Statistical Theory for Long-memory Property of Economic Time Series and Structural Breaks

经济时间序列长记忆性和结构性断裂的统计理论

• 批准号: 13630027
• 负责人: TANAKA Katsuto
• 金额: $ 1.09万
• 依托单位: Hitotsubashi University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2002
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13630027/
• 关键词: deterministic trend; stochastic trend; long-memory; fractional ARIMA; maximum likelihood estimation; wavelet; simulation; 長記憶時系列; 構造変化; 共和文

The following are main results obtained in the present research project.1. Trend, which is the source of nonstationarity of economic time series, can be classified into two categories : one is deterministic trend, and the other stochastic trend. The difference between the two was made clear. The power of statistical tests for determining which trend the actual time series has is quite low. Thus the probability is rather high that we mistakenly conclude the nature of the trend.2. Stochastic trend may be modeled as fractional ARIMA. In this project, various statistical properties were explored in terms of asymptotic theory.3. A statistical test was developed if actual time series data is contaminated by noise. At first the test was devised in the time domain, but it was found that the test becomes eventually meaningless as the variation of the noise becomes larger. This is because the signal becomes negligible as the noise becomes larger so that the signal tends to be unidentifiable.4. Various estimation methods based on wavelets were devised for the long-memory signal plus noise models. The methods were compared with frequency domain methods. The estimation methods employed were OLS and ML methods. It was found that the frequency domain MLE behaves better for stationary cases, but the wavelet-based MLE behaves better for nonstationary case. Since most economic time series exhibits nonstaionarity, this is an advantage of wavelet methods.

以下是本研究项目取得的主要成果。趋势是经济时间序列非平稳性的根源，可以分为确定性趋势和随机性趋势两类。两者之间的区别是显而易见的。统计检验用于确定实际时间序列具有哪种趋势的能力相当低。因此，我们错误地断定趋势的性质的可能性相当高。随机趋势可以用分数ARIMA模型来描述。在本项目中，根据渐近理论探索了各种统计性质。如果实际的时间序列数据受到噪声的污染，则进行统计检验。最初的测试是在时间域设计的，但人们发现随着噪声的变化变得更大，测试最终变得没有意义。这是因为当噪声变大时，信号变得可以忽略不计，因此信号往往是无法识别的。针对长记忆信号加噪声模型，提出了各种基于小波的估计方法。并与频域方法进行了比较。所采用的估计方法是OLS和ML方法。结果表明，频域最大似然估计在平稳情况下表现得更好，而基于小波的最大似然估计在非平稳情况下表现得更好。由于大多数经济时间序列具有非平稳性，这是小波方法的优势所在。

项目成果

田中 勝人: "K-Asymptotics Associated with Deterministic Trends in the Integrated and Near-Integrated Processes"The Japanese Economic Review. Vol.52,No.1. 35-63 (2001)

Katsuto Tanaka：“K-渐近与集成和近集成过程中的确定性趋势相关”《日本经济评论》第 52 卷，第 35-63 期（2001 年）。

Tanaka, K.: "K-asymptotics associated with deterministic trends in the integrated and near-integrated processes"The Japan Economic Review. 52. 35-63 (2001)

Tanaka, K.：“K-渐近与一体化和近一体化过程中的确定性趋势相关”《日本经济评论》。

田中 勝人: "共和分分析"経済時系列の統計(岩波書店). (未定). (2002)

Katsuto Tanaka：“协整分析”经济时间序列统计（岩波书店）（待定）。

Tanaka, K.: "K-asymptotics associated with deterministic trends in the integrated and near-integrated processes"The Japanese Economic Review. 52. 35-63 (2001)

Tanaka, K.：“K-渐近与集成和近集成过程中的确定性趋势相关”《日本经济评论》。

Tanaka, K.: "A unified approach to the measurement error problem in time series models"Econometric Theory. 18. 278-296 (2002)

Tanaka, K.：“时间序列模型中测量误差问题的统一方法”计量经济学理论。