A Note on the Coefficient of Determination in Models with Infinite Variance Variables
Author: Jeong-Ryeol Kurz-Kim
Publisher:
Published: 2007
Total Pages: 40
ISBN-13:
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A Note on the Coefficient of Determination in Regression Models with Infinite-variance Variables
Author: Jeong-Ryeol Kurz-Kim
Publisher:
Published: 2007
Total Pages: 0
ISBN-13: 9783865582959
DOWNLOAD EBOOKSince Mandelbrot's seminal work (1963), alpha-stable distributions with infinite variance have been regarded as a more realistic distributional assumption than the normal distribution for some economic variables, especially financial data. After providing a brief survey of theoretical results on estimationand hypothesis testing in regression models with infinite variance variables, we examine the statistical properties of the coefficient of determination in regression models with infinite variance variables. These properties differ in several important aspects from those in the well known finite variance case. In the infinite variance case when the regressor and error term share the same index of stability, the coefficient of determination has a non degenerate asymptotic distribution on the entire (0,1) interval, and the probability density function of this distribution is unbounded at 0 and 1. We provide closed form expressions for the cumulative distribution function and probability density function of this limit random variable. In an empirical application, we revisit the Fama-MacBeth two-stage regression and show that in the infinite variance case the coefficient of determination of the second-stage regression converges to zero asymptotically.
International Finance Discussion Papers
Author:
Publisher:
Published: 2007
Total Pages: 66
ISBN-13:
DOWNLOAD EBOOKDesign for Tomorrow—Volume 2
Author: Amaresh Chakrabarti
Publisher: Springer Nature
Published: 2021-04-26
Total Pages: 989
ISBN-13: 9811601194
DOWNLOAD EBOOKThis book showcases cutting-edge research papers from the 8th International Conference on Research into Design (ICoRD 2021) written by eminent researchers from across the world on design processes, technologies, methods and tools, and their impact on innovation, for supporting design for a connected world. The theme of ICoRD‘21 has been “Design for Tomorrow”. The world as we know it in our times is increasingly becoming connected. In this interconnected world, design has to address new challenges of merging the cyber and the physical, the smart and the mundane, the technology and the human. As a result, there is an increasing need for strategizing and thinking about design for a better tomorrow. The theme for ICoRD’21 serves as a provocation for the design community to think about rapid changes in the near future to usher in a better tomorrow. The papers in this book explore these themes, and their key focus is design for tomorrow: how are products and their development be addressed for the immediate pressing needs within a connected world? The book will be of interest to researchers, professionals and entrepreneurs working in the areas on industrial design, manufacturing, consumer goods, and industrial management who are interested in the new and emerging methods and tools for design of new products, systems and services.
What Can the Data Tell Us about Carry Trades in Japanese Yen?
Author: Joseph E. Gagnon
Publisher:
Published: 2007
Total Pages: 40
ISBN-13:
DOWNLOAD EBOOK"This paper examines the available data that may shed light on the carry trade in Japanese yen. We define an individual or a sector to be engaged in the carry trade if it has a short position in yen and a long position in other currencies. The tendency of large yen movements to be skewed toward appreciations is consistent with the existence of substantial carry positions, and other evidence from market prices provides some modest support for an effect from the carry trade. Data on bank loans and bond holdings by currency reveal a large apparent yen carry position of the Japanese official sector and modest carry positions in the Japanese and foreign banking sectors. The Japanese private non-banking sector has a large long foreign-currency position, but does not have a short yen position, and is thus not engaged in the yen carry trade in the aggregate. However, it is possible that exporters and investors in Japan use the derivatives markets to hedge some of their long foreign-currency exposure, with the private non-banking sector outside of Japan (including most hedge funds) likely to be taking on most of the associated carry exposure"--Federal Reserve Board web site.
Analysis of Variance, Design, and Regression
Author: Ronald Christensen
Publisher: CRC Press
Published: 1996-06-01
Total Pages: 608
ISBN-13: 9780412062919
DOWNLOAD EBOOKThis text presents a comprehensive treatment of basic statistical methods and their applications. It focuses on the analysis of variance and regression, but also addressing basic ideas in experimental design and count data. The book has four connecting themes: similarity of inferential procedures, balanced one-way analysis of variance, comparison of models, and checking assumptions. Most inferential procedures are based on identifying a scalar parameter of interest, estimating that parameter, obtaining the standard error of the estimate, and identifying the appropriate reference distribution. Given these items, the inferential procedures are identical for various parameters. Balanced one-way analysis of variance has a simple, intuitive interpretation in terms of comparing the sample variance of the group means with the mean of the sample variance for each group. All balanced analysis of variance problems are considered in terms of computing sample variances for various group means. Comparing different models provides a structure for examining both balanced and unbalanced analysis of variance problems and regression problems. Checking assumptions is presented as a crucial part of every statistical analysis. Examples using real data from a wide variety of fields are used to motivate theory. Christensen consistently examines residual plots and presents alternative analyses using different transformation and case deletions. Detailed examination of interactions, three factor analysis of variance, and a split-plot design with four factors are included. The numerous exercises emphasize analysis of real data. Senior undergraduate and graduate students in statistics and graduate students in other disciplines using analysis of variance, design of experiments, or regression analysis will find this book useful.
A Residual-based Cointegration Test for Near Unit Root Variables
Author: Erik Hjalmarsson
Publisher:
Published: 2007
Total Pages: 40
ISBN-13:
DOWNLOAD EBOOKMethods of inference based on a unit root assumption in the data are typically not robust to even small deviations from this assumption. In this paper, we propose robust procedures for a residual-based test of cointegration when the data are generated by a near unit root process. A Bonferroni method is used to address the uncertainty regarding the exact degree of persistence in the process. We thus provide a method for valid inference in multivariate near unit root processes where standard cointegration tests may be subject to substantial size distortions and standard OLS inference may lead to spurious results. Empirical illustrations are given by: (i) a re-examination of the Fisher hypothesis, and (ii) a test of the validity of the cointegrating relationship between aggregate consumption, asset holdings, and labor income, which has attracted a great deal of attention in the recent finance literature.
Linear Models in Statistics
Author: Alvin C. Rencher
Publisher: John Wiley & Sons
Published: 2008-01-07
Total Pages: 690
ISBN-13: 0470192607
DOWNLOAD EBOOKThe essential introduction to the theory and application of linear models—now in a valuable new edition Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed. Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models. This modern Second Edition features: New chapters on Bayesian linear models as well as random and mixed linear models Expanded discussion of two-way models with empty cells Additional sections on the geometry of least squares Updated coverage of simultaneous inference The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS® code for all numerical examples. Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.
Frequency of Observation and the Estimation of Integrated Volatility in Deep and Liquid Financial Markets
Author: Alain P. Chaboud
Publisher:
Published: 2007
Total Pages: 58
ISBN-13:
DOWNLOAD EBOOKUsing two newly available ultrahigh-frequency datasets, we investigate empirically how frequently one can sample certain foreign exchange and U.S. Treasury security returns without contaminating estimates of their integrated volatility with market microstructure noise. Using volatility signature plots and a recently-proposed formal decision rule to select the sampling frequency, we find that one can sample FX returns as frequently as once every 15 to 20 seconds without contaminating volatility estimates; bond returns may be sampled as frequently as once every 2 to 3 minutes on days without U.S. macroeconomic announcements, and as frequently as once every 40 seconds on announcement days. With a simple realized kernel estimator, the sampling frequencies can be increased to once every 2 to 5 seconds for FX returns and to about once every 30 to 40 seconds for bond returns. These sampling frequencies, especially in the case of FX returns, are much higher than those often recommended in the empirical literature on realized volatility in equity markets. We suggest that the generally superior depth and liquidity of trading in FX and government bond markets contributes importantly to this difference.
Applied Linear Statistical Models
Author: Michael H. Kutner
Publisher: McGraw-Hill/Irwin
Published: 2005
Total Pages: 1396
ISBN-13: 9780072386882
DOWNLOAD EBOOKLinear regression with one predictor variable; Inferences in regression and correlation analysis; Diagnosticis and remedial measures; Simultaneous inferences and other topics in regression analysis; Matrix approach to simple linear regression analysis; Multiple linear regression; Nonlinear regression; Design and analysis of single-factor studies; Multi-factor studies; Specialized study designs.
