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Author: Peter M. Robinson Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
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.
Author: Peter M. Robinson Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
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.
Author: Ibrahim Dulger Publisher: ISBN: 9781423529293 Category : Economic forecasting Languages : en Pages : 153
Book Description
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.
Author: Helmut Lütkepohl Publisher: Springer Science & Business Media ISBN: 3540277528 Category : Business & Economics Languages : en Pages : 765
Book Description
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.
Author: Justinian Rosca Publisher: Springer ISBN: 3540326316 Category : Computers Languages : en Pages : 1000
Book Description
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.
Author: Keigo Watanabe Publisher: ISBN: Category : Technology & Engineering Languages : en Pages : 618
Book Description
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.
Author: Aapo Hyvärinen Publisher: John Wiley & Sons ISBN: 0471464198 Category : Science Languages : en Pages : 505
Book Description
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.
Author: Peter M. Robinson
Author: Peter M. Robinson
Author: Douglas Gardiner Steigerwald
Author: Qi Li
Author: Helmut Lütkepohl
Author: Ibrahim Dulger
Author: 
Author: Helmut Lütkepohl
Author: Justinian Rosca
Author: Keigo Watanabe
Author: Aapo Hyvärinen