Forecasts of Linear and Nonlinear Time Sevice Models" Discussin Paper, Center for the Study of Complex Economic Systems, Institute of Economic Researchi, Kyoto University. A-49. 1-29 (1998)

Nobuhiko Terui、Herman van Dijk：“线性和非线性时间服务模型的综合预测”讨论论文，京都大学经济研究所复杂经济系统研究中心。

Nobuhiko Terui and Herman van Dijk: "Composite Forecasts of Linear and Nonlinear Time Series Models"Working Paper, Institute of Economic Research, Kyoto Univ.. A-49. (1998)

Nobuhiko Terui 和 Herman van Dijk：“线性和非线性时间序列模型的复合预测”工作论文，京都大学经济研究所。A-49。

Nobuhiko Terui and Herman van Dijk: "Composite Forecasts of Linear and Nonlinear Time Series Models"Working Paper, Institute of Economic Research Kyoto University. A-49. (1998)

Nobuhiko Terui 和 Herman van Dijk：“线性和非线性时间序列模型的复合预测”工作论文，京都大学经济研究所。

Nobuhiko Terui: "Forecasting Dynamic Market Share Relationships"Marketing Intelligence and Planning. 18. 67-77 (2000)

Nobuhiko Terui：“预测动态市场份额关系”营销情报和规划。