Fitting time series models to nonstationary processes

Dahlhaus, Rainer

doi:10.1214/aos/1034276620

Cited by 760 publications

(743 citation statements)

References 24 publications

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“…Dahlhaus (1997) defined a class of locally stationary processes for which a rigorous asymptotic theory can be obtained. Mallat et al (1998) modelled locally stationary processes with pseudo-differential operators that are time-varying convolutions.…”

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confidence: 99%

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Testing parametric assumptions of trends of a nonstationary time series

Zhang

2011

Biometrika

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SUMMARYThe paper considers testing whether the mean trend of a nonstationary time series is of certain parametric forms. A central limit theorem for the integrated squared error is derived, and with that a hypothesis-testing procedure is proposed. The method is illustrated in a simulation study, and is applied to assess the mean pattern of lifetime-maximum wind speeds of global tropical cyclones from 1981 to 2006. We also revisit the trend pattern in the central England temperature series.

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confidence: 99%

“…Cheng & Tong (1998) applied wavelet representations. Nason et al (2000) proposed to use a set of discrete non-decimated wavelets rather than 60 the Fourier complex exponentials as in Dahlhaus (1997). Giurcanu & Spokoiny (2004) treated nonstationarity by assuming that correlation functions could be well approximated by those of stationary processes.…”

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confidence: 99%

Testing parametric assumptions of trends of a nonstationary time series

Zhang

2011

Biometrika

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“…Following Dahlhaus (1997) and Palma and Olea (2010), a class of locally stationary process is given by the infinite moving average expansion…”

Section: Methodsmentioning

confidence: 99%

“…This approach is based on the evolutionary spectra developed by Priestley (1965) and formally introduced in Dahlhaus (1996Dahlhaus ( , 1997. In this context, the parameters of the spectral density vary smoothly over time so that these nonstationary processes can be locally approximated by stationary models.…”

Section: Introductionmentioning

confidence: 99%

On the Estimation of Locally Stationary Long-Memory Processes

Chan¹,

Manríquez²

2019

STAT SINICA

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This paper establishes the statistical properties of a spectrum-based Whittle parameter estimation procedure for long-range dependent locally stationary processes. Both theoretical and empirical behaviors are investigated. In particular, a central limit theorem for the Whittle likelihood estimation method is derived under mild distributional conditions, extending its application to a wide range of non-Gaussian time series. The finite sample properties of the estimators are examined via Monte Carlo experiments with Gamma and Log-normal noise distributions. These simulation studies demonstrate that the proposed method behaves properly even for small to moderate sample sizes. Finally, the practical application of this methodology is illustrated by means a well-known real-life data example.

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“…Neumann and von Sachs (1997) and Nason, von Sachs, and Kroisandt (2000) discussed the estimation of evolutionary spectra by wavelet methods. Dahlhaus (1997) gave a definition of locally stationary processes on the basis of a time varying spectral representation and established the asymptotic theory for statistical inference in such cases (see also Dahlhaus (2000), Dahlhaus and Polonik (2006), and Dahlhaus (2009)). Alternative concepts to model time varying dependencies have recently been introduced by Wu (2009, 2010) and cover a wide range of non-stationary processes.…”

Section: Introductionmentioning

confidence: 99%

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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Fitting time series models to nonstationary processes

Cited by 760 publications

References 24 publications

Testing parametric assumptions of trends of a nonstationary time series

Testing parametric assumptions of trends of a nonstationary time series

On the Estimation of Locally Stationary Long-Memory Processes

Measuring stationarity in long-memory processes

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