Information tradeoffs in using the sample autocorrelation function in ARMA parameter estimation

Bruzzone, S.; Kaveh, M.

doi:10.1109/tassp.1984.1164389

Cited by 38 publications

(16 citation statements)

References 27 publications

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“…In fact, there exists an optimal weight matrix W(8), as given by the following theorem. This theorem shows that the weight matrix (16) provides an optimal (in the sense of minimum asymptotic variance) weighted least squares estimate, i.e. it is optimal in the class of estimates (12).…”

Section: Theoremmentioning

confidence: 99%

Performance analysis of parameter estimation algorithms based on high‐order moments

Porat

Friedlander

1989

Adaptive Control & Signal

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Recently, there has been a considerable interest in parametric estimation of non-Gaussian processes, based on high-order moments. Several researchers have proposed algorithms for estimating the parameters of AR, MA and ARMA processes, based on the third-order and fourth-order cumulants. These algorithms are capable of handling non-minimum phase processes, and some of them provide a good trade-off between computational complexity and statistical efficiency.This paper presents some results about the performance of algorithms based on high-order moments. A general lower bound is derived for the variance of estimates based on high-order sample moments. This bound, which is shown to be asymptotically tight, is neither the Cramer-Rao bound nor a trivial extension thereof. The performance of weighted least squares estimates of the type recently proposed in the literature is investigated. An expression for the variance of such estimates is derived and the existence of an optimal weight matrix is proven. The general formulae are specialized to MA and ARMA processes and used to analyse the performance of some algorithms in detail. The analytic results are verified by Monte Carlo simulations for some specific test cases.A by-product of this paper is the derivation of asymptotic formulae for the variances and covariances of the sample third-order moments of a certain class of processes.

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Section: Theoremmentioning

confidence: 99%

Performance analysis of parameter estimation algorithms based on high‐order moments

Porat

Friedlander

1989

Adaptive Control & Signal

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“…Applying the operator ¢(Bl) to equation (3.6) and using the previous corollary we obtain (ii). [] We end this section with a generalization of the Bruzzone and Kaveh's result (see Bruzzone and Kaveh (1984)). Although Corollary 1.1 shows that Rg(k) can be obtained as the solution of the difference equation ¢2(B)Rg(k) = O, for k > 2q+ 1, subject to the initial conditions given by the even property of Rg(k), we state the result in the form obtained in Bruzzone and Kaveh (1984).…”

Section: Some Sufficient Conditionsmentioning

confidence: 84%

“…This is indeed the case. Bruzzone and Kaveh (1984) obtained closed form formulae for Fk,t in the ARMA case under some restrictions on the roots of the ARMA polynomials (they should be complex and simple). Their solution is in terms of the roots of the ARMA polynomials.…”

Section: Introductionmentioning

confidence: 99%

Bartlett's formulae?Closed forms and recurrent equations

Boshnakov

1996

Ann Inst Stat Math

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“…Then we have the inequalities 0 ≤ n 1 ≤ n and 0 ≤ m 1 ≤ m. Because all coefficients of A(q) and B(q) are real-valued, the pure complex poles and zeros occur in complex conjugate pairs, and consequently the differences n − n 1 and m − m 1 are both even integers. For the pure complex poles and zeros we apply the parametrization in [5]:…”

Section: Appendix: the Asymptotic Fisher Information Matrixmentioning

confidence: 99%

“…We evaluate next the entry (u, v) of the Fisher information matrix for u ∈ P ρ Z ρ and v ∈ P µ P φ Z µ Z φ . It is not difficult to prove that When u, v ∈ P µ Z µ P φ Z φ , we can apply the formulas given in [5] for the computation of J u,v in case all the poles and the zeros are purely complex. Analyzing the sign of the product S u S v , we find that the matrix J(θ) can be re-written more compactly as J(θ) =…”

Section: Appendix: the Asymptotic Fisher Information Matrixmentioning

confidence: 99%

Estimation of AR and ARMA models by stochastic complexity

Giurcăneanu¹,

Rissanen²

2006

Institute of Mathematical Statistics Lecture Notes - Monograph Series

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In this paper the stochastic complexity criterion is applied to estimation of the order in AR and ARMA models. The power of the criterion for short strings is illustrated by simulations. It requires an integral of the square root of Fisher information, which is done by Monte Carlo technique. The stochastic complexity, which is the negative logarithm of the Normalized Maximum Likelihood universal density function, is given. Also, exact asymptotic formulas for the Fisher information matrix are derived.

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Information tradeoffs in using the sample autocorrelation function in ARMA parameter estimation

Cited by 38 publications

References 27 publications

Performance analysis of parameter estimation algorithms based on high‐order moments

Performance analysis of parameter estimation algorithms based on high‐order moments

Bartlett's formulae?Closed forms and recurrent equations

Estimation of AR and ARMA models by stochastic complexity

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