The Estimation of the Prediction Error Variance

Hannan, E. J.; Nicholls, D. F.

doi:10.1080/01621459.1977.10479966

Cited by 35 publications

(43 citation statements)

References 9 publications

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“…In this special but important situation when the space is defined by (23), there exists yet another characterization of the reproducing kernel which will be of great utility in later developments. [20]): The reproducing kernel for in (23) is given by (27) Proof: See [21]. Finally, in the multidimensional situation, one example with will be especially important for later applications.…”

Section: Lemma 32 (Orthonormal Basis For Fixed Denominator Spaces)mentioning

confidence: 98%

Variance Error Quantifications That Are Exact for Finite-Model Order

Ninness¹,

Hjalmarsson²

2004

IEEE Trans. Automat. Contr.

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This paper is concerned with the frequency domain quantification of noise induced errors in dynamic system estimates. Preceding and seminal work on this problem has suggested general expressions that are approximations whose accuracy increases with observed data length and model order. In the interests of improved accuracy, this paper provides new expressions whose accuracy depends only on data length. They are therefore "exact" for arbitrarily small true model order. Other authors have recognized the importance of such expressions and have derived them for the case of finite-impulse response-like model structures in which denominators are fixed at true values and only numerator terms are estimated. This paper progresses beyond this situation to address the more general output-error and Box-Jenkins structures in which full dynamics models (both numerator and denominator terms) and noise models may be estimated. A key aspect of the work here is that it establishes that the variance quantification problem is equivalent to that of deriving the reproducing kernel for a subspace that depends on the model structure being employed.

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Section: Lemma 32 (Orthonormal Basis For Fixed Denominator Spaces)mentioning

confidence: 98%

Variance Error Quantifications That Are Exact for Finite-Model Order

Ninness¹,

Hjalmarsson²

2004

IEEE Trans. Automat. Contr.

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“…Some of these procedures used the periodogram I(a), (1.2) I(~)= Z Y, exp (i2t) t=0 where Y0, "', y~-L are observations. The logarithm of the periodogram or that of the smoothed periodogram was used for estimating some parameters by Davis and Jones [5], Bloomfield [2] and Hannah and 83 Nicholls [8]. Wahba [11] also used the log periodogram to obtain an estimate of the log spectral density by a spline approach.…”

Section: 1) Yt Jr Bly~_1 -K " 9 9 -~-Bpyt_p-'-ut '}-Alut_l"}-" 9 9 mentioning

confidence: 99%

Parameter estimation of an autoregressive moving average model

Nakano

1982

Ann Inst Stat Math

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SummaryAn estimator of the set of parameters of an autoregressive moving average model is obtained by applying the method of least squares to the log smoothed periodogram. It is shown to be asymptotically efficient and normally distributed under the normality and the circular condition of the generating process. A computational procedure is constructed by the Newton-Raphson method. Several computer simulation results are given to demonstrate the usefulness of the present procedure.

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“…It can also be based on the normalised spectral densities of the two processes, in which case the autocorrelations ρ pk replace the autocovariances in (27).…”

Section: Time Series Cluster and Discriminant Analysismentioning

confidence: 99%

“…The p-sd (27) encompasses the Euclidean distance (p = 1), referred to as the quadratic distance in Hong (1996) and the Hellinger distance (p = 1/2). It can also be based on the normalised spectral densities of the two processes, in which case the autocorrelations ρ pk replace the autocovariances in (27).…”

Section: Time Series Cluster and Discriminant Analysismentioning

confidence: 99%

The Generalised Autocovariance Function

Proietti

Luati

2013

SSRN Journal

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The generalised autocovariance function is defined for a stationary stochastic process as the inverse Fourier transform of the power transformation of the spectral density function.Depending on the value of the transformation parameter, this function nests the inverse and the traditional autocovariance functions. A frequency domain non-parametric estimator based on the power transformation of the pooled periodogram is considered and its asymptotic distribution is derived. The results are employed to construct classes of tests of the white noise hypothesis, for clustering and discrimination of stochastic processes and to introduce a novel feature matching estimator of the spectrum.

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The Estimation of the Prediction Error Variance

Cited by 35 publications

References 9 publications

Variance Error Quantifications That Are Exact for Finite-Model Order

Variance Error Quantifications That Are Exact for Finite-Model Order

Parameter estimation of an autoregressive moving average model

The Generalised Autocovariance Function

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