White noise testing using wavelets
White noise testing using wavelets
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DOI：
10.1002/sta4.69
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发表时间：
2014-01-01
期刊：
影响因子：
1.7
通讯作者：
Savchev, Delyan
中科院分区：
文献类型：
--
作者：
Nason, Guy P.;Savchev, Delyan
检验时间序列是否与白色噪声一致是时间序列分析中的一项重要任务，也是通过残差诊断进行模型拟合和评判的重要任务。我们介绍了三种快速有效的白色噪声测试，通过周期图的小波系数评估光谱恒定性。Haar小波白色噪声测试在温和的条件下导出渐近周期图的Haar小波系数的精确分布。单系数白色噪声测试使用单个Haar小波系数，获得作为奇数索引自相关的线性组合的测试统计量。一般小波白色噪声测试使用紧支Daubechies小波，证明了它的系数是渐近正态的，并推导出其理论功率为任意的频谱。我们所有的测试都可以在R系统的免费hwwntest包中获得。我们提出了一项全面的模拟研究，显示了我们的新测试相对于可用软件中常见的替代方案的良好性能，并显示了应用于风电时间序列的示例。(C)2014作者出版社：John Wiley & Sons Ltd
Testing whether a time series is consistent with white noise is an important task within time series analysis and for model fitting and criticism via residual diagnostics. We introduce three fast and efficient white noise tests that assess spectral constancy via the wavelet coefficients of a periodogram. The Haar wavelet white noise test derives the exact distribution of the Haar wavelet coefficients of the asymptotic periodogram under mild conditions. The single-coefficient white noise test uses a single Haar wavelet coefficient obtaining a test statistic as a linear combination of odd-indexed autocorrelations. The general wavelet white noise test uses compactly supported Daubechies wavelets, shows that its coefficients are asymptotically normal and derives its theoretical power for an arbitrary spectrum. All our tests are available in the freely available hwwntest package for the R system. We present a comprehensive simulation study that shows the good performance of our new tests against alternatives commonly found in available software and show an example applied to a wind power time series. (C) 2014 The Authors. Stat published by John Wiley & Sons Ltd.