Journal ArticleDOI
More on autoregressive model fitting with noisy data by Akaike's information criterion (Corresp.)
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This correspondence exploits one well-known fact concerning autoregressive (AR) signals plus white noise, and uses Akaike's information criterion to develop one efficient procedure for determining the order of the AR signal from noisy data.Abstract:
Davisson [131, [141 has considered the problem of determining the "order" of the signal from noisy data. Although interesting theoretically, his result is difficult to use in practice. In this correspondence, we exploit one well-known fact concerning autoregressive (AR) signals plus white noise, and using Akaike's information criterion [15], [17], we have developed one efficient procedure for determining the order of the AR signal from noisy data. The procedure is illustrated numerically using both artificially generated and real data. The connection between the preceding problem and the classical statistical problem of factor analysis is discussed.read more
Citations
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Spectrum analysis—A modern perspective
Steven Kay,S.L. Marple +1 more
TL;DR: In this paper, a summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented, including classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods.
Journal ArticleDOI
Asymptotically Efficient Selection of the Order of the Model for Estimating Parameters of a Linear Process
TL;DR: In this article, a linear stationary process of the form $x_t + \Sigma{1\leqslant i<\infty}a_ix_{t-i} = e_t, where e is a sequence of i.i.d. normal random variables with mean 0 and variance $\sigma^2", is considered.
Book
Identification of Dynamic Systems: An Introduction with Applications
Rolf Isermann,Marco Münchhof +1 more
TL;DR: This book treats the determination of dynamic models based on measurements taken at the process, known as system identification or process identification, and covers the following subjects: determination of the non-parametric frequency response, (fast) Fourier transform, correlation analysis, parameter estimation and subspace methods.
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Factor Analysis as a Statistical Method
Journal ArticleDOI
On Markov Chain Modeling to Some Weather Data
TL;DR: In this article, the Akaike Information Criterion (AIC) is used to determine the order of an ergodic Markov chain with a finite number of states.
References
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A new look at the statistical model identification
TL;DR: In this article, a new estimate minimum information theoretical criterion estimate (MAICE) is introduced for the purpose of statistical identification, which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure.
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Time series analysis, forecasting and control
TL;DR: In this article, a complete revision of a classic, seminal, and authoritative book that has been the model for most books on the topic written since 1970 is presented, focusing on practical techniques throughout, rather than a rigorous mathematical treatment of the subject.
Proceedings Article
Information Theory and an Extention of the Maximum Likelihood Principle
TL;DR: The classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion to provide answers to many practical problems of statistical model fitting.
Book ChapterDOI
Information Theory and an Extension of the Maximum Likelihood Principle
TL;DR: In this paper, it is shown that the classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion.
Book
An Introduction to Multivariate Statistical Analysis
TL;DR: In this article, the distribution of the Mean Vector and the Covariance Matrix and the Generalized T2-Statistic is analyzed. But the distribution is not shown to be independent of sets of Variates.