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Adaptive Estimation In Multiple Time Series With Independent Component Errors
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Book Synopsis Adaptive Estimation in Multiple Time Series with Independent Component Errors by : Peter M. Robinson
Download or read book Adaptive Estimation in Multiple Time Series with Independent Component Errors written by Peter M. Robinson and published by . This book was released on 2017 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article develops statistical methodology for semiparametric models for multiple time series of possibly high dimension N. The objective is to obtain precise estimates of unknown parameters (which characterize autocorrelations and cross-autocorrelations) without fully parameterizing other distributional features, while imposing a degree of parsimony to mitigate a curse of dimensionality. The innovations vector is modelled as a linear transformation of independent but possibly non-identically distributed random variables, whose distributions are nonparametric. In such circumstances, Gaussian pseudo-maximum likelihood estimates of the parameters are typically √n-consistent, where n denotes series length, but asymptotically inefficient unless the innovations are in fact Gaussian. Our parameter estimates, which we call 'adaptive,' are asymptotically as first-order efficient as maximum likelihood estimates based on correctly specified parametric innovations distributions. The adaptive estimates use nonparametric estimates of score functions (of the elements of the underlying vector of independent random varables) that involve truncated expansions in terms of basis functions; these have advantages over the kernel-based score function estimates used in most of the adaptive estimation literature. Our parameter estimates are also √n -consistent and asymptotically normal. A Monte Carlo study of finite sample performance of the adaptive estimates, employing a variety of parameterizations, distributions and choices of N, is reported.
Book Synopsis Adaptive Estimation in Time Series Regression Models by : Douglas Gardiner Steigerwald
Download or read book Adaptive Estimation in Time Series Regression Models written by Douglas Gardiner Steigerwald and published by . This book was released on 1989 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Adaptive Estimation in the Panel Data Error Component Model with Heteroskedasticity of Unknown Form by : Qi Li
Download or read book Adaptive Estimation in the Panel Data Error Component Model with Heteroskedasticity of Unknown Form written by Qi Li and published by . This book was released on 1993 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Multiple Time Series Analysis by : Helmut Lütkepohl
Download or read book Introduction to Multiple Time Series Analysis written by Helmut Lütkepohl and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Multiple Model Adaptive Estimation for Time Series Analysis by : Ibrahim Dulger
Download or read book Multiple Model Adaptive Estimation for Time Series Analysis written by Ibrahim Dulger and published by . This book was released on 2001-03 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Model Adaptive Estimation (MMAE) is a Bayesian technique that applies a bank of Kalman filters to predict future observations. Each Kalman filter is based on a different set of parameters and hence produces different residuals. The likelihood of each Kalman filter's prediction is determined by a magnitude of the residuals. Since some researchers have obtained good forecasts using a single Kalman filter, we tested MMAE's ability to make time series predictions. Our Kalman filters have a dynamics model based on a Box-Jenkins Auto-Regressive Moving Average (ARMA) model and a measure model with additive noise. The time-series prediction is based on the probabilistic weighted Kalman filter predictions. We make a probability interval about that estimate also based on the filter probabilities. In a Monte Carlo analysis, we test this MMAE approach and report the results based on many different criteria. Our analysis tests the robustness of the approach by testing its ability to make predictions when the Kalman filter dynamics models did not match the data generation time-series model. Our analysis indicates benefits in applying multiple model adaptive estimation for time series analysis.
Book Synopsis New Introduction to Multiple Time Series Analysis by : Helmut Lütkepohl
Download or read book New Introduction to Multiple Time Series Analysis written by Helmut Lütkepohl and published by Springer Science & Business Media. This book was released on 2007-07-26 with total page 792 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the new and totally revised edition of Lütkepohl’s classic 1991 work. It provides a detailed introduction to the main steps of analyzing multiple time series, model specification, estimation, model checking, and for using the models for economic analysis and forecasting. The book now includes new chapters on cointegration analysis, structural vector autoregressions, cointegrated VARMA processes and multivariate ARCH models. The book bridges the gap to the difficult technical literature on the topic. It is accessible to graduate students in business and economics. In addition, multiple time series courses in other fields such as statistics and engineering may be based on it.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1992 with total page 1572 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Adaptive Estimation and Control by : Keigo Watanabe
Download or read book Adaptive Estimation and Control written by Keigo Watanabe and published by . This book was released on 1991 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unifies the partitioned adaptive estimators for stochastic systems and applies them to other estimation and control problems. The techniques, not restricted to lumped-parameter systems with unknown constant parameters, serve as a starting point for more complicated problems.
Book Synopsis Independent Component Analysis by : Aapo Hyvärinen
Download or read book Independent Component Analysis written by Aapo Hyvärinen and published by John Wiley & Sons. This book was released on 2004-04-05 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to ICA for students and practitioners Independent Component Analysis (ICA) is one of the most exciting new topics in fields such as neural networks, advanced statistics, and signal processing. This is the first book to provide a comprehensive introduction to this new technique complete with the fundamental mathematical background needed to understand and utilize it. It offers a general overview of the basics of ICA, important solutions and algorithms, and in-depth coverage of new applications in image processing, telecommunications, audio signal processing, and more. Independent Component Analysis is divided into four sections that cover: * General mathematical concepts utilized in the book * The basic ICA model and its solution * Various extensions of the basic ICA model * Real-world applications for ICA models Authors Hyvarinen, Karhunen, and Oja are well known for their contributions to the development of ICA and here cover all the relevant theory, new algorithms, and applications in various fields. Researchers, students, and practitioners from a variety of disciplines will find this accessible volume both helpful and informative.
Book Synopsis Independent Component Analysis and Blind Signal Separation by : Justinian Rosca
Download or read book Independent Component Analysis and Blind Signal Separation written by Justinian Rosca and published by Springer. This book was released on 2006-02-27 with total page 1000 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 6th International Conference on Independent Component Analysis and Blind Source Separation, ICA 2006, held in Charleston, SC, USA, in March 2006. The 120 revised papers presented were carefully reviewed and selected from 183 submissions. The papers are organized in topical sections on algorithms and architectures, applications, medical applications, speech and signal processing, theory, and visual and sensory processing.
Book Synopsis Adaptive Estimation in Time-series Models by : Feike C. Drost
Download or read book Adaptive Estimation in Time-series Models written by Feike C. Drost and published by . This book was released on 1994 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Lasso for Autoregressive and Moving Average Coeffi[ci]ents Via Residuals of Unobservable Time Series by : Hanh Nguyen
Download or read book Lasso for Autoregressive and Moving Average Coeffi[ci]ents Via Residuals of Unobservable Time Series written by Hanh Nguyen and published by . This book was released on 2018 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: This dissertation contains four topics in time series data analysis. First, we propose the oracle model selection for autoregressive time series when the observations are contaminated with trend. An adaptive least absolute shrinkage and selection operator (LASSO) type model selection method is used after the trend is estimated by non-parametric B-splines method. The first step is to estimate the trend by B-splines method and then calculate the detrended residuals. The second step is to use the residuals as if they were observations to optimize an adaptive LASSO type objective function. The oracle properties of such an Adaptive Lasso model selection procedure are established; that is, the proposed method can identify the true model with probability approaching one as the sample size increases, and the asymptotic properties of estimators are not affected by the replacement of observations with detrended residuals. The extensive simulation studies of several constrained and unconstrained autoregressive models also confirm the theoretical results. The method is illustrated by two time series data sets, the annual U.S. tobacco production and annual tree ring width measurements. Second, we generalize our first topic to a more general class of time series using the autoregressive and moving-average (ARMA) model. The ARMA model class is the building block for stationary time series analysis. We adopt the two-step method non-parametric trend estimation with B-spline and model selection and model estimation with the adaptive LASSO. We prove that such model selection and model estimation procedure possesses the oracle properties. Another important objective of this topic is forecasting time series with trend. We approach the forecasting problem by two methods: the empirical method by using the one-step ahead prediction in time series and the bagging method. Our simulation studies show that both methods are efficient with the decreased mean square error when the sample size increases. Simulation studies are adopted to illustrate the asymptotic result of our proposed method for model selection and model estimation with twelve ARMA(p, q) models, in which p an q are in the range from 1 to 15. The method is also illustrated by two time series data sets from the New York State Energy Research and Development Authority (NYSERDA), a public benefit corporation which offers data and analysis to help New Yorkers increase energy efficiency. Third, we propose a new model class, which is motivated by lag effects of covariates on the dependent variable. Our paper aims at providing more accurate statistical analysis for the relationship, for example, between the outcome of an event that occurs once every several years and the covariates that have observations every year. Lag effects have received a great deal of attention since Almon (1965) proposed linear distributed lag models to model the dependence of time series on several regressors from a correlated sequence. Motivated by the linear distributed lag model, we propose distributed generalized linear models as well as the estimation procedure for the model coefficients. The estimators from our proposed procedure are shown to be oracle or asymptotically efficient. Simulation studies confirm the asymptotic properties of the estimators and present consequences of model misspecification as well as better model prediction accuracy. The application is illustrated by analysis of the presidential election data in 2016. Fourth, we aim to provide an easy-to-use data analysis procedure for linear regression with non-independent errors. In practice, errors in regression model may be non-independent. In such situation, it is usually suitable to assume that the error terms for the model follow a time series structure. In fact, this type of model structure (reffered as RegARMA) has received great interests from researchers. Pierce (1971) discussed a nonlinear least squares estimation of RegARMA; Greenhouse et al. (1987) studied biological rhythm data by using the RegARMA model. Recently, Wu and Wang (2012) used the shrinkage estimation procedure to analyze data using RegARMA. However, in the literature the trend factor of the time series has not been considered. We will use the same idea of the two step-procedure as in the first project and the second project for our approach. We first estimate the trend of the time series by using a non-parametric method such as B-spline or linear Kernel. We then use the adaptive LASSO method for model selection and model estimation of the linear part and the time series error part. Simulation results show that our approach works quite well. However, it would be very interesting and challenging to improve the estimations and extend the estimation method to more complicated models, which will be the focus of the future research.
Book Synopsis Adaptive Estimation for Financial Time Series by : Danilo Mercurio
Download or read book Adaptive Estimation for Financial Time Series written by Danilo Mercurio and published by . This book was released on 2004 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis New Algorithms for Moving-Bank Multiple Model Adaptive Estimation by : Juan R. Vasquez
Download or read book New Algorithms for Moving-Bank Multiple Model Adaptive Estimation written by Juan R. Vasquez and published by . This book was released on 1998-05-01 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this research is to provide methods for generating precise parameter estimates in the face of potentially significant parameter variations such as system component failures. The standard Multiple Model Adaptive Estimation (MMAE) algorithm uses a bank of Kalman filters, each based on a different model of the system. A new moving-bank MMAE algorithm is developed based on exploitation of the density data available from the MMAE. The methods used to exploit this information include various measures of the density data and a decision-making logic used to move, expand, and contract the MMAE bank of filters. Parameter discretization within the MMAE refers to selection of the parameter values assumed by the elemental Kalman filters. A new parameter discretization method is developed based on the probabilities associated with the generalized Chi-Squared random variables formed by residual information from the elemental Kalman filters within the MMAE. Modifications to an existing discretization method are also presented, permitting application of this method in real time and to nonlinear system models or linear/linearized models that are unstable or astable. These new algorithms are validated through computer simulation of an aircraft navigation system subjected to interference/jamming while attempting a successful precision landing of the aircraft.
Book Synopsis Efficient and Adaptive Estimation for Semiparametric Models by : Peter J. Bickel
Download or read book Efficient and Adaptive Estimation for Semiparametric Models written by Peter J. Bickel and published by . This book was released on 1993 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating with the 1983 Mathematical Sciences Lectures at Johns Hopkins given by Peter J. Bickel and Jon A. Wellner, this volume is about estimation in situations where enough is known to model some features of the data parametrically but not enough is known to assume anything for other features. Such models have arisen in a wide variety of contexts in recent years, particularly in economics, epidemiology, and astronomy. The focus is on asymptotic theory, and the scope is limited to models for independent, identically distributed observations. Annotation c. by Book News, Inc., Portland, Or.
Book Synopsis New Variations of Multiple Model Adaptive Estimation for Improved Tracking and Identification by : Christopher K. Nebelecky
Download or read book New Variations of Multiple Model Adaptive Estimation for Improved Tracking and Identification written by Christopher K. Nebelecky and published by . This book was released on 2013 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple model adaptive estimation (MMAE) is a recursive algorithm that uses a bank of estimators, each purposefully dependent on a particular hypothesis, to determine an estimate of an uncertain system under consideration while simultaneously tracking the system state. The first generation of MMAE, introduced by Magill in 1965 considered the estimators to act independently and in parallel, determining state estimates conditional with each hypothesis. Through computation of a normalized mode-conditioned likelihood, the conditional probability that each hypothesis correctly models the system is computed. Since Magill's seminal work, many offshoots of MMAE have been developed. Modifications have been reported, but are typically on on an application specific basis which limits their versatility. In this dissertation, two variations of MMAE are considered. The first variation is based on an observed flaw which leads to degenerate tracking performance. The second variation is motivated by previous research which showed improved convergence performance by considering a generalized mode-conditioned likelihood function for determining the hypothesis conditional probabilities. Each estimator, or specifically Kalman filter, is designed around a particular system hypothesis. If the hypothesis is not sufficiently close to the true system, the resulting filter will generally produce erroneous estimates which do not track the system. This is because each filter believes that the hypothesized system is optimal. Further, the state error covariances resulting from such a suboptimal filter will be inconsistent because they have no knowledge of the incorrect hypothesized model. By explicitly accounting for the deviation of the hypothesis, recursions are developed which, when combined with MMAE are shown to provide superior tracking performance over the standard MMAE. Additionally the proposed variation, called model error MMAE, is shown to provide acceptable tracking performance for dynamically switching systems at a fraction of the computational expense of other algorithms specifically developed for that application. The second variation, referred to as generalized multiple model adaptive estimation (GMMAE), uses an augmented vector of current and past residuals to drive the recursion for the hypothesis conditional probabilities. Necessary for that recursion is evaluation of the time-domain autocovariance matrix of the residual sequence. When filtering linear (and linearized) systems, the autocovariance can be analytically expressed as a function of the system matrices, covariances and filter gain. When filtering nonlinear systems using the Unscented filter, analytic expressions for the autocovariance are not possible.^Motivated to include Unscented filters within the GMMAE framework, a method for calculating the time-domain autocovariance of the residual sequence from an Unscented filter is presented. The proposed method is validated analytically on a simplified system and simulation results are presented using the algorithm for process noise estimation in a planar tracking problem.
Book Synopsis Long-Range Dependence and Self-Similarity by : Vladas Pipiras
Download or read book Long-Range Dependence and Self-Similarity written by Vladas Pipiras and published by Cambridge University Press. This book was released on 2017-04-18 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This modern and comprehensive guide to long-range dependence and self-similarity starts with rigorous coverage of the basics, then moves on to cover more specialized, up-to-date topics central to current research. These topics concern, but are not limited to, physical models that give rise to long-range dependence and self-similarity; central and non-central limit theorems for long-range dependent series, and the limiting Hermite processes; fractional Brownian motion and its stochastic calculus; several celebrated decompositions of fractional Brownian motion; multidimensional models for long-range dependence and self-similarity; and maximum likelihood estimation methods for long-range dependent time series. Designed for graduate students and researchers, each chapter of the book is supplemented by numerous exercises, some designed to test the reader's understanding, while others invite the reader to consider some of the open research problems in the field today.
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