Download or read book Bayesian Bandwidth Estimation in Varying coefficient Time Series Models written by Tingting Cheng and published by . This book was released on 2014 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis investigates three main topics, which are bandwidth selection for local linear estimation of time-varying coefficient time series models, nonparametric estimation of functional coefficient time series models with trending regressors and semiparametric localised bandwidth selection in kernel density estimation. First, we propose a Bayesian approach to bandwidth selection for local linear estimation of time-varying coefficient time series models, where the errors are assumed to follow the Gaussian kernel error density. A Markov chain Monte Carlo algorithm is presented to simultaneously estimate the bandwidths for local linear estimators in the regression function and the bandwidth for the Gaussian kernel error-density estimator. A Monte Carlo simulation study shows that: 1) our proposed Bayesian approach achieves better performance in estimating the bandwidths for local linear estimators than normal reference rule and cross-validation; and 2) compared with the parametric assumption of either the Gaussian or a mixture of two Gaussians, Gaussian kernel error-density assumption is a data-driven choice and helps gain robustness in terms of different specifications of the true error density. Moreover, we apply our proposed Bayesian sampling method to the estimation of bandwidth for the time-varying coefficient models that explain Okun's law and the relationship between consumption growth and income growth in the U.S. For each model, we also provide calibrated parametric forms of its time-varying coefficients. Second, we develop a functional coefficient time series model with trending regressors. We propose a local linear estimation method to estimate the unknown coefficient functions. The asymptotic distributions of the proposed local linear estimator are established under mild conditions. We further propose a Bayesian approach to select bandwidths involved in the proposed local linear estimator. Several numerical examples are provided to illustrate the finite sample behavior of the proposed methods. The results show that the local linear estimator works very well and the proposed Bayesian bandwidth selection method is better than cross-validation method. Furthermore, we employ the functional coefficient model to study the relationship between consumption per capita and income per capita in the U.S. and the results show that this functional coefficient model with our proposed local linear estimator and Bayesian bandwidth selection method performs better than other competing models in terms of both in-sample fitting and out-of-sample forecasting. Third, we propose a semiparametric localised bandwidth estimator for kernel density estimation based on strictly stationary mixing processes. We prove that the semiparametric localised bandwidth estimator is asymptotically normally distributed with root-n rate of convergence. To carry out the computation of the semiparametric localised bandwidth estimator for a given sample of data, we propose a sampling-based likelihood approach to hyperparameter estimation. Monte Carlo simulation studies show that the proposed hyperparameter estimation approach works very well, and that the proposed semiparametric localised bandwidth estimator outperforms its competitors. Applications of the new bandwidth estimator to the kernel density estimation of Eurodollar deposit rate, as well as the S&P 500 daily return under conditional heteroscedasticity, demonstrate the effectiveness and competitiveness of the proposed semiparametric localised bandwidth. In addition, we present an easily computable expression for integrated squared error of normal density estimators, mixture of two normals density estimators and Gaussian kernel density estimators under different specifications of the true density. This provides a new way of evaluating the performance of the above three common-used density estimators. The numerical studies show that: 1) closed-form of integrated squared error is more accurate than grid-point approximation; 2) gird-point approximation is not robust, especially when the true density is asymmetric; 3) when the true density is neither normal nor mixture normal densities, Gaussian kernel density estimators can provide us with more accurate estimation.

Download or read book Bayesian Bandwidth Selection in Nonparametric Time varying Coefficient Models written by Tingting Cheng and published by . This book was released on 2013 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bayesian Multivariate Time Series Methods for Empirical Macroeconomics written by Gary Koop and published by Now Publishers Inc. This book was released on 2010 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian Multivariate Time Series Methods for Empirical Macroeconomics provides a survey of the Bayesian methods used in modern empirical macroeconomics. These models have been developed to address the fact that most questions of interest to empirical macroeconomists involve several variables and must be addressed using multivariate time series methods. Many different multivariate time series models have been used in macroeconomics, but Vector Autoregressive (VAR) models have been among the most popular. Bayesian Multivariate Time Series Methods for Empirical Macroeconomics reviews and extends the Bayesian literature on VARs, TVP-VARs and TVP-FAVARs with a focus on the practitioner. The authors go beyond simply defining each model, but specify how to use them in practice, discuss the advantages and disadvantages of each and offer tips on when and why each model can be used.

Download or read book Applied Bayesian Forecasting and Time Series Analysis written by Andy Pole and published by CRC Press. This book was released on 2018-10-08 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Bayesian Sampling for Smoothing Parameter Estimation written by Shuowen Hu and published by . This book was released on 2015 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kernel density estimation is one of the most important techniques for understanding the distributional properties of data. It is understood that the effectiveness of such approach depends on the choice of a kernel function and the choice of a smoothing parameter (bandwidth). This thesis has undertaken some important topics in bandwidth selection for kernel density estimation for data that behave in various nature. The first issue evolves around selecting appropriate bandwidth given the characteristics of the local data in multivariate setting. In Chapter 3, the study proposes a kernel density estimator with tail-adaptive bandwidths. The study derives posterior of bandwidth parameters based on the Kullback-Leibler information and presented an MCMC sampling algorithm to estimate bandwidths. The Monte Carlo simulation study shows that the kernel density estimator with tail-adaptive bandwidths estimated through the proposed sampling algorithm outperforms its competitor. The tail-adaptive kernel density estimator is applied to the estimation of bivariate density of the paired daily returns of the Australian Ordinary index and S&P 500 index during the period of global financial crisis. The results show that this estimator could capture richer dynamics in the tail area than the density estimator with a global bandwidth estimated through the normal reference rule and a Bayesian sampling algorithm. The second research project investigates bandwidth selection for multimodal distributions or data that exhibits clustering behaviours. Chapter 4 proposes a cluster-adaptive bandwidth kernel density estimator for data with multimodality. This method employs a clustering algorithm to assign a different bandwidth to each cluster identified in the data set. The study derives a posterior of bandwidth parameters based on the Kullback-Leibler information and presented an MCMC sampling algorithm to estimate bandwidths. The Monte Carlo simulation study shows that when the underlying density is a mixture of normals, the kernel density estimator with cluster-adaptive bandwidths estimated through the proposed sampling algorithm outperforms its competitor. When the underlying densities are fat-tailed, the combined approach of tail- and cluster-adaptive density estimator performs the best. In an empirical study, bandwidth matrices are estimated for the cluster-adaptive kernel density estimator of eruption duration and waiting time to the next eruption collected from Old Faithful greyer, which is often analysed due to its clustering nature. The results again shows clear advantage of the proposed cluster-adaptive kernel density estimator over traditional approaches. The third topic extends the Bayesian bandwidth selection method to volatility models of financial asset return series. The study is motivated by the fact that only limited attention in the literature has been invested on the estimation of nonparametric nonlinear type of volatility models through a Bayesian approach. Chapter 5 presents a new volatility model called the semiparametic nonlinear volatility (SNV) model. Based on financial return series of major stock indices in the world, the performance of the proposed volatility model against the competing models are examined in both in-sample and out-of-sample periods. The proposed model and the Bayesian estimation method show strong and convincing performance results. The study also evaluates the empirical value-at-risk (VaR) performance of the competing models. The proposed volatility model shows the best performance in most cases.

Download or read book Nonlinear Time Series written by Jianqing Fan and published by Springer Science & Business Media. This book was released on 2008-09-11 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book that integrates useful parametric and nonparametric techniques with time series modeling and prediction, the two important goals of time series analysis. Such a book will benefit researchers and practitioners in various fields such as econometricians, meteorologists, biologists, among others who wish to learn useful time series methods within a short period of time. The book also intends to serve as a reference or text book for graduate students in statistics and econometrics.

Download or read book Time Series written by Raquel Prado and published by CRC Press. This book was released on 2010-05-21 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 t

Download or read book Partially Linear Models written by Wolfgang Härdle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.

Download or read book Smoothness Priors Analysis of Time Series written by Genshiro Kitagawa and published by Springer Science & Business Media. This book was released on 1996-08-09 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Smoothness Priors Analysis of Time Series addresses some of the problems of modeling stationary and nonstationary time series primarily from a Bayesian stochastic regression "smoothness priors" state space point of view. Prior distributions on model coefficients are parametrized by hyperparameters. Maximizing the likelihood of a small number of hyperparameters permits the robust modeling of a time series with relatively complex structure and a very large number of implicitly inferred parameters. The critical statistical ideas in smoothness priors are the likelihood of the Bayesian model and the use of likelihood as a measure of the goodness of fit of the model. The emphasis is on a general state space approach in which the recursive conditional distributions for prediction, filtering, and smoothing are realized using a variety of nonstandard methods including numerical integration, a Gaussian mixture distribution-two filter smoothing formula, and a Monte Carlo "particle-path tracing" method in which the distributions are approximated by many realizations. The methods are applicable for modeling time series with complex structures.

Download or read book Enhanced Bayesian Network Models for Spatial Time Series Prediction written by Monidipa Das and published by Springer Nature. This book was released on 2019-11-07 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph is highly contextual in the present era of spatial/spatio-temporal data explosion. The overall text contains many interesting results that are worth applying in practice, while it is also a source of intriguing and motivating questions for advanced research on spatial data science. The monograph is primarily prepared for graduate students of Computer Science, who wish to employ probabilistic graphical models, especially Bayesian networks (BNs), for applied research on spatial/spatio-temporal data. Students of any other discipline of engineering, science, and technology, will also find this monograph useful. Research students looking for a suitable problem for their MS or PhD thesis will also find this monograph beneficial. The open research problems as discussed with sufficient references in Chapter-8 and Chapter-9 can immensely help graduate researchers to identify topics of their own choice. The various illustrations and proofs presented throughout the monograph may help them to better understand the working principles of the models. The present monograph, containing sufficient description of the parameter learning and inference generation process for each enhanced BN model, can also serve as an algorithmic cookbook for the relevant system developers.

Download or read book Nonparametric Kernel Density Estimation and Its Computational Aspects written by Artur Gramacki and published by Springer. This book was released on 2017-12-21 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes computational problems related to kernel density estimation (KDE) – one of the most important and widely used data smoothing techniques. A very detailed description of novel FFT-based algorithms for both KDE computations and bandwidth selection are presented. The theory of KDE appears to have matured and is now well developed and understood. However, there is not much progress observed in terms of performance improvements. This book is an attempt to remedy this. The book primarily addresses researchers and advanced graduate or postgraduate students who are interested in KDE and its computational aspects. The book contains both some background and much more sophisticated material, hence also more experienced researchers in the KDE area may find it interesting. The presented material is richly illustrated with many numerical examples using both artificial and real datasets. Also, a number of practical applications related to KDE are presented.

Download or read book Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA written by Elias T. Krainski and published by CRC Press. This book was released on 2018-12-07 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling spatial and spatio-temporal continuous processes is an important and challenging problem in spatial statistics. Advanced Spatial Modeling with Stochastic Partial Differential Equations Using R and INLA describes in detail the stochastic partial differential equations (SPDE) approach for modeling continuous spatial processes with a Matérn covariance, which has been implemented using the integrated nested Laplace approximation (INLA) in the R-INLA package. Key concepts about modeling spatial processes and the SPDE approach are explained with examples using simulated data and real applications. This book has been authored by leading experts in spatial statistics, including the main developers of the INLA and SPDE methodologies and the R-INLA package. It also includes a wide range of applications: * Spatial and spatio-temporal models for continuous outcomes * Analysis of spatial and spatio-temporal point patterns * Coregionalization spatial and spatio-temporal models * Measurement error spatial models * Modeling preferential sampling * Spatial and spatio-temporal models with physical barriers * Survival analysis with spatial effects * Dynamic space-time regression * Spatial and spatio-temporal models for extremes * Hurdle models with spatial effects * Penalized Complexity priors for spatial models All the examples in the book are fully reproducible. Further information about this book, as well as the R code and datasets used, is available from the book website at http://www.r-inla.org/spde-book. The tools described in this book will be useful to researchers in many fields such as biostatistics, spatial statistics, environmental sciences, epidemiology, ecology and others. Graduate and Ph.D. students will also find this book and associated files a valuable resource to learn INLA and the SPDE approach for spatial modeling.

Download or read book Bayesian Time Series Models written by David Barber and published by Cambridge University Press. This book was released on 2011-08-11 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first unified treatment of time series modelling techniques spanning machine learning, statistics, engineering and computer science.

Download or read book Geographically Weighted Regression written by A. Stewart Fotheringham and published by John Wiley & Sons. This book was released on 2003-02-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geographical Weighted Regression (GWR) is a new local modelling technique for analysing spatial analysis. This technique allows local as opposed to global models of relationships to be measured and mapped. This is the first and only book on this technique, offering comprehensive coverage on this new 'hot' topic in spatial analysis. * Provides step-by-step examples of how to use the GWR model using data sets and examples on issues such as house price determinants, educational attainment levels and school performance statistics * Contains a broad discussion of and basic concepts on GWR through to ideas on statistical inference for GWR models * uniquely features accompanying author-written software that allows users to undertake sophisticated and complex forms of GWR within a user-friendly, Windows-based, front-end (see book for details).

Download or read book Intermediate Statistics and Econometrics written by Dale J. Poirier and published by MIT Press. This book was released on 1995 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: The standard introductory texts to mathematical statistics leave the Bayesian approach to be taught later in advanced topics courses-giving students the impression that Bayesian statistics provide but a few techniques appropriate in only special circumstances. Nothing could be further from the truth, argues Dale Poirier, who has developed a course for teaching comparatively both the classical and the Bayesian approaches to econometrics. Poirier's text provides a thoroughly modern, self-contained, comprehensive, and accessible treatment of the probability and statistical foundations of econometrics with special emphasis on the linear regression model. Written primarily for advanced undergraduate and graduate students who are pursuing research careers in economics, Intermediate Statistics and Econometrics offers a broad perspective, bringing together a great deal of diverse material. Its comparative approach, emphasis on regression and prediction, and numerous exercises and references provide a solid foundation for subsequent courses in econometrics and will prove a valuable resource to many nonspecialists who want to update their quantitative skills. The introduction closes with an example of a real-world data set-the Challengerspace shuttle disaster-that motivates much of the text's theoretical discussion. The ten chapters that follow cover basic concepts, special distributions, distributions of functions of random variables, sampling theory, estimation, hypothesis testing, prediction, and the linear regression model. Appendixes contain a review of matrix algebra, computation, and statistical tables.

Download or read book Applied Bayesian Hierarchical Methods written by Peter D. Congdon and published by CRC Press. This book was released on 2010-05-19 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of Markov chain Monte Carlo (MCMC) methods for estimating hierarchical models involves complex data structures and is often described as a revolutionary development. An intermediate-level treatment of Bayesian hierarchical models and their applications, Applied Bayesian Hierarchical Methods demonstrates the advantages of a Bayesian approach

Download or read book Kernel Smoothing written by M.P. Wand and published by CRC Press. This book was released on 1994-12-01 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kernel smoothing refers to a general methodology for recovery of underlying structure in data sets. The basic principle is that local averaging or smoothing is performed with respect to a kernel function. This book provides uninitiated readers with a feeling for the principles, applications, and analysis of kernel smoothers. This is facilita