Download or read book Stability of First order Autoregressive Models Case of Small Samples written by Hocine Fellag and published by LAP Lambert Academic Publishing. This book was released on 2012 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies the stability of estimators of autoregressive models in the case of finite samples (nonasymptotic setup). The stability is one of aspects of approaches of robustness proposed by Zielinki (institute of mathematics, academy of sciences, Warsaw, Poland). When an autoregressive model is violated, the well known least square estimator presents a high variability which makes this estimator rather useless. An unexpected fact we discovered is the lack of monotonicity of the bias when the amount of contamination is growing. Similar effects for the Student and ANOVA tests are studied in this document. Also, a review on various approaches of robustness and some results on estimation of a gaussian autoregressive model are presented. This document is very useful for beginners in research works connected with robust inference in time series."
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.
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:
Download or read book A Continuous Time Approximation to the Unstable First order Autoregressive Process written by Pierre Perron and published by . This book was released on 1988 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Models for Intensive Longitudinal Data written by Theodore A. Walls and published by Oxford University Press. This book was released on 2006-01-19 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new class of longitudinal data has emerged with the use of technological devices for scientific data collection called Intensive Longitudinal Data. This volume features state-of-the-art applied statistical modelling strategies developed by leading statisticians and methodologists.
Download or read book Handbook of Mathematics written by Thierry Vialar and published by BoD - Books on Demand. This book was released on 2016-12-07 with total page 1134 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book, revised, consists of XI Parts and 28 Chapters covering all areas of mathematics. It is a tool for students, scientists, engineers, students of many disciplines, teachers, professionals, writers and also for a general reader with an interest in mathematics and in science. It provides a wide range of mathematical concepts, definitions, propositions, theorems, proofs, examples, and numerous illustrations. The difficulty level can vary depending on chapters, and sustained attention will be required for some. The structure and list of Parts are quite classical: I. Foundations of Mathematics, II. Algebra, III. Number Theory, IV. Geometry, V. Analytic Geometry, VI. Topology, VII. Algebraic Topology, VIII. Analysis, IX. Category Theory, X. Probability and Statistics, XI. Applied Mathematics. Appendices provide useful lists of symbols and tables for ready reference. Extensive cross-references allow readers to find related terms, concepts and items (by page number, heading, and objet such as theorem, definition, example, etc.). The publisher’s hope is that this book, slightly revised and in a convenient format, will serve the needs of readers, be it for study, teaching, exploration, work, or research.
Download or read book Resources Booms and Macroeconomic Adjustments in Developing Countries written by Mamta Banu Chowdhury and published by Routledge. This book was released on 2017-11-28 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Chowdhury addresses fundamental issues of policy management in resource-based developing countries, by providing an extension of the existing 'Dutch Disease' theory and its applications to the developing country context. The impact of resources booms is of paramount importance for the developing economies. To date the analytical and empirical investigations of these issues have not been available. Essentially, this study will fill this gap. The book investigates the macroeconomic impact of a resources boom and the long-term growth implications of related policy choices with reference to Papua New Guinea. Like many other primary commodity exporting developing economies, Papua New Guinea experienced several short-lived export booms over the past two and a half decades, providing a fascinating case study of potential gains from resources booms and the accompanying complex problems of policy management. This study also incorporates a comparative study of resources boom and policy management issues between Papua New Guinea, Indonesia and Nigeria.
Download or read book Multiple Time Series Models written by Patrick T. Brandt and published by SAGE. This book was released on 2007 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many analyses of time series data involve multiple, related variables. Modeling Multiple Time Series presents many specification choices and special challenges. This book reviews the main competing approaches to modeling multiple time series: simultaneous equations, ARIMA, error correction models, and vector autoregression. The text focuses on vector autoregression (VAR) models as a generalization of the other approaches mentioned. Specification, estimation, and inference using these models is discussed. The authors also review arguments for and against using multi-equation time series models. Two complete, worked examples show how VAR models can be employed. An appendix discusses software that can be used for multiple time series models and software code for replicating the examples is available. Key Features: * Offers a detailed comparison of different time series methods and approaches. * Includes a self-contained introduction to vector autoregression modeling. * Situates multiple time series modeling as a natural extension of commonly taught statistical models.
Download or read book Moment Approximation for Least Squares Estimator in First Order Regression Models with Unit Root and Nonnormal Errors written by Yong Bao and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: An extensive literature in econometrics focuses on finding the exact and approximate first and second moments of the least-squares estimator in the stable first-order linear autoregressive model with normally distributed errors. Recently, Kiviet and Phillips (2005) developed approximate moments for the linear autoregressive model with a unit root and normally distributed errors. An objective of this paper is to analyze moments of the estimator in the first-order autoregressive model with a unit root and nonnormal errors. In particular, we develop new analytical approximations for the first two moments in terms of model parameters and the distribution parameters. Through Monte Carlo simulations, we find that our approximate formula perform quite well across different distribution specifications in small samples. However, when the noise to signal ratio is huge, bias distortion can be quite substantial, and our approximations do not fare well.
Download or read book Theory of Econometrics written by A. Koutsoyiannis and published by [London] : Macmillan. This book was released on 1973 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: PMIn reviewing the first edition, the IJournal of Economic Literature hailed it as a "textbook which emphasizes clarity of exposition and simplification of the mathematical presentation of topics. It] assumes only college algebra and introductory statistics since 'the greatest attention is given to economic aspects of econometrics.'" The author's extensive revisions of several chapters and sections are aimed at further clarification of important and relevant data.
Download or read book Global Financial Stability Report September 2003 written by International Monetary Fund. Monetary and Capital Markets Department and published by International Monetary Fund. This book was released on 2003-09-04 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This September 2003 issue of the Global Financial Stability Report highlights that since March 2003, further progress has been made in addressing the lingering effects of the bursting of the equity price bubble. Household and corporate balance sheets have continued to improve gradually and corporate default levels have declined. Companies in mature markets have cut costs, enhancing their ability to cope with slower growth and other potential difficulties. Corporations—particularly in the United States—have made good progress in their financial consolidation efforts and are in a better financial position to increase investment spending.
Download or read book Empirical Vector Autoregressive Modeling written by Marius Ooms and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. 1 Integrating results The empirical study of macroeconomic time series is interesting. It is also difficult and not immediately rewarding. Many statistical and economic issues are involved. The main problems is that these issues are so interrelated that it does not seem sensible to address them one at a time. As soon as one sets about the making of a model of macroeconomic time series one has to choose which problems one will try to tackle oneself and which problems one will leave unresolved or to be solved by others. From a theoretic point of view it can be fruitful to concentrate oneself on only one problem. If one follows this strategy in empirical application one runs a serious risk of making a seemingly interesting model, that is just a corollary of some important mistake in the handling of other problems. Two well known examples of statistical artifacts are the finding of Kuznets "pseudo-waves" of about 20 years in economic activity (Sargent (1979, p. 248)) and the "spurious regression" of macroeconomic time series described in Granger and Newbold (1986, §6. 4). The easiest way to get away with possible mistakes is to admit they may be there in the first place, but that time constraints and unfamiliarity with the solution do not allow the researcher to do something about them. This can be a viable argument.
Download or read book Distribution of the Least Squares Estimator in a First Order Autoregressive Model written by Mukhtar M. Ali and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper investigates the finite sample distribution of the least squares estimator of the autoregressive parameter in a first-order autoregressive model. Uniform asymptotic expansion for the distribution applicable to both stationary and nonstationary cases is obtained. Accuracy of the approximation to the distribution by a first few terms of this expansion is then investigated. It is found that the leading term of this expansion approximates well the distribution. The approximation is, in almost all cases, accurate to the second decimal place throughout the distribution. In the literature, there exists a number of approximations to this distribution which are specifically designed to apply in some special cases of this model. The present approximation compares favorably with those approximations and in fact, its accuracy is, with almost no exception, as good as or better than these other approximations. Convenience of numerical computations seems also to favor the present approximations over the others. An application of the finding is illustrated with examples.
Download or read book Econometric Model Performance written by Lawrence R. Klein and published by University of Pennsylvania Press. This book was released on 2016-11-11 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Models of the American economy exist in government, research institutes, universities, and private corporations. Given the proliferation, it is wise to take stock because these models come from diverse sources and describe different conditions from alternative points of view. They could be saying different things about the economy. The high-level comparative studies in this volume, gathered from several issues of the International Economic Review, with a substantive introduction and the addition of more comparative material, evaluate the performance of eleven models of the American economy: the Wharton Mark Ill Model; Brookings Model; Hickman-Coen Annual Model; Liu-Hwa Monthly Model; Data Resources, Inc. (DRI) Model; Federal Reserve Bank of St. Louis Model; Michigan Quarterly Econometric (MOEM) Model; Wharton Annual and Industry Model; Anticipation Version of the Wharton Mark Ill Model/Fair Model; U.S. Department of Commerce (BEA) Model. Each of the proprietors or builders of these models describes his own system in his own words. These studies come closer than ever before to standardizing model operations for testing purposes. Some of the models are monthly, while others are annual. but the quarterly unit of time is the most frequent. Some are demand oriented, others are supply oriented, and focus on the input-output sectors of the economy. Some use only observed. objective data; others use subjective. anticipatory data. Both large and small models are included. In spite of the diversity, the contributors have cooperated to trace the differences between their models to root causes and to report jointly the results of their research. There are also some general papers that look at model performance from outside the CEME group.
Download or read book Discussiones Mathematicae written by and published by . This book was released on 2002 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Estimation and Inference in Autoregressive Models with Trending Innovation Variance written by Nikolaos Kourogenis and published by . This book was released on 2009 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops the asymptotic theory for stable autoregressive models in which the noise variance grows in a polynomial-like fashion. It is shown that the asymptotic distribution of the OLS estimator of the coefficient vector is multivariate normal with a covariance matrix that depends on the order, k, of the variance growth. A consistent estimator of k is proposed, which delivers heteroscedasticity-robust test statistics. The opposite case of quot;variance declinequot; is studied as well. It is demonstrated that by means of a simple data transformation producing the time reversed image of the original series, the problem of quot;variance decreasequot; can be reformulated in terms of that of polynomial-like variance growth. Simulation evidence suggests that the new procedures work quite well in small samples.
Download or read book A Test of the Economic Base Hypothesis in the Small Forest Communities of Southeast Alaska written by Guy C. Robertson and published by . This book was released on 2003 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent harvest declines in the Western United States have focused attention on the question of economic impacts at the community level. The impact of changing timber-related economic activity in a given community on other local activity and the general economic health of the community at large has been a persistent and often contentious issue in debates surrounding forest policy decisions. The economic base hypothesis, in which changes in local export-related economic activity are assumed to cause changes in economic activity serving local demand, is a common framework for understanding impacts of forest policy decisions and forms the basis of models commonly used to provide estimates of expected local impacts under different policy options. This study uses community-specific, time-series employment data to test the economic base hypothesis in the small, semi-isolated communities of southeast Alaska. Estimates were derived for each of 15 communities. Export-related activity was not found to cause changes in economic activity serving local demand for the average community. However, the results indicated statistically significant differences among communities in their response to shocks in export related activity. The implications of these results for policy, and for the theory and practice of modeling economic impacts at small spatial scales, are explored in the final sections of this study. Specifically, secondary economic impacts cannot be taken as a foregone conclusion in policy analysis, and the fundamental assumptions of static impact modeling approaches deserve greater scrutiny.
