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Author: Jian Chen Publisher: ISBN: Category : Bayesian statistical decision theory Languages : en Pages : 242
Book Description
We consider the different loss functions that are appropriate for the Bayesian analysis of some time series models. The Bayes inference and forecasting under these loss functions are given. For the autoregressive model, with the Normal-Gamma and Jeffreys' priors, the posteriors are found and Bayes estimates for the parameters in the model under the different loss functions are derived, the probability density function of k-step ahead Bayes prediction is derived in a concise matrix format. In particular, Bayes estimates of the one-step ahead forecasting under the different loss functions are given. We provide the practical k-step ahead Bayesian forecasting under these loss functions. The Bayes estimates and one-step ahead and two-step ahead forecasting results under these loss functions are calculated. Under the Normal-Gamma and Jeffreys' priors, Wolfer sunspot numbers data is used to illustrate Bayes inferences and forecasts to the real life data. For the moving average model, under the Gamma-Normal and Jeffreys' priors, based on the approximate likelihood function, the posteriors and one-step ahead forecasting probability density function are derived. Then we obtain the Bayes estimates for the parameters and predictive inferences for moving average processes under the different loss functions. The simulation of MA(2) model and the Bayes analysis and forecasting of the simulated data are performed. The IBM common stock closing prices from May 17th, 1961 to November 2nd, 1962, are used to demonstrate the model identification and the derived Bayes posterior and predictive inference for a real life data with ARIMA(0,1,1) model. The author uses SAS for Bayesian data simulation and complex Bayesian analysis.
Author: Jian Chen Publisher: ISBN: Category : Bayesian statistical decision theory Languages : en Pages : 242
Book Description
We consider the different loss functions that are appropriate for the Bayesian analysis of some time series models. The Bayes inference and forecasting under these loss functions are given. For the autoregressive model, with the Normal-Gamma and Jeffreys' priors, the posteriors are found and Bayes estimates for the parameters in the model under the different loss functions are derived, the probability density function of k-step ahead Bayes prediction is derived in a concise matrix format. In particular, Bayes estimates of the one-step ahead forecasting under the different loss functions are given. We provide the practical k-step ahead Bayesian forecasting under these loss functions. The Bayes estimates and one-step ahead and two-step ahead forecasting results under these loss functions are calculated. Under the Normal-Gamma and Jeffreys' priors, Wolfer sunspot numbers data is used to illustrate Bayes inferences and forecasts to the real life data. For the moving average model, under the Gamma-Normal and Jeffreys' priors, based on the approximate likelihood function, the posteriors and one-step ahead forecasting probability density function are derived. Then we obtain the Bayes estimates for the parameters and predictive inferences for moving average processes under the different loss functions. The simulation of MA(2) model and the Bayes analysis and forecasting of the simulated data are performed. The IBM common stock closing prices from May 17th, 1961 to November 2nd, 1962, are used to demonstrate the model identification and the derived Bayes posterior and predictive inference for a real life data with ARIMA(0,1,1) model. The author uses SAS for Bayesian data simulation and complex Bayesian analysis.
Author: Raquel Prado Publisher: CRC Press ISBN: 1498747043 Category : Mathematics Languages : en Pages : 473
Book Description
• Expanded on aspects of core model theory and methodology. • Multiple new examples and exercises. • Detailed development of dynamic factor models. • Updated discussion and connections with recent and current research frontiers.
Author: Andy Pole Publisher: CRC Press ISBN: 1482267438 Category : Business & Economics Languages : en Pages : 432
Book Description
Practical in its approach, Applied Bayesian Forecasting and Time Series Analysis provides the theories, methods, and tools necessary for forecasting and the analysis of time series. The authors unify the concepts, model forms, and modeling requirements within the framework of the dynamic linear mode (DLM). They include a complete theoretical development of the DLM and illustrate each step with analysis of time series data. Using real data sets the authors: Explore diverse aspects of time series, including how to identify, structure, explain observed behavior, model structures and behaviors, and interpret analyses to make informed forecasts Illustrate concepts such as component decomposition, fundamental model forms including trends and cycles, and practical modeling requirements for routine change and unusual events Conduct all analyses in the BATS computer programs, furnishing online that program and the more than 50 data sets used in the text The result is a clear presentation of the Bayesian paradigm: quantified subjective judgements derived from selected models applied to time series observations. Accessible to undergraduates, this unique volume also offers complete guidelines valuable to researchers, practitioners, and advanced students in statistics, operations research, and engineering.
Author: Raquel Prado Publisher: CRC Press ISBN: 1420093363 Category : Mathematics Languages : en Pages : 375
Book Description
Focusing on Bayesian approaches and computations using simulation-based methods for inference, Time Series: Modeling, Computation, and Inference integrates mainstream approaches for time series modeling with significant recent developments in methodology and applications of time series analysis. It encompasses a graduate-level account of Bayesian time series modeling and analysis, a broad range of references to state-of-the-art approaches to univariate and multivariate time series analysis, and emerging topics at research frontiers. The book presents overviews of several classes of models and related methodology for inference, statistical computation for model fitting and assessment, and forecasting. The authors also explore the connections between time- and frequency-domain approaches and develop various models and analyses using Bayesian tools, such as Markov chain Monte Carlo (MCMC) and sequential Monte Carlo (SMC) methods. They illustrate the models and methods with examples and case studies from a variety of fields, including signal processing, biomedicine, and finance. Data sets, R and MATLAB® code, and other material are available on the authors’ websites. Along with core models and methods, this text offers sophisticated tools for analyzing challenging time series problems. It also demonstrates the growth of time series analysis into new application areas.
Author: Mike West Publisher: Springer Science & Business Media ISBN: 1475793650 Category : Mathematics Languages : en Pages : 720
Book Description
In this book we are concerned with Bayesian learning and forecast ing in dynamic environments. We describe the structure and theory of classes of dynamic models, and their uses in Bayesian forecasting. The principles, models and methods of Bayesian forecasting have been developed extensively during the last twenty years. This devel opment has involved thorough investigation of mathematical and sta tistical aspects of forecasting models and related techniques. With this has come experience with application in a variety of areas in commercial and industrial, scientific and socio-economic fields. In deed much of the technical development has been driven by the needs of forecasting practitioners. As a result, there now exists a relatively complete statistical and mathematical framework, although much of this is either not properly documented or not easily accessible. Our primary goals in writing this book have been to present our view of this approach to modelling and forecasting, and to provide a rea sonably complete text for advanced university students and research workers. The text is primarily intended for advanced undergraduate and postgraduate students in statistics and mathematics. In line with this objective we present thorough discussion of mathematical and statistical features of Bayesian analyses of dynamic models, with illustrations, examples and exercises in each Chapter.
Author: Dinesh C.S. Bisht Publisher: CRC Press ISBN: 1000433846 Category : Mathematics Languages : en Pages : 183
Book Description
Future predictions are always a topic of interest. Precise estimates are crucial in many activities as forecasting errors can lead to big financial loss. The sequential analysis of data and information gathered from past to present is call time series analysis. This book covers the recent advancements in time series forecasting. The book includes theoretical as well as recent applications of time series analysis. It focuses on the recent techniques used, discusses a combination of methodology and applications, presents traditional and advanced tools, new applications, and identifies the gaps in knowledge in engineering applications. This book is aimed at scientists, researchers, postgraduate students and engineers in the areas of supply chain management, production, inventory planning, and statistical quality control.
Author: Donald A. Berry Publisher: John Wiley & Sons ISBN: 9780471118565 Category : Business & Economics Languages : en Pages : 610
Book Description
This book is a definitive work that captures the current state of knowledge of Bayesian Analysis in Statistics and Econometrics and attempts to move it forward. It covers such topics as foundations, forecasting inferential matters, regression, computation and applications.
Author: David Barber Publisher: Cambridge University Press ISBN: 0521196760 Category : Computers Languages : en Pages : 432
Book Description
The first unified treatment of time series modelling techniques spanning machine learning, statistics, engineering and computer science.
Author: Chris Chatfield Publisher: CRC Press ISBN: 1420036203 Category : Business & Economics Languages : en Pages : 281
Book Description
From the author of the bestselling "Analysis of Time Series," Time-Series Forecasting offers a comprehensive, up-to-date review of forecasting methods. It provides a summary of time-series modelling procedures, followed by a brief catalogue of many different time-series forecasting methods, ranging from ad-hoc methods through ARIMA and state-space
Author: Jian Chen
Author: Jian Chen
Author: Raquel Prado
Author: Andy Pole
Author: Raquel Prado
Author: Mike West
Author: Dinesh C.S. Bisht
Author: Donald A. Berry
Author: David Barber
Author: Chris Chatfield
Author: