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Author: Chun Yip Yau Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
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.
Author: Chun Yip Yau Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
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.
Author: Yan Liu Publisher: Springer ISBN: 9811001529 Category : Mathematics Languages : en Pages : 136
Book Description
This book integrates the fundamentals of asymptotic theory of statistical inference for time series under nonstandard settings, e.g., infinite variance processes, not only from the point of view of efficiency but also from that of robustness and optimality by minimizing prediction error. This is the first book to consider the generalized empirical likelihood applied to time series models in frequency domain and also the estimation motivated by minimizing quantile prediction error without assumption of true model. It provides the reader with a new horizon for understanding the prediction problem that occurs in time series modeling and a contemporary approach of hypothesis testing by the generalized empirical likelihood method. Nonparametric aspects of the methods proposed in this book also satisfactorily address economic and financial problems without imposing redundantly strong restrictions on the model, which has been true until now. Dealing with infinite variance processes makes analysis of economic and financial data more accurate under the existing results from the demonstrative research. The scope of applications, however, is expected to apply to much broader academic fields. The methods are also sufficiently flexible in that they represent an advanced and unified development of prediction form including multiple-point extrapolation, interpolation, and other incomplete past forecastings. Consequently, they lead readers to a good combination of efficient and robust estimate and test, and discriminate pivotal quantities contained in realistic time series models.
Author: Ramadha D Piyadi Gamage Publisher: ISBN: Category : Change-point problems Languages : en Pages : 113
Book Description
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.
Author: Wilfredo Palma Publisher: John Wiley & Sons ISBN: 0470131454 Category : Mathematics Languages : en Pages : 306
Book Description
A self-contained, contemporary treatment of the analysis of long-range dependent data Long-Memory Time Series: Theory and Methods provides an overview of the theory and methods developed to deal with long-range dependent data and describes the applications of these methodologies to real-life time series. Systematically organized, it begins with the foundational essentials, proceeds to the analysis of methodological aspects (Estimation Methods, Asymptotic Theory, Heteroskedastic Models, Transformations, Bayesian Methods, and Prediction), and then extends these techniques to more complex data structures. To facilitate understanding, the book: Assumes a basic knowledge of calculus and linear algebra and explains the more advanced statistical and mathematical concepts Features numerous examples that accelerate understanding and illustrate various consequences of the theoretical results Proves all theoretical results (theorems, lemmas, corollaries, etc.) or refers readers to resources with further demonstration Includes detailed analyses of computational aspects related to the implementation of the methodologies described, including algorithm efficiency, arithmetic complexity, CPU times, and more Includes proposed problems at the end of each chapter to help readers solidify their understanding and practice their skills A valuable real-world reference for researchers and practitioners in time series analysis, economerics, finance, and related fields, this book is also excellent for a beginning graduate-level course in long-memory processes or as a supplemental textbook for those studying advanced statistics, mathematics, economics, finance, engineering, or physics. A companion Web site is available for readers to access the S-Plus and R data sets used within the text.
Author: Art B. Owen Publisher: CRC Press ISBN: 1420036157 Category : Mathematics Languages : en Pages : 322
Book Description
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
Author: Kun Chen Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
Bartlett correction, which improves the coverage accuracies of confidence regions, is one of the desirable features of empirical likelihood. For empirical likelihood with dependent data, previous studies on the Bartlett correction are mainly concerned with Gaussian processes. By establishing the validity of Edgeworth expansion for the signed root empirical log-likelihood ratio statistics, we show that the Bartlett correction is applicable to empirical likelihood for short-memory time series with possibly non-Gaussian innovations. The Bartlett correction is established under the assumptions that the variance of the innovation is known and the mean of the underlying process is zero for a single parameter model. In particular, the order of the coverage errors of Bartlett-corrected confidence regions can be reduced from O(n-1) to O(n-2).
Author: Jan Beran Publisher: Springer Science & Business Media ISBN: 3642355129 Category : Mathematics Languages : en Pages : 892
Book Description
Long-memory processes are known to play an important part in many areas of science and technology, including physics, geophysics, hydrology, telecommunications, economics, finance, climatology, and network engineering. In the last 20 years enormous progress has been made in understanding the probabilistic foundations and statistical principles of such processes. This book provides a timely and comprehensive review, including a thorough discussion of mathematical and probabilistic foundations and statistical methods, emphasizing their practical motivation and mathematical justification. Proofs of the main theorems are provided and data examples illustrate practical aspects. This book will be a valuable resource for researchers and graduate students in statistics, mathematics, econometrics and other quantitative areas, as well as for practitioners and applied researchers who need to analyze data in which long memory, power laws, self-similar scaling or fractal properties are relevant.
Author: Yan Liu Publisher: Springer Nature ISBN: 9819908035 Category : Mathematics Languages : en Pages : 591
Book Description
This book compiles theoretical developments on statistical inference for time series and related models in honor of Masanobu Taniguchi's 70th birthday. It covers models such as long-range dependence models, nonlinear conditionally heteroscedastic time series, locally stationary processes, integer-valued time series, Lévy Processes, complex-valued time series, categorical time series, exclusive topic models, and copula models. Many cutting-edge methods such as empirical likelihood methods, quantile regression, portmanteau tests, rank-based inference, change-point detection, testing for the goodness-of-fit, higher-order asymptotic expansion, minimum contrast estimation, optimal transportation, and topological methods are proposed, considered, or applied to complex data based on the statistical inference for stochastic processes. The performances of these methods are illustrated by a variety of data analyses. This collection of original papers provides the reader with comprehensive and state-of-the-art theoretical works on time series and related models. It contains deep and profound treatments of the asymptotic theory of statistical inference. In addition, many specialized methodologies based on the asymptotic theory are presented in a simple way for a wide variety of statistical models. This Festschrift finds its core audiences in statistics, signal processing, and econometrics.
Author: Chun Yip Yau
Author: Chun Yip Yau
Author: Yan Liu
Author: Ramadha D Piyadi Gamage
Author: Wilfredo Palma
Author: Ming Li
Author: Art B. Owen
Author: Kun Chen
Author: Jan Beran
Author: 小方浩明
Author: Yan Liu