On the Kullback-Leibler information divergence of locally stationary processes

Dahlhaus, Rainer

doi:10.1016/0304-4149(95)00090-9

Cited by 225 publications

(246 citation statements)

References 16 publications

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“…Notice that by the extension of the Kolmogorov's formula provided by Theorem 3.2 of Dahlhaus (1996), log f θ (u, λ) dλ = 2π log σ 2 β (u). As a consequence, ∇ α log f θ (u, λ) dλ = 0 and thus, the term W α vanishes from the asymptotic variance.…”

Section: Propertiesmentioning

confidence: 99%

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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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Section: Propertiesmentioning

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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“…, n, as a multivariate nonstationary process. The problem of modeling nonstationary processes has been studied in the literature by means of spectral representations (Priestley (1965), Dahlhaus (1996Dahlhaus ( , 1997), pseudo-differential operators (Mallat, Papanicolaou, and Zhang (1998)), discrete non-decimated wavelets (Nason, von Sachs, and Kroisandt (2000)) and smooth localized complex exponentials (Ombao, von Sachs, and Guo (2005)). Other contributions can be found in Cheng and Tong (1998), Giurcanu and Spokoiny (2004), and Draghicescu, Guillas, and Wu (2009), among others.…”

Section: Multivariate Nonstationary Processesmentioning

confidence: 99%

Testing additive assumptions on means of regular monitoring data: a multivariate nonstationary time series approach

Zhang¹

2017

STAT SINICA

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In the analysis of surface meteorological data, observations are usually recorded regularly and frequently in time at multiple but fixed locations in space. The data can thus be viewed as multivariate time series in which a small number of lengthy time series is observed. Motivated by a temperature data, the current paper considers the problem of testing the additive assumption of location and time effects via a multivariate time series approach. Test statistics based on both maximum absolute and integrated squared deviations are proposed and their asymptotic properties are studied for a general class of multivariate nonstationary processes. The results are illustrated in a simulation study and applied to temperature data.

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“…That is, the locally stationary process depends on both t and T , which allows us to use asymptotic considerations. A justification of the locally stationary approach and a comparison with the approach of Priestley can be found in Dahlhaus (1996bDahlhaus ( , 1996c.…”

Section: Called the Time Varying Spectral Density Of The Processmentioning

confidence: 99%

“…However, the assumption of stationarity is insufficient to describe the real time series data. Recently, an important class of nonstationary processes has been proposed by Dahlhaus (1996aDahlhaus ( , 1996bDahlhaus ( , 1996c, called locally stationary processes. We give the precise definition which is due to Dahlhaus (1996aDahlhaus ( , 1996b.…”

Section: Introductionmentioning

confidence: 99%

Generalized Information Criteria in Model Selection for Locally Stationary Processes

Hirukawa

Kato

Tamaki

et al. 2008

JJSS

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The problem of fitting a parametric model of time series with time varying parameters attracts our attention. We evaluate a goodness of time varying spectral models from an information theoretic point of view. We propose model selection criteria for locally stationary processes based on nonlinear functionals of a time varying spectral density without assuming that the true time varying spectral density belongs to the model. Also, we obtain a sufficient condition such that our information criteria coincide with Akaike's information criterion.

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On the Kullback-Leibler information divergence of locally stationary processes

Cited by 225 publications

References 16 publications

On the Estimation of Locally Stationary Long-Memory Processes

On the Estimation of Locally Stationary Long-Memory Processes

Testing additive assumptions on means of regular monitoring data: a multivariate nonstationary time series approach

Generalized Information Criteria in Model Selection for Locally Stationary Processes

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