Author: Pentti Saikkonen
Publisher:
ISBN: 9789514532917
Category :
Languages : en
Pages : 31

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Author: Stanford University. Department of Statistics
Publisher:
ISBN:
Category : Time-series analysis
Languages : en
Pages : 318

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Book Description
The author considers estimation procedures for the moving average model of order q. Walker's method uses k sample autocovariances (k> or = q). Assume that k depends on T in such a way that k nears infinity as T nears infinity. The estimates are consistent, asymptotically normal and asymptotically efficient if k = k (T) dominates log T and is dominated by (T sub 1/2). The approach in proving these theorems involves obtaining an explicit form for the components of the inverse of a symmetric matrix with equal elements along its five central diagonals, and zeroes elsewhere. The asymptotic normality follows from a central limit theorem for normalized sums of random variables that are dependent of order k, where k tends to infinity with T. An alternative form of the estimator facilitates the calculations and the analysis of the role of k, without changing the asymptotic properties.

Author: Norbert Miethe
Publisher:
ISBN:
Category :
Languages : de
Pages : 22

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Author: M. Lawrence Clevenson
Publisher:
ISBN:
Category : Time-series analysis
Languages : en
Pages : 212

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The thesis is concerned with the estimation of the parameters of a moving average time series, (x sub t, t= 0, plus or minus 1, plus or minus 2 ...), of order M. By definition, such a series has the representation x sub t = (eta sub t) + (b sub 1)(eta sub (t-1)) + (b sub 2)(eta sub (t-2)) + ... + (b sub M)(eta sub (+-M)) for some series of uncorrelated, identically distributed random variables eta sub t, t = 0, plus or minus 1, plus or minus 2 ...). It is assumed that the process has mean zero and is a Gaussian process; hence eta sub t has a normal distribution with mean and some unknown variance (sigma sub n) squared. The goal is to find asymptotically normal and efficient estimates of the parameters of the model. (Author).

Author: Aman Ullah
Publisher: CRC Press
ISBN: 9780203911075
Category : Business & Economics
Languages : en
Pages : 754

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Book Description
Summarizing developments and techniques in the field, this reference covers sample surveys, nonparametric analysis, hypothesis testing, time series analysis, Bayesian inference, and distribution theory for applications in statistics, economics, medicine, biology, engineering, sociology, psychology, and information technology. It supplies a geometric proof of an extended Gauss-Markov theorem, approaches for the design and implementation of sample surveys, advances in the theory of Neyman's smooth test, and methods for pre-test and biased estimation. It includes discussions ofsample size requirements for estimation in SUR models, innovative developments in nonparametric models, and more.

Author: D. F. Gingras
Publisher:
ISBN:
Category :
Languages : en
Pages : 30

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Book Description
The extended Yule-Walker equations are used to estimate the autoregressive parameters of an autoregressive moving-average time series. The asymptotic statistical properties of these estimates are derived. It is shown that they are asymptotically unbiased and normal; the covariance matrix of the limit distribution is calculated. The special case of estimating the autoregressive parameters of a noise corrupted autoregressive series is also treated. (Author).

Author: Richard Alan Lewis
Publisher:
ISBN:
Category : Time-series analysis
Languages : en
Pages : 444

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Author: Boaz Porat
Publisher:
ISBN:
Category :
Languages : en
Pages : 24

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Author: E. J. Hannan
Publisher: SIAM
ISBN: 9781611972191
Category : Business & Economics
Languages : en
Pages : 425

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Book Description
Originally published in 1988, The Statistical Theory of Linear Systems deals with identification (in the sense of obtaining a model from data) of multi-input and multi-output linear systems, in particular systems in ARMAX and state space form. The book emphasizes the underlying theory. It covers structure theory, in particular realization and parameterization of linear systems, with special emphasis on the analysis of properties of parameter spaces and parameterizations relevant for estimation and model selection; Gaussian maximum likelihood estimation of the real-valued parameters of linear systems, with an emphasis on asymptotic theory; model selection, in particular order estimation, by information criteria such as AIC or BIC, with an emphasis on asymptotic theory; procedures for calculation of estimates; and approximation by rational functions. This edition includes an extensive new introduction that outlines central ideas and features of the subject matter, as well as developments since the book's original publication, such as subspace identification, data-driven local coordinates, and the results on post-model-selection estimators. It also provides a section of errata and an updated bibliography.

Author: Beth Andrews
Publisher:
ISBN:
Category :
Languages : en
Pages : 0

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Book Description
We establish asymptotic normality and consistency for rank-based estimators of autoregressive-moving average model parameters. The estimators are obtained by minimizing a rank-based residual dispersion function similar to the one given by L.A. Jaeckel [Ann. Math. Stat. Vol. 43 (1972) 1449-1458]. These estimators can have the same asymptotic efficiency as maximum likelihood estimators and are robust. The quality of the asymptotic approximations for finite samples is studied via simulation.