Download or read book An Adaptive Empirical Likelihood Test for Nonlinear Time Series Models written by Songxi Chen and published by . This book was released on 2004 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book EMPIRICAL LIKELIHOOD FOR CHANGE POINT DETECTION AND ESTIMATION IN TIME SERIES MODELS written by Ramadha D Piyadi Gamage and published by . This book was released on 2017 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical Likelihood (EL) method introduced by Owen (1988) is a widely used nonparametric tool for constructing confidence regions due to its appealing asymptotic distribution of the likelihood-ratio-type statistic which is same as the one under the parametric settings. However, the EL method was introduced to be used for independent data, hence it becomes difficult to apply it to dependent data such as time series data. Owen (2001) suggested using the conditional likelihood to remove the dependence structure and generate the estimating equations. Monti (1997) developed the idea of extending the EL method to short-memory time series models using the Whittle's (1953) estimation method to obtain an M-estimator of the periodogram ordinates of a time series which are asymptotically independent. This reduces a dependent data problem into an independent data problem. Nordman and Lahiri (2006) also formulated a frequency domain empirical likelihood (FDEL) using spectral estimating equations which can be used for short- and long- range dependent data. FDEL applies a data transformation which weakens the dependence structure of the data hence, allowing to use the EL method for the transformed data which is considered to be asymptotically independent. Unfortunately, there is a good chance that the solution to the profile empirical likelihood function computation which involves constrained maximization does not exist which raises some computational issues as mentioned by Chen et al. (2008). To overcome this difficulty, Chen et al. (2008) proposed an adjusted empirical likelihood (AEL) ratio function by adding a pseudo term to guarantee the zero to be an interior point of the convex hull, therefore, the required numerical maximization is guaranteed to have a solution always. This dissertation focuses on developing novel nonparametric tests based on the empirical likelihood to estimate and detect changes in parameters of various times series models. First part is focused on the AEL for short-memory time series models such as autoregression (AR), moving average (MA), autoregressive moving average (ARMA), etc. I incorporated Monti's (1997) approach along with Nordman and Lahiri's (2006) formulation, to propose an AEL for short-memory dependence data. In the second part, an AEL-type statistic has been established for long-memory time series models suggested by Yau (2012). The third part of the dissertation focuses on the detection of changes in structures of time series models based on the EL method. Real data sets are used in each section to illustrate the performance of the proposed methods.

Download or read book Empirical Likelihood written by Art B. Owen and published by CRC Press. This book was released on 2001-05-18 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Empirical likelihood provides inferences whose validity does not depend on specifying a parametric model for the data. Because it uses a likelihood, the method has certain inherent advantages over resampling methods: it uses the data to determine the shape of the confidence regions, and it makes it easy to combined data from multiple sources. It al

Download or read book Empirical Likelihood in Long Memory Time Series Models written by Chun Yip Yau and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article studies the empirical likelihood method for long-memory time series models. By virtue of the Whittle likelihood, one obtains a score function that can be viewed as an estimating equation of the parameters of a fractional integrated autoregressive moving average (ARFIMA) model. This score function is used to obtain an empirical likelihood ratio which is shown to be asymptotically chi-square distributed. Confidence regions for the parameters are constructed based on the asymptotic distribution of the empirical likelihood ratio. Bartlett correction and finite sample properties of the empirical likelihood confidence regions are examined.

Download or read book Non Linear Time Series Models in Empirical Finance written by Philip Hans Franses and published by Cambridge University Press. This book was released on 2000-07-27 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2000 volume reviews non-linear time series models, and their applications to financial markets.

Download or read book Nonlinear Time Series Analysis written by Ruey S. Tsay and published by John Wiley & Sons. This book was released on 2018-09-14 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive resource that draws a balance between theory and applications of nonlinear time series analysis Nonlinear Time Series Analysis offers an important guide to both parametric and nonparametric methods, nonlinear state-space models, and Bayesian as well as classical approaches to nonlinear time series analysis. The authors—noted experts in the field—explore the advantages and limitations of the nonlinear models and methods and review the improvements upon linear time series models. The need for this book is based on the recent developments in nonlinear time series analysis, statistical learning, dynamic systems and advanced computational methods. Parametric and nonparametric methods and nonlinear and non-Gaussian state space models provide a much wider range of tools for time series analysis. In addition, advances in computing and data collection have made available large data sets and high-frequency data. These new data make it not only feasible, but also necessary to take into consideration the nonlinearity embedded in most real-world time series. This vital guide: • Offers research developed by leading scholars of time series analysis • Presents R commands making it possible to reproduce all the analyses included in the text • Contains real-world examples throughout the book • Recommends exercises to test understanding of material presented • Includes an instructor solutions manual and companion website Written for students, researchers, and practitioners who are interested in exploring nonlinearity in time series, Nonlinear Time Series Analysis offers a comprehensive text that explores the advantages and limitations of the nonlinear models and methods and demonstrates the improvements upon linear time series models.

Download or read book Modern Mathematical Tools and Techniques in Capturing Complexity written by Leandro Pardo and published by Springer Science & Business Media. This book was released on 2011-05-26 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real-life problems are often quite complicated in form and nature and, for centuries, many different mathematical concepts, ideas and tools have been developed to formulate these problems theoretically and then to solve them either exactly or approximately. This book aims to gather a collection of papers dealing with several different problems arising from many disciplines and some modern mathematical approaches to handle them. In this respect, the book offers a wide overview on many of the current trends in Mathematics as valuable formal techniques in capturing and exploiting the complexity involved in real-world situations. Several researchers, colleagues, friends and students of Professor María Luisa Menéndez have contributed to this volume to pay tribute to her and to recognize the diverse contributions she had made to the fields of Mathematics and Statistics and to the profession in general. She had a sweet and strong personality, and instilled great values and work ethics in her students through her dedication to teaching and research. Even though the academic community lost her prematurely, she would continue to provide inspiration to many students and researchers worldwide through her published work.

Download or read book Handbook of Approximate Bayesian Computation written by Scott A. Sisson and published by CRC Press. This book was released on 2018-09-03 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the world becomes increasingly complex, so do the statistical models required to analyse the challenging problems ahead. For the very first time in a single volume, the Handbook of Approximate Bayesian Computation (ABC) presents an extensive overview of the theory, practice and application of ABC methods. These simple, but powerful statistical techniques, take Bayesian statistics beyond the need to specify overly simplified models, to the setting where the model is defined only as a process that generates data. This process can be arbitrarily complex, to the point where standard Bayesian techniques based on working with tractable likelihood functions would not be viable. ABC methods finesse the problem of model complexity within the Bayesian framework by exploiting modern computational power, thereby permitting approximate Bayesian analyses of models that would otherwise be impossible to implement. The Handbook of ABC provides illuminating insight into the world of Bayesian modelling for intractable models for both experts and newcomers alike. It is an essential reference book for anyone interested in learning about and implementing ABC techniques to analyse complex models in the modern world.

Download or read book Empirical Likelihood Method for Time Series Analysis written by 小方浩明 and published by . This book was released on 2007 with total page 80 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Nonlinear Time Series Analysis with R written by Ray Huffaker and published by Oxford University Press. This book was released on 2017-10-20 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Time Series Analysis with R provides a practical guide to emerging empirical techniques allowing practitioners to diagnose whether highly fluctuating and random appearing data are most likely driven by random or deterministic dynamic forces. It joins the chorus of voices recommending 'getting to know your data' as an essential preliminary evidentiary step in modelling. Time series are often highly fluctuating with a random appearance. Observed volatility is commonly attributed to exogenous random shocks to stable real-world systems. However, breakthroughs in nonlinear dynamics raise another possibility: highly complex dynamics can emerge endogenously from astoundingly parsimonious deterministic nonlinear models. Nonlinear Time Series Analysis (NLTS) is a collection of empirical tools designed to aid practitioners detect whether stochastic or deterministic dynamics most likely drive observed complexity. Practitioners become 'data detectives' accumulating hard empirical evidence supporting their modelling approach. This book is targeted to professionals and graduate students in engineering and the biophysical and social sciences. Its major objectives are to help non-mathematicians — with limited knowledge of nonlinear dynamics — to become operational in NLTS; and in this way to pave the way for NLTS to be adopted in the conventional empirical toolbox and core coursework of the targeted disciplines. Consistent with modern trends in university instruction, the book makes readers active learners with hands-on computer experiments in R code directing them through NLTS methods and helping them understand the underlying logic (please see www.marco.bittelli.com). The computer code is explained in detail so that readers can adjust it for use in their own work. The book also provides readers with an explicit framework — condensed from sound empirical practices recommended in the literature — that details a step-by-step procedure for applying NLTS in real-world data diagnostics.

Download or read book Nonlinear Time Series written by Jiti Gao and published by CRC Press. This book was released on 2007-03-22 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: Useful in the theoretical and empirical analysis of nonlinear time series data, semiparametric methods have received extensive attention in the economics and statistics communities over the past twenty years. Recent studies show that semiparametric methods and models may be applied to solve dimensionality reduction problems arising from using fully

Download or read book Empirical Likelihood Estimation and Testing in the Restricted Linear Model written by Clifford L. F. Attfield and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book New Directions in Time Series Analysis written by David Brillinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications NEW DIRECTIONS IN TIME SERIES ANALYSIS, PART II is based on the proceedings of the IMA summer program "New Directions in Time Series Analysis. " We are grateful to David Brillinger, Peter Caines, John Geweke, Emanuel Parzen, Murray Rosenblatt, and Murad Taqqu for organizing the program and we hope that the remarkable excitement and enthusiasm of the participants in this interdisciplinary effort are communicated to the reader. A vner Friedman Willard Miller, Jr. PREFACE Time Series Analysis is truly an interdisciplinary field because development of its theory and methods requires interaction between the diverse disciplines in which it is applied. To harness its great potential, strong interaction must be encouraged among the diverse community of statisticians and other scientists whose research involves the analysis of time series data. This was the goal of the IMA Workshop on "New Directions in Time Series Analysis. " The workshop was held July 2-July 27, 1990 and was organized by a committee consisting of Emanuel Parzen (chair), David Brillinger, Murray Rosenblatt, Murad S. Taqqu, John Geweke, and Peter Caines. Constant guidance and encouragement was provided by Avner Friedman, Director of the IMA, and his very helpful and efficient staff. The workshops were organized by weeks. It may be of interest to record the themes that were announced in the IMA newsletter describing the workshop: l.

Download or read book Empirical Likelihood Methods in Econometrics written by Yuichi Kitamura and published by . This book was released on 2006 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments in empirical likelihood (EL) methods are reviewed. First, to put the method in perspective, two interpretations of empirical likelihood are presented, one as a nonparametric maximum likelihood estimation method (NPMLE) and the other as a generalized minimum contrast estimator (GMC). The latter interpretation provides a clear connection between EL, GMM, GEL and other related estimators. Second, EL is shown to have various advantages over other methods. The theory of large deviations demonstrates that EL emerges naturally in achieving asymptotic optimality both for estimation and testing. Interestingly, higher order asymptotic analysis also suggests that EL is generally a preferred method. Third, extensions of EL are discussed in various settings, including estimation of conditional moment restriction models, nonparametric specification testing and time series models. Finally, practical issues in applying EL to real data, such as computational algorithms for EL, are discussed. Numerical examples to illustrate the efficacy of the method are presented.

Download or read book Empirical Likelihood with Applications in Time Series written by Yuyi Li and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis investigates the statistical properties of Kernel Smoothed Empirical Likelihood (KSEL, e.g. Smith, 1997 and 2004) estimator and various associated inference procedures in weakly dependent data. New tests for structural stability are proposed and analysed. Asymptotic analyses and Monte Carlo experiments are applied to assess these new tests, theoretically and empirically. Chapter 1 reviews and discusses some estimation and inferential properties of Empirical Likelihood (EL, Owen, 1988) for identically and independently distributed data and compares it with Generalised EL (GEL), GMM and other estimators. KSEL is extensively treated, by specialising kernel-smoothed GEL in the working paper of Smith (2004), some of whose results and proofs are extended and refined in Chapter 2. Asymptotic properties of some tests in Smith (2004) are also analysed under local alternatives. These special treatments on KSEL lay the foundation for analyses in Chapters 3 and 4, which would not otherwise follow straightforwardly. In Chapters 3 and 4, subsample KSEL estimators are proposed to assist the development of KSEL structural stability tests to diagnose for a given breakpoint and for an unknown breakpoint, respectively, based on relevant work using GMM (e.g. Hall and Sen, 1999; Andrews and Fair, 1988; Andrews and Ploberger, 1994). It is also original in these two chapters that moment functions are allowed to be kernel-smoothed after or before the sample split, and it is rigorously proved that these two smoothing orders are asymptotically equivalent. The overall null hypothesis of structural stability is decomposed according to the identifying and overidentifying restrictions, as Hall and Sen (1999) advocate in GMM, leading to a more practical and precise structural stability diagnosis procedure. In this framework, these KSEL structural stability tests are also proved via asymptotic analysis to be capable of identifying different sources of instability, arising from parameter value change or violation of overidentifying restrictions. The analyses show that these KSEL tests follow the same limit distributions as their counterparts using GMM. To examine the finite-sample performance of KSEL structural stability tests in comparison to GMM's, Monte Carlo simulations are conducted in Chapter 5 using a simple linear model considered by Hall and Sen (1999). This chapter details some relevant computational algorithms and permits different smoothing order, kernel type and prewhitening options. In general, simulation evidence seems to suggest that compared to GMM's tests, these newly proposed KSEL tests often perform comparably. However, in some cases, the sizes of these can be slightly larger, and the false null hypotheses are rejected with much higher frequencies. Thus, these KSEL based tests are valid theoretical and practical alternatives to GMM's.

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 Likelihood ratio Test Statistic for the Finite sample Case in Nonlinear Ordinary Differential Equation Models written by Christian Tönsing and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: Likelihood ratios are frequently utilized as basis for statistical tests, for model selection criteria and for assessing parameter and prediction uncertainties, e.g. using the profile likelihood. However, translating these likelihood ratios into p-values or confidence intervals requires the exact form of the test statistic's distribution. The lack of knowledge about this distribution for nonlinear ordinary differential equation (ODE) models requires an approximation which assumes the so-called asymptotic setting, i.e. a sufficiently large amount of data. Since the amount of data from quantitative molecular biology is typically limited in applications, this finite-sample case regularly occurs for mechanistic models of dynamical systems, e.g. biochemical reaction networks or infectious disease models. Thus, it is unclear whether the standard approach of using statistical thresholds derived for the asymptotic large-sample setting in realistic applications results in valid conclusions. In this study, empirical likelihood ratios for parameters from 19 published nonlinear ODE benchmark models are investigated using a resampling approach for the original data designs. Their distributions are compared to the asymptotic approximation and statistical thresholds are checked for conservativeness. It turns out, that corrections of the likelihood ratios in such finite-sample applications are required in order to avoid anti-conservative results