ON TESTING FOR SERIAL CORRELATION WITH A WAVELET-BASED SPECTRAL DENSITY ESTIMATOR IN MULTIVARIATE TIME SERIES
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基于小波谱密度估计的多元时间序列序列相关检验
- 研究问题
- 研究如何检验多元时间序列的序列相关，尤其关注强自相关或季节性导致谱密度出现峰值等不规则形状的情形。
- 方法与思路
- 作者比较小波谱密度估计与无序列相关原假设下的谱密度，构造单侧检验，并提出数据驱动的最细尺度选择方法。
- 材料陈述的贡献
- 摘要称，检验在原假设下渐近服从标准正态分布；模拟比较支持其在谱密度具有峰值或凸起时的功效表现。
- 阅读关注点
- 应核对谱密度差异的度量、最细尺度选择规则及渐近条件，并检查模拟中小波与核方法的尺寸和功效比较。
- 阅读边界
- 所给出版社摘要未列出依赖条件、尺度选择公式及模拟数值，因而不能据此认定小波检验在所有谱形状下都更优。
原文摘要
A new one-sided test for serial correlation in multivariate time series models is proposed. The test is based on a comparison between a multivariate spectral density estimator and the spectral density under the null hypothesis of no serial correlation. Duchesne and Roy (2004, Journal of Multivariate Analysis 89, 148–180) considered a multivariate kernel-based spectral density estimator. However, when the spectral density exhibits irregular features (because of strong autocorrelation or seasonality, among other factors), it is expected that a multivariate wavelet-based spectral density estimator will capture more effectively the local behavior of the spectral density. We consider a test based on a wavelet spectral density estimator, which represents a generalization of a test proposed by Lee and Hong (2001, Econometric Theory 17, 386–423). The asymptotic distribution of the new test is established under the null hypothesis, which is N(0,1). We propose and justify a suitable data-driven method to choose the smoothing parameter of the wavelet estimator (called the finest scale in that context). The new test should be powerful when the spectral density contains peaks or bumps. This is confirmed in a simulation study, where kernel-based and wavelet-based estimators are compared.The author thanks the co-editor Pentti Saikkonen and two referees for their constructive remarks and suggestions. Many thoughtful comments of the referees led to significant improvements of the paper. This work was supported by grants from the National Science and Engineering Research Council of Canada and the Fonds québécois de la recherche sur la nature et les technologies du Québec (Canada).