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

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；密度和置信区间的样本外预测的评价序列相关的非参数熵测度的渐近分布理论。小波分析为估计经济时间序列的频谱提供了天然的工具，由于强自相关性、季节性和商业周期，经济时间序列通常具有峰值/峰值。一个例子是异方差和自相关一致（HAC）协方差估计。流行的Andrews-Newey内核方法倾向于低估峰值（以及HAC），从而导致测试中的过度拒绝和过于狭窄的置信区间估计。本课题开发了一类基于小波的HAC估计器。一些仿真研究表明，对于测试的大小，小波估计器优于核估计器，特别是在序列相关性强的情况下。谋求两项实质性延长。首先是通过非参数频域预白化过程来改进小波HAC估计。这提供了一种比常用的参数向量自回归（VAR）预白化更快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。当前在面板中进行内核HAC估计的实践使用的带宽仅取决于时间段的数量。该项目发现，对于核函数和小波，面板的最佳平滑参数取决于时间段和个体的数量。小波还用于区分平稳趋势时间序列和单位根过程，并用于检验面板模型中未知形式的序列相关性。评估样本外密度和区间预测的综合程序是使用广义谱方法开发的。这些过程补充了一类单独的推理过程，这些推理过程可以揭示关于次优密度和间隔预测来源的信息。应用于股票市场和外汇市场评估各种流行的密度预测模型。对于一类基于核的序列依赖的光滑非参数熵测度，本项目发展了一个渐近分布理论，并展示了如何使用它来推导文献中现有熵测度的极限分布。该项目开发的测试要么在文献中不可用，要么比现有过程渐近地更强大。熵测度可用于检验随机漫步假设，评估密度预测模型，识别时间序列的显著滞后，并检查动态似然模型的充分性。

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.