Validating Stationarity Assumptions in Time Series Analysis by Rolling Local Periodograms

Paparoditis, Efstathios

doi:10.1198/jasa.2010.tm08243

Cited by 47 publications

(76 citation statements)

References 15 publications

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“…Sakiyama and Taniguchi (2003) considered the problem of testing stationarity versus local stationarity in a parametric locally stationary model, while Lee et al (2003) investigated the constancy over time of a finite number of autocovariances. von Sachs and Neumann (2000) proposed a multiple testing procedure based on empirical wavelet coefficients estimated using localized versions of the periodogram, while Paparoditis (2010) used L 2 -distances between the local sample spectral density and an overall spectral density estimator [see also Paparoditis (2009)]. A common feature in many of these methods is the fact that the statistical inference depends on the choice of a regularization parameter.…”

Section: Introductionmentioning

confidence: 99%

“…A common feature in many of these methods is the fact that the statistical inference depends on the choice of a regularization parameter. For example, Paparoditis (2009) and Paparoditis (2010) compare nonparametric estimators of the spectral density of the stationary and locally stationary process, and as a consequence, the resulting statistical analysis depends sensitively on the choice of a smoothing parameter which is required for the density estimation. An alternative approach in this context is the application of the empirical spectral measure for inference in locally stationary time series [see Dahlhaus and Polonik (2009)].…”

Section: Introductionmentioning

confidence: 99%

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A Measure of Stationarity in Locally Stationary Processes With Applications to Testing

Dette

Preuß

Vetter

2011

Journal of the American Statistical Association

131

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July 28, 2010 AbstractIn this paper we investigate the problem of measuring deviations from stationarity in locally stationary time series. Our approach is based on a direct estimate of the L 2 -distance between the spectral density of the locally stationary process and its best approximation by a spectral density of a stationary process. An explicit expression of the minimal distance is derived, which depends only on integrals of the spectral density of the stationary process and its square. These integrals can be estimated directly without estimating the spectral density, and as a consequence, the estimation of the measure of stationarity does not require the specification of smoothing parameters. We show weak convergence of an appropriately standardized version of the statistic to a standard normal distribution. The results are used to construct confidence intervals for the measure of stationarity and to develop a new test for the hypothesis of stationarity which does not require regularization. Finally, we investigate the finite sample properties of the resulting confidence intervals and tests by means of a small simulation study and illustrate the methodology in three data examples.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Measure of Stationarity in Locally Stationary Processes With Applications to Testing

Dette

Preuß

Vetter

2011

Journal of the American Statistical Association

131

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“…Theorem 4 and the arguments in Paparoditis (2010) indicate that this procedure yields an asymptotic level α-test. To prove this, we follow Bickel and Freedman (1981) by considering the Mallows metric d 2 (F, G) = inf √ E(X − Y ) 2 between two distributions F and G, where the infimum is taken over all pairs (X, Y ) of random variables with marginal distributions F and G. Theorem 4 then yields the following.…”

Section: The Estimate In (D) Also Holds If the Null Hypothesis (37) mentioning

confidence: 99%

“…These kinds of alternatives were investigated by several authors in the context of locally stationary shortmemory processes (see Paparoditis (2010) and Dahlhaus (1997)). The rejection frequencies for the bootstrap test better for the process (5.5).…”

Section: Size and Power Of The Testmentioning

confidence: 99%

“…Recently, Nason (2013) used the same principle and examined the constancy of a wavelet spectrum by examining its Haar wavelet coefficients over a finite set of wavelet scales. Paparoditis (2009Paparoditis ( , 2010 suggested an L 2 -distance between the estimated spectral densities under the assumptions of stationarity and of local stationarity. Many authors have used the localized periodogram to construct a test for stationarity.…”

Section: Introductionmentioning

confidence: 99%

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Measuring stationarity in long-memory processes

Sen¹,

Preuß²,

Dette³

2017

STAT SINICA

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In this paper we consider the problem of measuring stationarity in locally stationary long-memory processes. We introduce an L2-distance between the spectral density of the locally stationary process and its best approximation under the assumption of stationarity. The distance is estimated by a numerical approximation of the integrated spectral periodogram and asymptotic normality of the resulting estimate is established. The results can be used to construct a simple test for the hypothesis of stationarity in locally stationary long-range dependent processes. We also propose a bootstrap procedure to improve the approximation of the nominal level and prove its consistency. Throughout the paper, we work with Riemann sums of a squared periodogram instead of integrals (as it is usually done in the literature) and as a by-product of independent interest it is demonstrated that the two approaches behave differently in the limit.

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Measuring the degree of non‐stationarity of a time series

Das

Nason

2016

Stat

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In time series analysis, there is an extensive literature on hypothesis tests that attempt to distinguish a stationary time series from a non‐stationary one. However, the binary distinction provided by a hypothesis test can be somewhat blunt when trying to determine the degree of non‐stationarity of a time series. This article creates an index that estimates a degree of non‐stationarity. This index might be used, for example, to classify or discriminate between series. Our index is based on measuring the roughness of a statistic estimated from the time series, which is calculated from the roughness penalty associated with a spline smoothing/penalized least‐squares method. We further use a resampling technique to obtain a likely range of index values obtained from a single realization of a time series. We apply our method to ascertain and compare the non‐stationarity index of the well‐known earthquake and explosion data. © 2016 The Authors. Stat Published by John Wiley & Sons Ltd

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Validating Stationarity Assumptions in Time Series Analysis by Rolling Local Periodograms

Cited by 47 publications

References 15 publications

A Measure of Stationarity in Locally Stationary Processes With Applications to Testing

A Measure of Stationarity in Locally Stationary Processes With Applications to Testing

Measuring stationarity in long-memory processes

Measuring the degree of non‐stationarity of a time series

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