Testing temporal constancy of the spectral structure of a time series

By Efstathios Paparoditis. 2009

62 citations recorded by the source corpus.

Statistical inference for stochastic processes with time-varying spectral characteristics has received considerable attention in recent decades. We develop a nonparametric test for stationarity against the alternative of a smoothly time-varying spectral structure. The test is based on a comparison between the sample spectral density calculated locally on a moving window of data and a global spectral density estimator based on the whole stretch of observations. Asymptotic properties of the nonparametric estimators involved and of the test statistic under the null hypothesis of stationarity are derived. Power properties under the alternative of a time-varying spectral structure are discussed and the behavior of the test for fixed alternatives belonging to the locally stationary processes class is investigated.

Subfields: Computer Networks and Communications, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3a6579f4f03aefa4e662e2918c5b4c8499f2b531

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In Computer Networks and Communications

In Finance

In Statistics and Probability

Citations in the corpus

A test for second order stationarity of a multivariate time series (2015, background): “However, as far as we are aware there does not exist any tests for second order stationarity of multivariate time series (Jentsch (2012) does propose a test for multivariate stationarity, but the test was designed to the detect the alternative of a periodic multivariate stationary time series).”
A Measure of Stationarity in Locally Stationary Processes With Applications to Testing (2011, methodology): “…and Neumann (2000) proposed a multiple testing procedure estimating empirical wavelet coefficients by localized versions of the periodogram, while Paparoditis (2010) used L2-distances between the local sample spectral density and an overall spectral density estimator (see also Paparoditis 2009).”
Testing for stationarity of functional time series in the frequency domain (2017, methodology): “Other contributions building on this work include von Sachs & Neumann (2000), who used local periodograms and wavelet analysis, and Paparoditis (2009), whose test is based on comparing a local estimate of the spectral density to a global estimate.”
Validating Stationarity Assumptions in Time Series Analysis by Rolling Local Periodograms (2010, unknown): “By lemma 3 of Papar- oditis (2000), it follows that N √ b ∑M r=1 ar(Qn, (ur) − μn) ⇒ N(0, τ 2 ∑M r=1 a2r ).”
Detecting gradual changes in locally stationary processes (2013, background): “Most of these tests for second-order stationarity are based on comparing a local spectral density with a global version; see Paparoditis [22, 23], Dette et al.”
Locally Stationary Processes (2011, methodology): “Paparoditis (2009) developed a nonparametric test for stationarity against the alternative of a smoothly time varying spectral structure based on a local spectral density estimate.”
Local inference for locally stationary time series based on the empirical spectral measure (2009, methodology): “We mention that Paparoditis (2006) has given a complete solution of this testing problem by using spectral density type statistics.”
An updated review of Goodness-of-Fit tests for regression models (2013, background): “The comparison of regression curves can be useful in other contexts such as time series (see Dette and Paparoditis 2009) or spatio-temporal models, allowing for a comparison of correlation structures from the spectral domain.”
A test for second‐order stationarity of a time series based on the discrete Fourier transform (2009, methodology): “In Section 5, we compare our test to the test for stationarity recently proposed in Paparoditis (2009).”