A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate

Giraitis, Liudas; Сургайлис, Донатас

doi:10.1007/bf01207515

Cited by 301 publications

(281 citation statements)

References 7 publications

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“…Hence, our asymptotic covariance matrix coincides with those presented in Theorem 4 of Giraitis and Surgailis (1990) and Theorem 2 of Velasco and Robinson (2000) for p = 1, i.e. the untapered case.…”

Section: Whittle Estimator (M = 0)supporting

confidence: 53%

“…Early work by Walker (1964) and Hannan (1973b) dealt with short-range dependent process. For long-range dependent process, see Fox and Taqqu (1986), Dahlhaus (1989), Giraitis and Surgailis (1990) and Velasco and Robinson (2000) among others. All the works mentioned above assume either Gaussian processes or linear processes with iid or conditionally homescedastic martingale difference innovations.…”

Section: Whittle Estimator (M = 0)mentioning

confidence: 99%

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Nonstationarity-Extended Whittle Estimation

Shao

2009

Econom. Theory

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For long memory time series models with uncorrelated but dependent errors, we establish the asymptotic normality of the Whittle estimator under mild conditions. Our framework includes the widely used FARIMA models with GARCH-type innovations. To cover nonstationary fractionally integrated processes, we extend the idea of Abadir, Distaso and Giraitis (2007, Journal of Econometrics 141, 1353-1384) and develop the nonstationarity-extended Whittle estimation. The resulting estimator is shown to be asymptotically normal and is more efficient than the tapered Whittle estimator. Finally, the results from a small simulation study are presented to corroborate our theoretical findings.

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Section: Whittle Estimator (M = 0)supporting

confidence: 53%

Section: Whittle Estimator (M = 0)mentioning

confidence: 99%

Nonstationarity-Extended Whittle Estimation

Shao

2009

Econom. Theory

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“…This means that for Gaussian and linear models the estimator is capable of providing the probability distribution of the parameters, which allows one to derive their confidence limits. Asymptotic normality and consistency is assured under mild conditions also in the non-Gaussian case [Giraitis and Surgailis, 1990], while asymptotic normality is no more guaranteed for nonlinear models, as it is the case in many practical applications in hydrology. Nonetheless, the absence of asymptotic normality does not affect the consistency of the estimator but only the computation of the confidence limits of the parameters.…”

Section: Approximation Proposed By Whittle To the Gaussian Maximum LImentioning

confidence: 99%

Calibration of hydrological models in the spectral domain: An opportunity for scarcely gauged basins?

Montanari

Toth

2007

Water Resources Research

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[1] This study considers the use of the maximum likelihood estimator proposed by Whittle for calibrating the parameters of hydrological models. Whittle's likelihood provides asymptotically consistent estimates for Gaussian and non-Gaussian data, even in the presence of long-range dependence. This method may represent a valuable opportunity in the context of ungauged or scarcely gauged catchments. In fact, the only information required for model parameterization is essentially the spectral density function of the actual process simulated by the model. When long series of calibration data are not available, the spectral density can be inferred by using old and sparse records, regionalization methods, or information on the correlation properties of the process itself. The proposed procedure is applied to the case studies of two Italian river basins, for which a lumped rainfall-runoff model has been calibrated by emulating scarcely gauged situations. It is shown that the Whittle estimator can be applied in such context with satisfactory results.Citation: Montanari, A., and E. Toth (2007), Calibration of hydrological models in the spectral domain: An opportunity for scarcely gauged basins?, Water Resour. Res., 43, W05434,

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“…Our assumptions are compatible with the assumption set (B1-B6) of (Giraitis and Surgailis [11]) so that the Whittle contrast minimizer is proved to be √ n-convergent for linear long-range dependent time series under some additional regularity conditions on the parametric set {g * (·; θ), θ ∈ Θ}.…”

Section: Remark 4 Note That a √mentioning

confidence: 88%

Goodness-of-fit test for long range dependent processes

Faÿ

Philippe

2002

ESAIM: PS

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Abstract. In this paper, we make use of the information measure introduced by Mokkadem (1997) for building a goodness-of-fit test for long-range dependent processes. Our test statistic is performed in the frequency domain and writes as a non linear functional of the normalized periodogram. We establish the asymptotic distribution of our statistic under the null hypothesis. Under specific alternative hypotheses, we prove that the power converges to one. The performance of our test procedure is illustrated from different simulated series. In particular, we compare its size and its power with test of Chen and Deo.Mathematics Subject Classification. 60F05, 62F03.

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A central limit theorem for quadratic forms in strongly dependent linear variables and its application to asymptotical normality of Whittle's estimate

Cited by 301 publications

References 7 publications

Nonstationarity-Extended Whittle Estimation

Nonstationarity-Extended Whittle Estimation

Calibration of hydrological models in the spectral domain: An opportunity for scarcely gauged basins?

Goodness-of-fit test for long range dependent processes

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