On Conditional Least Squares Estimation for Stochastic Processes

Klimko, Lawrence A.; Nelson, Paul I.

doi:10.1214/aos/1176344207

Cited by 415 publications

(239 citation statements)

References 16 publications

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“…where the variance c 2 and the covariance matrix can be respectively expressed in terms of the moments, up to the third order, of the offspring and immigration distributions (see Klimko and Nelson [11]); closely related estimators were proposed and studied by Heyde and Seneta [5], [6] and Quine [14].…”

Section: Fluctuation Limit Of Branching Processesmentioning

confidence: 99%

Fluctuation limit of branching processes with immigration and estimation of the means

Ispány¹,

Pap²,

Zuijlen³

2005

Adv. Appl. Probab.

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We investigate a sequence of Galton-Watson branching processes with immigration, where the offspring mean tends to its critical value 1 and the offspring variance tends to 0. It is shown that the fluctuation limit is an Ornstein-Uhlenbeck-type process. As a consequence, in contrast to the case in which the offspring variance tends to a positive limit, it transpires that the conditional least-squares estimator of the offspring mean is asymptotically normal. The norming factor is n 3/2 , in contrast to both the subcritical case, in which it is n 1/2 , and the nearly critical case with positive limiting offspring variance, in which it is n.

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Section: Fluctuation Limit Of Branching Processesmentioning

confidence: 99%

Fluctuation limit of branching processes with immigration and estimation of the means

Ispány¹,

Pap²,

Zuijlen³

2005

Adv. Appl. Probab.

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“…Except for the thresholds, they can be derived by combining the approach of Azrak (1996) with that of Klimko and Nelson (1978), and Tjøstheim (1984bTjøstheim ( , 1986 …”

Section: Resultsmentioning

confidence: 99%

The exact quasi-likelihood of time-dependent ARMA models

Azrak

Mélard

1998

Journal of Statistical Planning and Inference

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Abstract. The purpose of the paper is to propose a simple and efficient algorithm to evaluate the exact quasi-likelihood of (possibly marginally heteroscedastic) ARMA models with time-dependent coefficients. The algorithm is based on the Kalman filter and is therefore simpler than a previous algorithm based on a Cholesky factorisation. Computational efficiency is obtained by taking the ARMA structure into account. Empirical evidence is given. It is also shown how the algorithm can be used as an approximation in the following non-linear models: conditionally heteroscedastic ARMA models (with GARCH errors) and threshold ARMA models, in order to improve the treatment of the initial observations when the parameters of these models are estimated.

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“…e., a fixed positive definite matrix, Klimko and Nelson (1978) derived the consistency and the large sample distribution ofθ:…”

Section: Approximate Clsmentioning

confidence: 99%

“…Specifically, Klimko and Nelson (1978) showed the existence of a local minimizer of the objective function in the interior of a shrinking neighborhood of the true parameter, with probability approaching 1 as sample size n → ∞, and the local minimizer constitutes the CLS estimator which is then shown to be asymptotically normal.…”

Section: Approximate Clsmentioning

confidence: 99%

“…The method of conditional least squares (CLS) provides a general approach for estimating a state-space model and it enjoys consistency and asymptotic normality, under some mild regularity conditions, see Klimko and Nelson (1978). However, its applicability is limited by the tractability of the conditional mean function of the future process given the data, which is generally intractable for nonlinear state-space models.…”

Section: Introductionmentioning

confidence: 99%

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Approximate conditional least squares estimation of a nonlinear state-space model via an unscented Kalman filter

Ahn

Chan

2014

Computational Statistics & Data Analysis

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We consider the problem of estimating a nonlinear state-space model whose state process is driven by an ordinary differential equation (ODE) or a stochastic differential equation (SDE), with discrete-time data. We propose a new estimation method by minimizing the conditional least squares (CLS) with the conditional mean function computed approximately via unscented Kalman filter (UKF). We derive conditions 1 under which the UKF-CLS estimator preserves the limiting properties of the exact CLS estimator, namely, consistency and asymptotic normality. We demonstrate the efficacy of the proposed method by simulation and a real application.--------------

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On Conditional Least Squares Estimation for Stochastic Processes

Cited by 415 publications

References 16 publications

Fluctuation limit of branching processes with immigration and estimation of the means

Fluctuation limit of branching processes with immigration and estimation of the means

The exact quasi-likelihood of time-dependent ARMA models

Approximate conditional least squares estimation of a nonlinear state-space model via an unscented Kalman filter

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