Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence
为时间序列中基于核平滑的非参数熵测度建立了渐近分布理论，推导了Granger-Lin归一化熵的极限分布，并构造了新的序列依赖检验，适用于随机游走假设检验、密度预测评估等场景。
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. Copyright The Econometric Society 2005.