Wavelets, Generalized Spectrum, and Nonparametric Analysis and Applications in Time Series Econometrics

小波、广义谱、非参数分析及其在时间序列计量经济学中的应用

• 批准号: 0111769
• 负责人: Yongmiao Hong
• 金额: --
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-15 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0111769&HistoricalAwards=false
• 关键词: Wavelets; Generalized; Spectrum; Nonparametric; Analysis

This project consists of three areas of research in econometrics: wavelet analysis in time series/dynamic panels; evaluation of out-of-sample forecasts for densities and confidence inter-vals; and asymptotic distribution theory for nonparametric entropy measures of serial dependence. Wavelet analysis provides natural tools for estimating the spectrum of an economic time series, which typically has peaks/spikes, due to strong autocorrelation, seasonality and business cycles. One example is heteroskedasticity and autocorrelation con-sistent (HAC) covariance estimation. The popular Andrews-Newey kernel methods tend to underestimate the peak (and so the HAC), leading to overrejection in testing, and too narrow confidence interval estimates. This project develops a class of wavelet-based HAC estimators. Some simulation studies show that for the size of tests, the wavelet estimators outperform their kernel counterparts, particularly when serial correlation is strong. Two substantive extensions are pursued. The first is to refine the wavelet HAC estimators via a nonparametric frequency-domain prewhitening pro-cedure. This provides a faster convergent and more stable alternative than the commonly used parametric vector autoregression (VAR) prewhitening. The second extension is wavelet HAC estimation for panel models. The cur-rent practice for kernel HAC estimation in panels uses a bandwidth depending only on the number of time periods. This project finds that for both kernels and wavelets, the optimal smoothing parameters in panels depend on both the numbers of time periods and individuals. Wavelets are also used to distinguish a trend-stationary time series from a unit root process and to test serial correlation of unknown form in panel models.Omnibus procedures for evaluating out-of-sample density and intervals forecasts are developed using a generalized spectral ap-proach. These procedures are supplemented with a class of separate inference procedures that can reveal information on sources of suboptimal density- and intervals forecasts. Appli-cations to stock markets and foreign exchange markets evaluate a variety of popular density forecast models.For a class of kernel-based smoothed nonparametric entropy measures of serial dependence, this project develops an asymptotic distribution theory and shows how it can be used to derive the limit distributions for the existing entropy measures in the literature. The project develops tests that are either not available in the literature or are asymptotically more powerful than the existing procedures. Entropy measures can be used to test the random walk hypothesis, evaluate density- forecast models, identify significant lags of a time series and check the adequacy of dynamic likelihood models.

该项目包括计量经济学的三个研究领域：时间序列/动态面板中的小波分析；密度和置信度区间的样本外预测的评估；以及序列相关性非参数熵度量的渐近分布理论。小波分析为估计经济时间序列的频谱提供了自然的工具，由于强烈的自相关性、季节性和商业周期，经济时间序列通常具有峰值/尖峰。异方差和自相关相容(HAC)协方差估计就是一个例子。流行的Andrews-Newey核方法倾向于低估峰值(以及HAC)，导致测试中的过度拒绝，以及太窄的可信区间估计。该项目开发了一类基于小波的HAC估计器。一些模拟研究表明，对于测试的规模，小波估计器的性能优于核估计器，特别是在序列相关性较强的情况下。正在寻求两次实质性的延期。第一种是通过非参数频域预白化过程来改进小波HAC估值器。这提供了比常用的参数向量自回归(VAR)预白化更快的收敛和更稳定的替代方案。第二个扩展是面板模型的小波HAC估计。面板中内核HAC估计的当前做法使用的带宽仅取决于时间段的数量。这个项目发现，对于核函数和小波，面板中的最优平滑参数既取决于时间段的数量，也取决于个体的数量。小波还被用来区分趋势平稳时间序列和单位根过程，并在面板模型中检验未知形式的序列相关性。利用广义谱方法开发了估计样本外密度和区间预测的综合程序。这些程序辅以一类独立的推理程序，可以揭示次优密度和区间预测的来源信息。将密度预测模型应用于股票市场和外汇市场，对一类具有序列相关性的基于核的光滑非参数熵度量，发展了一种渐近分布理论，并证明了它可以用来推导文献中已有的熵度量的极限分布。该项目开发的测试要么在文献中不可用，要么逐渐比现有程序更强大。熵度量可用于检验随机游走假设、评估密度预测模型、识别时间序列的显著滞后以及检查动态似然模型的充分性。