Cumulants of estimates of the spectrum of a stationary time series

Bentkus, R.

doi:10.1007/bf00968366

Cited by 13 publications

(23 citation statements)

References 2 publications

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“…For the spectral density estimate we obtain that σ 2 N = 4π K 2 2 + 2πf 4 (0)M −1 , using the techniques of Bentkus (1976), and with similar arguments the first cross cumulants of u arē …”

Section: Then Immediately We Havementioning

confidence: 78%

“…In particular, this is the case in the work of Bentkus (1976), Bentkus and Rudzkis (1982) and Rudzkis (1985) on higher-order asymptotic theory for nonparametric spectral estimates, whose approach we in other respects follow. It is also the case in the econometric work referred to above on consistency of autocorrelation-consistent or long run variance estimates and on the first-order limiting distribution of studentized statistics, which resorts to summability conditions on mixing numbers.…”

Section: Introductionmentioning

confidence: 95%

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Edgeworth Expansions for Spectral Density Estimates and Studentized Sample Mean

Velasco

Robinson²

2001

Econ. Theory

113

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We establish valid Edgeworth expansions for the distribution of smoothed nonparametric spectral estimates, and of studentized versions of linear statistics such as the same mean, where the studentization employs such a nonparametric spectral estimate. Particular attention is paid to the spectral estimate at zero frequency and, correspondingly, the studentized sample mean, to reflect econometric interest in autocorrelation-consistent or long-run variance estimation. Our main focus is on stationary Gaussian series, though we discuss relaxation of the Gaussianity assumption. Only smoothness conditions on the spectral density that are local to the frequency of interest are imposed. We deduce empirical expansions from our Edgeworth expansions designed to improve on the normal approximation in practice, and also a feasible rule of bandwidth choice.

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Section: Then Immediately We Havementioning

confidence: 78%

Section: Introductionmentioning

confidence: 95%

Edgeworth Expansions for Spectral Density Estimates and Studentized Sample Mean

Velasco

Robinson²

2001

Econ. Theory

113

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“…In the non-tapered case, when h(t) ≡ 1, this was shown in [13,14]. In the case under consideration, when the taper factorizes (as defined in Section 2.2), and the domain of observation is a cube L T = [−T, T ] d , this fact follows as a straightforward generalization of the corresponding result by [19] for dimension d = 1.…”

Section: Spatial Gegenbauer Random Fields: Singularities At the Originmentioning

confidence: 66%

“…Details of calculations of the cumulants of spectral functionals can be found, for example, in [2], [10], [14] for the nontapered case, and in [3], [19], [20] for the tapered case. The calculations are based on the so-called product formula for cumulants which gives the expression for cumulants of products of random variables in terms of cumulants of the individual variables, the mentioned formula reduces to a particular simple form in the Gaussian case.…”

Section: Spatial Gegenbauer Random Fields: Singularities At the Originmentioning

confidence: 99%

Asymptotic properties of parameter estimates for random fields with tapered data

Alomari¹,

Frías²,

Leonenko³

et al. 2017

Electron. J. Statist.

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“…Since f (·) and f T (·) which we consider are 2 -periodic and even, it is sufficient to confine ourselves to the study of the interval 0 . Asymptotic normality of [4,11,Chapter 5,24,15,2], among others). Various asymptotic statistical analyses of stationary processes, including stationary long memory processes, have received a great deal of attention (see [22,1,34,12,9,38] and references therein).…”

Section: Introductionmentioning

confidence: 98%