Frequency Domain Tests of Semiparametric Hypotheses for Locally Stationary Processes

Σεργίδης, Μάριος; Paparoditis, Efstathios

doi:10.1111/j.1467-9469.2009.00652.x

Cited by 17 publications

(28 citation statements)

References 27 publications

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“…Moreover F n (φ) occurs with local polynomial fits (Kim, 2001;Jentsch, 2006) and several statistics suitable for goodness of fit testing (a goodness-of-fit test based on a different statistic can be found in Sergides and Paparoditis, 2007). These applications are quite involved.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Local inference for locally stationary time series based on the empirical spectral measure

Dahlhaus

2009

Journal of Econometrics

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Please cite this article as: Dahlhaus, R., Local inference for locally stationary time series based on the empirical spectral measure. Journal of Econometrics (2009Econometrics ( ), doi:10.1016Econometrics ( /j.jeconom.2009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. A C C E P T E D M A N U S C R I P T ACCEPTED MANUSCRIPT Local Inference for Locally Stationary Time SeriesBased on the Empirical Spectral MeasureRainer Dahlhaus, Universität HeidelbergOctober 24, 2008 AbstractThe time varying empirical spectral measure plays a major role in the treatment of inference problems for locally stationary processes. The properties of the empirical spectral measure and related statistics are studied -both when its index function is fixed or dependent on the sample size. In particular we prove a general central limit theorem. Several applications and examples are given including semiparametric Whittle estimation, local least squares estimation and spectral density estimation.

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Section: Accepted Manuscriptmentioning

confidence: 99%

Local inference for locally stationary time series based on the empirical spectral measure

Dahlhaus

2009

Journal of Econometrics

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“…In contrast to the "classical inference" mentioned in the previous paragraph, the problem of testing semiparametric hypotheses (such as time varying autoregressive structure or stationarity) for a time varying spectral density has found much less attention in the literature. Sergides and Paparoditis (2009) investigated semiparametric hypotheses and proposed a bootstrap test in this context. Several authors have pointed out the importance of validating stationarity in locally stationary processes, such that the statistician is able to decide at an early stage whether an observed time series can be considered as covariance stationary or not.…”

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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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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“…Recently, Sergides and Paparoditis () proposed to use the local periodogram for bootstrapping certain quantities such as ratio statistics at a given time point

1 ⩽ t_{0} ⩽ T

. To this end, they calculate the periodogram based on the time series of an appropriate environment of this point only.…”

Section: Moving Local Fourier Transformmentioning

confidence: 99%

“…For stationary time series, frequency domain bootstrap methods have proven quite useful in many situations; see Paparoditis (). Using the local Fourier transform (related to the local periodogram) for a local bootstrap works fine as long as it is only used for inference of the local structure such as the local autocorrelation (Sergides and Paparoditis, ). However, to obtain a global locally stationary bootstrap sample, the full dependency between local Fourier coefficients corresponding to different time points needed to be mimicked correctly by the bootstrap, which seems a very difficult task.…”

Section: Introductionmentioning

confidence: 99%

Moving Fourier Analysis for Locally Stationary Processes with the Bootstrap in View

Häfner

Kirch

2017

Journal Time Series Analysis

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We introduce a moving Fourier transformation for locally stationary time series, which captures the time‐varying spectral density in a similar manner as the classical Fourier transform does for stationary time series. In particular, the resulting Fourier coefficients as well as moving local periodograms are shown to be (almost all) asymptotically uncorrelated. The moving local periodogram is obtained by thinning the local periodogram to avoid multiple information present at different but close points in time. We obtain consistent estimators for the local spectral density at each point in time by smoothing the moving local periodogram. Furthermore, the moving Fourier coefficients, respectively periodograms, are well suited to adapt stationary frequency domain bootstrap methods to the locally stationary case. For the wild time frequency toggle bootstrap, it is shown that the corresponding bootstrap covariance of a global locally stationary bootstrap samples captures the time‐varying covariance structure of the underlying locally stationary time series correctly. Furthermore, this bootstrap in addition to adaptations of other frequency domain bootstrap methods is used in a simulation study to obtain uniform confidence bands for the time‐varying autocorrelation at lag 1. Finally, this methodology is applied to a wind data set.

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Frequency Domain Tests of Semiparametric Hypotheses for Locally Stationary Processes

Cited by 17 publications

References 27 publications

Local inference for locally stationary time series based on the empirical spectral measure

Local inference for locally stationary time series based on the empirical spectral measure

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

Moving Fourier Analysis for Locally Stationary Processes with the Bootstrap in View

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