Asymptotic distribution theory for nonparametric entropy measures of serial dependence

• 成果类型: Article
• 署名作者: Hong, YM; White, H
• 署名单位: Cornell University; Cornell University; Tsinghua University; University of California System; University of California San Diego
• 刊物名称: ECONOMETRICA
• ISSN/ISSBN: 0012-9682
• DOI: 10.1111/j.1468-0262.2005.00597.x
• 发表日期: 2005
• 页码: 837-901
• 关键词: tests; INDEPENDENCE

摘要

Entropy is a classical statistical concept with appealing properties. Establishing asymptotic distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging. In this paper, we develop an asymptotic theory for a class of kernel-based smoothed nonparametric entropy measures of serial dependence in a time-series context. We use this theory to derive the limiting distribution of Granger and Lin's (1994) normalized entropy measure of serial dependence, which was previously not available in the literature. We also apply our theory to construct a new entropy-based test for serial dependence, providing an alternative to Robinson's (1991) approach. To obtain accurate inferences, we propose and justify a consistent smoothed bootstrap procedure. The naive bootstrap is not consistent for our test. Our test is useful in, for example, testing the random walk hypothesis, evaluating density forecasts, and identifying important lags of a time series. It is asymptotically locally more powerful than Robinson's (1991) test, as is confirmed in our simulation. An application to the daily S&P 500 stock price index illustrates our approach.