文章基本信息

标题：Wavelet-Based Test for Time Series Non-Stationary
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作者：Milan Bašta
期刊名称：Statistika : Statistics and Economy Journal
印刷版ISSN：0322-788X
电子版ISSN：1804-8765
出版年度：2015
卷号：4
出版社：Czech Statistical Office
摘要：In the present paper, we propose a wavelet-based hypothesis test for second-order stationarity in a Gaussian time series without any deterministic components or seasonality. The null hypothesis is that of a second-order stationary process, the alternative hypothesis being that of a non-stationary process with a time-varying autocovariance function (excluding processes with unit roots). The test is based on the smoothing of the series of squared maximal overlap discrete wavelet transform coefficients employing modern techniques, such as robust filtering and cross-validation. We propose several test statistics and use bootstrap to obtain their distributions under the null hypothesis. We examine the test in settings that may mimic the properties of economic time series, showing that it enjoys reasonable size and power characteristics. The test is also applied to a data set of the U.S. gross domestic product to demonstrate its practical usefulness in an economic time series analysis
关键词：Wavelets; time series; non-stationarity; bootstrap; hypothesis test; gross domestic product