White noise testing using wavelets. Issue 1 (4th December 2014)

• Record Type: Journal Article
• Authors: Nason, Guy P.; Savchev, Delyan
• Is Part Of: Stat. Volume 3:Issue 1(2014)
• Page Start: 351
• Page End: 362
• Publication Date: 2014-12-04
• Subjects: white noise test -- wavelet -- periodogram; Statistics -- Periodicals; 519.2
• DOI: 10.1002/sta4.69
• Languages: English
• ISSNs: 2049-1573

Abstract

Abstract : 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. © 2014 The Authors. Stat published by John Wiley & Sons Ltd.