Large Sample Inference for Long Memory Processes

Giraitis, Liudas; Koul, Hira L.; Сургайлис, Донатас

doi:10.1142/p591

Cited by 223 publications

(340 citation statements)

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“…This is true indeed and the limit distribution of the right-hand side of (3.16) can be obtained by using usual techniques for subordinated Gaussian processes (see, e.g., Giraitis and Surgailis (1985), Giraitis et al (2012)), and coincides with the limits in (3.2)-(3.3). However, a rigorous justification of the approximation in (3.16) in the case 0 < d < 1/4 is difficult and in the proof of (3.2) we use a different approach based on finite-memory approximations and a central limit theorem for m−dependent r.v.…”

Section: Resultssupporting

confidence: 59%

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Minimum distance lack-of-fit tests under long memory errors

Koul

Сургайлис

Mimoto

2014

Metrika

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This paper discusses some tests of lack-of-fit of a parametric regression model when errors form a long memory moving average process with the long memory parameter 0 < d < 1/2, and when design is non-random and uniform on [0, 1]. These tests are based on certain minimized distances between a nonparametric regression function estimator and the parametric model being fitted. The paper investigates the asymptotic null distribution of the proposed test statistics and of the corresponding minimum distance estimators under minimal conditions on the model being fitted. The limiting distribution of these statistics are Gaussian for 0 < d < 1/4 and non-Gaussian for 1/4 < d < 1/2. We also discuss the consistency of these tests against a fixed alternative.

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Section: Resultssupporting

confidence: 59%

“…Long memory processes have been found to arise in a variety of physical and social sciences, see, e.g. Beran (1994), Dehling, Mikosch, and Sørensen (2002), Doukhan, Oppenheim and Taqqu (2003), Robinson (2003), Giraitis, Koul and Surgailis (2012), and references therein.…”

Section: Introductionmentioning

confidence: 99%

Minimum distance lack-of-fit tests under long memory errors

Koul

Сургайлис

Mimoto

2014

Metrika

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“…Hence (2.7) follows from Theorem 1 in Hannan (1973). For more details of the proof, see Theorem 8.2.1 in Giraitis et al (2012). h…”

Section: Parametric Whittle Estimationmentioning

confidence: 77%

“…noises fg t g. Hannan assumed that E½g t jF tÀ1 ¼ r 2 is a constant a.s. Fox and Taqqu (1986), Giraitis and Surgailis (1990), Giraitis et al (2001) and others extended the parametric Whittle estimation technique to linear long memory time series fX t g with unbounded spectral densities and i.i.d. noise fg t g; see Chapter 8 in Giraitis et al (2012). Hosoya and Taniguchi (1982) showed that Whittle estimation remains valid for linear processes with uncorrelated noise fg t g whose fourth-order cumulants are summable and whose conditional moments satisfy some regularity conditions.…”

Section: Introductionmentioning

confidence: 99%

Estimation pitfalls when the noise is not i.i.d.

Giraitis

Taniguchi

Taqqu

2018

Jpn J Stat Data Sci

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This paper extends Whittle estimation to linear processes with a general stationary ergodic martingale difference noise. We show that such estimation is valid for standard parametric time series models with smooth bounded spectral densities, e.g., ARMA models. Furthermore, we clarify the impact of the hidden dependence in the noise on such estimation. We show that although the asymptotic normality of the Whittle estimates may still hold, the presence of dependence in the noise impacts the limit variance. Hence, the standard errors and confidence intervals valid under i.i.d. noise may not be applicable and thus require correction. The goal of this paper is to raise awareness to the impact of a non-i.i.d. noise in applied work.

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“…Remark 4 Fractionally integrated processes (Giraitis et al, 2012) arise as limiting cases. Consider for instance the case b(z) = 1 − z, so that…”

Section: Generalised Linear Cepstral Models For the Spectrummentioning

confidence: 99%

Generalised Linear Cepstral Models for the Spectrum of a Time Series

Proietti¹,

Luati²

2019

STAT SINICA

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The paper introduces the class of generalised linear models with BoxCox link for the spectrum of a time series. The Box-Cox transformation of the spectral density is represented as a finite Fourier polynomial, with coefficients, that we term generalised cepstral coefficients, providing a complete characterisation of the properties of the random process. The link function depends on a power transformation parameter and encompasses the exponential model (logarithmic link), the autoregressive model (inverse link), and the moving average model (identity link). One of the merits of this model class is the possibility of nesting alternative spectral estimation methods under the same likelihood-based framework, so that the selection of a particular parametric spectrum amounts to estimating the transformation parameter. We also show that the generalised cepstral coefficients are a one to one function of the inverse partial autocorrelations of the process, which can be used to evaluate the mutual information between the past and the future of the process.

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Large Sample Inference for Long Memory Processes

Cited by 223 publications

References 0 publications

Minimum distance lack-of-fit tests under long memory errors

Minimum distance lack-of-fit tests under long memory errors

Estimation pitfalls when the noise is not i.i.d.

Generalised Linear Cepstral Models for the Spectrum of a Time Series

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