Journal ArticleDOI
Asymptotic normality of prediction error estimators for approximate system models
Ljung Lennart,Peter E. Caines +1 more
- Vol. 3, pp 29-46
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TLDR
In this paper, a general class of parameter estimation methods for stochastic dynamical systems is studied and the class contains the least squares method, output-error methods, the maximum likelihood method and several other techniques.Abstract:
A general class of parameter estimation methods for stochastic dynamical systems is studied. The class contains the least squares method, output-error methods, the maximum likelihood method and several other techniques. It is shown that the class of estimates so obtained are asymptotically normal and expressions for the resulting asymptotic covariance matrices are given. The regularity conditions that are imposed to obtain these results, are fairly weak. It is, for example, not assumed that the true system can be described within the chosen model set, and, as a consequence, the results in this paper form a part of the so-called approximate modeling approach to system identification. It is also noteworthy that arbitrary feedback from observed system outputs to observed system inputs is allowed and stationarity is not requiredread more
Citations
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Universal coding, information, prediction, and estimation
TL;DR: A connection between universal codes and the problems of prediction and statistical estimation is established, and a known lower bound for the mean length of universal codes is sharpened and generalized, and optimum universal codes constructed.
Journal ArticleDOI
Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns
Andrew Harvey,Neil Shephard +1 more
TL;DR: In this paper, a stochastic volatility model may be estimated by a quasi-maximum likelihood procedure by transforming to a linear state-space form, which is extended to handle correlation between the two disturbances in the model and applied to data on stock returns
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Maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements
TL;DR: A simplified maximum-likelihood Gauss-Newton algorithm which provides asymptotically efficient estimates of these parameters is proposed and initial estimates for this algorithm are obtained by a variation of the overdetermined Yule-Walker method and periodogram-based procedure.
Journal ArticleDOI
Special section system identification tutorial: Maximum likelihood and prediction error methods
TL;DR: The basic ideas behind the parameter estimation methods are discussed in a general setting and an example is given which illustrates some properties of the methods and shows the usefulness of interactive computing.
Journal ArticleDOI
Asymptotic properties of black-box identification of transfer functions
Lennart Ljung,Zhen-Dong Yuan +1 more
TL;DR: In this article, the authors considered the problem of estimating the transfer function of a linear, stochastic system, where no given order is chosen a priori, and the transfer functions are parametrized as a black box.
References
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Maximum likelihood identification of Gaussian autoregressive moving average models
TL;DR: It is shown that the procedure described by Hannan (1969) for the estimation of the parameters of one-dimensional autoregressive moving average processes is equivalent to a three-stage realization of one step of the NewtonRaphson procedure for the numerical maximization of the likelihood function, using the gradient and the approximate Hessian.
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Convergence analysis of parametric identification methods
TL;DR: A certain class of methods to select suitable models of dynamical stochastic systems from measured input-output data is considered, based on a comparison between the measured outputs and the outputs of a candidate model.
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Numerical Identification of Linear Dynamic Systems from Normal Operating Records
Karl Johan Åström,Torsten Bohlin +1 more
TL;DR: In this paper, a technique for numerical identification of a discrete time system from input/output samples is described, and strategies for control of the system are obtained using linear stochastic control theory.
Journal ArticleDOI
On Asymptotic Distributions of Estimates of Parameters of Stochastic Difference Equations
TL;DR: In this article, it was shown that for any > 1, unless the distribution of the u's is independent, identically distributed with finite variance, the distribution has a limiting Cauchy distribution under the assumption that u's are not necessarily normally distributed.
Journal ArticleDOI
Vector linear time series models
TL;DR: In this article, the strong law of large numbers and the central limit theorem for estimators of the parameters in quite general finite-parameter linear models for vector time series are presented.