Semiparametric Inference in Seasonal and Cyclical Long Memory Processes - (Now Published in Journal of Time Series Analysis, 21 (2000), Pp.1-25.). PDF Download
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Author: Josu Artech Publisher: ISBN: Category : Languages : en Pages : 26
Book Description
Several semiparametric estimates of the memory parameter in standard long memory time series are now available. They consider only local behaviour of the spectrum near zero frequency, about which the spectrum is symmetric. However, long-range dependence can appear as a spectral pole at any Nyqvist frequency (reflecting seasonal or cyclical long memory), where the spectrym need display no such symmetry. We introduce Seasonal/Cyclical Asymmetric Long Memory (SCALM) processes that allow differing rates of increase on either side of such a pole. To estimate the two consequent memory parameters we extend two semiparametric methods that were proposed for the standard case of a spectrum diverging at the origin, namely the log-periodogram and Gaussian or Whittle methods. We also provide three tests of symmetry. Monte Carlo analysis of finite sample behaviour and an empirical application to UK inflation data are included. Our models and methods allow also for the posssibility of negative dependence, described by a possibly asymmetric spectral zero.
Author: Josu Artech Publisher: ISBN: Category : Languages : en Pages : 26
Book Description
Several semiparametric estimates of the memory parameter in standard long memory time series are now available. They consider only local behaviour of the spectrum near zero frequency, about which the spectrum is symmetric. However, long-range dependence can appear as a spectral pole at any Nyqvist frequency (reflecting seasonal or cyclical long memory), where the spectrym need display no such symmetry. We introduce Seasonal/Cyclical Asymmetric Long Memory (SCALM) processes that allow differing rates of increase on either side of such a pole. To estimate the two consequent memory parameters we extend two semiparametric methods that were proposed for the standard case of a spectrum diverging at the origin, namely the log-periodogram and Gaussian or Whittle methods. We also provide three tests of symmetry. Monte Carlo analysis of finite sample behaviour and an empirical application to UK inflation data are included. Our models and methods allow also for the posssibility of negative dependence, described by a possibly asymmetric spectral zero.
Author: Donatas Surgailis Publisher: World Scientific Publishing Company ISBN: 1911299387 Category : Mathematics Languages : en Pages : 594
Book Description
Box and Jenkins (1970) made the idea of obtaining a stationary time series by differencing the given, possibly nonstationary, time series popular. Numerous time series in economics are found to have this property. Subsequently, Granger and Joyeux (1980) and Hosking (1981) found examples of time series whose fractional difference becomes a short memory process, in particular, a white noise, while the initial series has unbounded spectral density at the origin, i.e. exhibits long memory.Further examples of data following long memory were found in hydrology and in network traffic data while in finance the phenomenon of strong dependence was established by dramatic empirical success of long memory processes in modeling the volatility of the asset prices and power transforms of stock market returns.At present there is a need for a text from where an interested reader can methodically learn about some basic asymptotic theory and techniques found useful in the analysis of statistical inference procedures for long memory processes. This text makes an attempt in this direction. The authors provide in a concise style a text at the graduate level summarizing theoretical developments both for short and long memory processes and their applications to statistics. The book also contains some real data applications and mentions some unsolved inference problems for interested researchers in the field./a
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: Uwe Hassler Publisher: John Wiley & Sons ISBN: 1119470285 Category : Mathematics Languages : en Pages : 292
Book Description
Provides a simple exposition of the basic time series material, and insights into underlying technical aspects and methods of proof Long memory time series are characterized by a strong dependence between distant events. This book introduces readers to the theory and foundations of univariate time series analysis with a focus on long memory and fractional integration, which are embedded into the general framework. It presents the general theory of time series, including some issues that are not treated in other books on time series, such as ergodicity, persistence versus memory, asymptotic properties of the periodogram, and Whittle estimation. Further chapters address the general functional central limit theory, parametric and semiparametric estimation of the long memory parameter, and locally optimal tests. Intuitive and easy to read, Time Series Analysis with Long Memory in View offers chapters that cover: Stationary Processes; Moving Averages and Linear Processes; Frequency Domain Analysis; Differencing and Integration; Fractionally Integrated Processes; Sample Means; Parametric Estimators; Semiparametric Estimators; and Testing. It also discusses further topics. This book: Offers beginning-of-chapter examples as well as end-of-chapter technical arguments and proofs Contains many new results on long memory processes which have not appeared in previous and existing textbooks Takes a basic mathematics (Calculus) approach to the topic of time series analysis with long memory Contains 25 illustrative figures as well as lists of notations and acronyms Time Series Analysis with Long Memory in View is an ideal text for first year PhD students, researchers, and practitioners in statistics, econometrics, and any application area that uses time series over a long period. It would also benefit researchers, undergraduates, and practitioners in those areas who require a rigorous introduction to time series analysis.
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: Subir Ghosh Publisher: CRC Press ISBN: 9780824700515 Category : Mathematics Languages : en Pages : 864
Book Description
"Contains over 2500 equations and exhaustively covers not only nonparametrics but also parametric, semiparametric, frequentist, Bayesian, bootstrap, adaptive, univariate, and multivariate statistical methods, as well as practical uses of Markov chain models."
Author: Steven Durlauf Publisher: Springer ISBN: 0230280838 Category : Business & Economics Languages : en Pages : 417
Book Description
Specially selected from The New Palgrave Dictionary of Economics 2nd edition, each article within this compendium covers the fundamental themes within the discipline and is written by a leading practitioner in the field. A handy reference tool.
Author: Josu Arteche Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
The concept of SCLM (seasonal or cyclical long memory) implies the existence of one or more spectral poles or zeros. The processes traditionally used to model such a behaviour assume the same persistence across different frequencies. In this paper, we propose semiparametric Wald and Lagrange multiplier (LM) tests of the equality of memory parameters at different frequencies (extendable to other linear restrictions) which are standard in the sense that they have well known C distributions under the null hypothesis - although Gaussianity is nowhere assumed - and are consistent against constant and local alternatives. They have also the advantage of being robust against misspecification at frequencies distant from those of interest. Their finite sample performance is compared with the asymptotically locally efficient Robinson's tests (1994). An empirical application to a UK inflation series is also included.
Author: Vladas Pipiras Publisher: Cambridge University Press ISBN: 1107039460 Category : Business & Economics Languages : en Pages : 693
Book Description
A modern and rigorous introduction to long-range dependence and self-similarity, complemented by numerous more specialized up-to-date topics in this research area.
Author: Josu Artech
Author: Josu Artech
Author: Josu Arteche
Author: Donatas Surgailis
Author: Jan Beran
Author: Uwe Hassler
Author: Wilfredo Palma
Author: Subir Ghosh
Author: Steven Durlauf
Author: Josu Arteche
Author: Vladas Pipiras