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Likelihood Analysis Of A First Order Autoregressive Model With Exponential Innovations
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Book Synopsis Likelihood Analysis of a First Order Autoregressive Model With Exponential Innovations by : Bent Nielsen
Download or read book Likelihood Analysis of a First Order Autoregressive Model With Exponential Innovations written by Bent Nielsen and published by . This book was released on 1999 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper derives the exact distribution of the maximum likelihood estimator of a first order linear autoregression with exponential innovations. We show that even if the process is stationary, the estimator is $T$-consistent, where $T$ is the sample size. In the unit root case the estimator is $T^{2}$-consistent, while in the explosive case the estimator is $ rho ^{T}$-consistent. Further, the likelihood ratio test statistic for a simple hypothesis on the autoregressive parameter is asymptotically uniform for all values of the parameter.
Book Synopsis Maximum Likelihood Estimation for a First-Order Bifurcating Autoregressive Process with Exponential Errors by : Jin Zhou
Download or read book Maximum Likelihood Estimation for a First-Order Bifurcating Autoregressive Process with Exponential Errors written by Jin Zhou and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter in a first-order bifurcating autoregressive process with exponential innovations are derived. The limit distributions for the stationary, critical and explosive cases are unified via a single pivot using a random normalization. The pivot is shown to be asymptotically exponential for all values of the autoregressive parameter.
Book Synopsis Non-Gaussian Autoregressive-Type Time Series by : N. Balakrishna
Download or read book Non-Gaussian Autoregressive-Type Time Series written by N. Balakrishna and published by Springer Nature. This book was released on 2022-01-27 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a variety of non-Gaussian autoregressive-type models to analyze time-series data. This book collects and collates most of the available models in the field and provide their probabilistic and inferential properties. This book classifies the stationary time-series models into different groups such as linear stationary models with non-Gaussian innovations, linear stationary models with non-Gaussian marginal distributions, product autoregressive models and minification models. Even though several non-Gaussian time-series models are available in the literature, most of them are focusing on the model structure and the probabilistic properties.
Book Synopsis Parameter Estimation in Stochastic Volatility Models by : Jaya P. N. Bishwal
Download or read book Parameter Estimation in Stochastic Volatility Models written by Jaya P. N. Bishwal and published by Springer Nature. This book was released on 2022-08-06 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.
Book Synopsis Financial Econometrics by : Yiu-Kuen Tse
Download or read book Financial Econometrics written by Yiu-Kuen Tse and published by MDPI. This book was released on 2019-10-14 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Financial econometrics has developed into a very fruitful and vibrant research area in the last two decades. The availability of good data promotes research in this area, specially aided by online data and high-frequency data. These two characteristics of financial data also create challenges for researchers that are different from classical macro-econometric and micro-econometric problems. This Special Issue is dedicated to research topics that are relevant for analyzing financial data. We have gathered six articles under this theme.
Book Synopsis Likelihood-Based Inference in Cointegrated Vector Autoregressive Models by : Søren Johansen
Download or read book Likelihood-Based Inference in Cointegrated Vector Autoregressive Models written by Søren Johansen and published by OUP Oxford. This book was released on 1995-12-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a detailed mathematical and statistical analysis of the cointegrated vector autoregresive model. This model had gained popularity because it can at the same time capture the short-run dynamic properties as well as the long-run equilibrium behaviour of many non-stationary time series. It also allows relevant economic questions to be formulated in a consistent statistical framework. Part I of the book is planned so that it can be used by those who want to apply the methods without going into too much detail about the probability theory. The main emphasis is on the derivation of estimators and test statistics through a consistent use of the Guassian likelihood function. It is shown that many different models can be formulated within the framework of the autoregressive model and the interpretation of these models is discussed in detail. In particular, models involving restrictions on the cointegration vectors and the adjustment coefficients are discussed, as well as the role of the constant and linear drift. In Part II, the asymptotic theory is given the slightly more general framework of stationary linear processes with i.i.d. innovations. Some useful mathematical tools are collected in Appendix A, and a brief summary of weak convergence in given in Appendix B. The book is intended to give a relatively self-contained presentation for graduate students and researchers with a good knowledge of multivariate regression analysis and likelihood methods. The asymptotic theory requires some familiarity with the theory of weak convergence of stochastic processes. The theory is treated in detail with the purpose of giving the reader a working knowledge of the techniques involved. Many exercises are provided. The theoretical analysis is illustrated with the empirical analysis of two sets of economic data. The theory has been developed in close contract with the application and the methods have been implemented in the computer package CATS in RATS as a result of a rcollaboation with Katarina Juselius and Henrik Hansen.
Book Synopsis A Bivariate First Order Autoregressive Time Series Model in Exponential Variables (BEAR(1)). by : Lee Samuel Dewald
Download or read book A Bivariate First Order Autoregressive Time Series Model in Exponential Variables (BEAR(1)). written by Lee Samuel Dewald and published by . This book was released on 1986 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: A simple time series model for bivariate exponential variables having first-order auto-regressive structure is presented. The linear random coefficient difference equation model is an adaptation of the New Exponential Autoregressive model (NEAR (2)). The process is Markovian in the bivariate sense and has correlation structure analogous to that of the Gaussian AR(1) bivariate time series model. The model exhibits a full range of positive correlations and cross-correlations. With some modification in either the innovation or the random coefficients, the model admits some negative values for the cross-correlations. The marginal processes are shown to have correlation structure of ARMA (2,1) models.
Book Synopsis Extension of Some Models for Positive-Valued Time Series by : David Kennedy Hugus
Download or read book Extension of Some Models for Positive-Valued Time Series written by David Kennedy Hugus and published by . This book was released on 1982 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Time series models with autoregressive, moving average and mixed autoregressive-moving average correlation structure and with positive-valued non-normal marginal distribution are considered. First, a flexible mixed model GLARMA(p, q) with Gamma marginals is investigated. The correlation structure for several special cases is derived. For the first-order autoregressive case, GLAR(1), the conditional density of X sub n given X sub n-1 is derived. This leads to the formation of a likelihood function and a numerical approximation to and a simulation study of the maximum likelihood method of parameter estimation. Multivariate extensions of the model are considered briefly. Second, three methods for generating first-order moving average sequences with Exponential marginals are examined. These generalize the EMA (1) Exponential model. Negative correlation using antithetic variables is investigated in the moving average models. A preliminary analysis of wind speed data obtained over a 15-year period in the Gulf of Alaska is presented. A model with four harmonic deterministic mean multiplying random innovative factors modeled by a GLAR (1) process is developed. Correlograms and periodograms are used to determine the model for the mean and the structure of the innovation process. (Author).
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1988 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Maximum Likelihood Estimation of Higher-Order Integer-Valued Autoregressive Processes by : Ruijun Bu
Download or read book Maximum Likelihood Estimation of Higher-Order Integer-Valued Autoregressive Processes written by Ruijun Bu and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this article, we extend the earlier work of Freeland and McCabe [Journal of time Series Analysis (2004) Vol. 25, pp. 70-722] and develop a general framework for maximum likelihood (ML) analysis of higher-order integer-valued autoregressive processes. Our exposition includes the case where the innovation sequence has a Poisson distribution and the thinning is binomial. A recursive representation of the transition probability of the model is proposed. Based on this transition probability, we derive expressions for the score function and the Fisher information matrix, which form the basis for ML estimation and inference. Similar to the results in Freeland and McCabe (2004), we show that the score function and the Fisher information matrix can be neatly represented as conditional expectations. Using the INAR(2) specification with binomial thinning and Poisson innovations, we examine both the asymptotic efficiency and finite sample properties of the ML estimator in relation to the widely used conditional least squares (CLS) and YuleWalker (YW) estimators. We conclude that, if the Poisson assumption can be justified, there are substantial gains to be had from using ML especially when the thinning parameters are large.
Book Synopsis Autoregressive Model Inference in Finite Samples by : Hans Einar Wensink
Download or read book Autoregressive Model Inference in Finite Samples written by Hans Einar Wensink and published by . This book was released on 1996 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Statistical Methods for Forecasting by : Bovas Abraham
Download or read book Statistical Methods for Forecasting written by Bovas Abraham and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists. "This book, it must be said, lives up to the words on its advertising cover: 'Bridging the gap between introductory, descriptive approaches and highly advanced theoretical treatises, it provides a practical, intermediate level discussion of a variety of forecasting tools, and explains how they relate to one another, both in theory and practice.' It does just that!" -Journal of the Royal Statistical Society "A well-written work that deals with statistical methods and models that can be used to produce short-term forecasts, this book has wide-ranging applications. It could be used in the context of a study of regression, forecasting, and time series analysis by PhD students; or to support a concentration in quantitative methods for MBA students; or as a work in applied statistics for advanced undergraduates." -Choice Statistical Methods for Forecasting is a comprehensive, readable treatment of statistical methods and models used to produce short-term forecasts. The interconnections between the forecasting models and methods are thoroughly explained, and the gap between theory and practice is successfully bridged. Special topics are discussed, such as transfer function modeling; Kalman filtering; state space models; Bayesian forecasting; and methods for forecast evaluation, comparison, and control. The book provides time series, autocorrelation, and partial autocorrelation plots, as well as examples and exercises using real data. Statistical Methods for Forecasting serves as an outstanding textbook for advanced undergraduate and graduate courses in statistics, business, engineering, and the social sciences, as well as a working reference for professionals in business, industry, and government.
Book Synopsis Research Papers in Statistical Inference for Time Series and Related Models by : Yan Liu
Download or read book Research Papers in Statistical Inference for Time Series and Related Models written by Yan Liu and published by Springer Nature. This book was released on 2023-05-31 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Recent Developments and the New Directions of Research, Foundations, and Applications by : Shahnaz N. Shahbazova
Download or read book Recent Developments and the New Directions of Research, Foundations, and Applications written by Shahnaz N. Shahbazova and published by Springer Nature. This book was released on 2023-06-26 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers presented during the 8th World Conference on Soft Computing in February 2022. The papers cover multiple areas important for soft computing. Some papers are dedicated to fundamental aspects of soft computing, i.e., fuzzy mathematics, type-2 fuzzy sets, evolutionary-based optimization, aggregation, and neural networks. Others emphasize the application of soft computing methods to data analysis, image processing, decision-making, classification, series prediction, economics, control, and modeling.
Book Synopsis Random Coefficient Autoregressive Models: An Introduction by : D.F. Nicholls
Download or read book Random Coefficient Autoregressive Models: An Introduction written by D.F. Nicholls and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph we have considered a class of autoregressive models whose coefficients are random. The models have special appeal among the non-linear models so far considered in the statistical literature, in that their analysis is quite tractable. It has been possible to find conditions for stationarity and stability, to derive estimates of the unknown parameters, to establish asymptotic properties of these estimates and to obtain tests of certain hypotheses of interest. We are grateful to many colleagues in both Departments of Statistics at the Australian National University and in the Department of Mathematics at the University of Wo110ngong. Their constructive criticism has aided in the presentation of this monograph. We would also like to thank Dr M. A. Ward of the Department of Mathematics, Australian National University whose program produced, after minor modifications, the "three dimensional" graphs of the log-likelihood functions which appear on pages 83-86. Finally we would like to thank J. Radley, H. Patrikka and D. Hewson for their contributions towards the typing of a difficult manuscript. IV CONTENTS CHAPTER 1 INTRODUCTION 1. 1 Introduction 1 Appendix 1. 1 11 Appendix 1. 2 14 CHAPTER 2 STATIONARITY AND STABILITY 15 2. 1 Introduction 15 2. 2 Singly-Infinite Stationarity 16 2. 3 Doubly-Infinite Stationarity 19 2. 4 The Case of a Unit Eigenvalue 31 2. 5 Stability of RCA Models 33 2. 6 Strict Stationarity 37 Appendix 2. 1 38 CHAPTER 3 LEAST SQUARES ESTIMATION OF SCALAR MODELS 40 3.
Book Synopsis The Art of Semiparametrics by : Stefan Sperlich
Download or read book The Art of Semiparametrics written by Stefan Sperlich and published by Springer Science & Business Media. This book was released on 2006-07-25 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This selection of articles emerged from different works presented "The Art of Semiparametrics" conference in 2003 in Berlin. It offers a collection of individual works that together show the large spectrum of semiparametric statistics. The book combines theoretical contributions with more applied and empirical studies. Although each article represents an original contribution to its own field, all are written in a self-contained way that may be read by non-experts.
