Download or read book Asymptotic Distribution of the Least Squares Estimator in the First order Autoregressive Process written by Mithat Gonen and published by . This book was released on 1996 with total page 78 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Seemingly Unrelated Regression Equations Models written by Virendera K. Srivastava and published by CRC Press. This book was released on 2020-08-14 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together the scattered literature associated with the seemingly unrelated regression equations (SURE) model used by econometricians and others. It focuses on the theoretical statistical results associated with the SURE model.
Download or read book Introduction to Statistical Time Series written by Wayne A. Fuller and published by John Wiley & Sons. This book was released on 1995-12-29 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of time series is of considerable interest, especiallyamong researchers in econometrics, engineering, and the naturalsciences. As part of the prestigious Wiley Series in Probabilityand Statistics, this book provides a lucid introduction to thefield and, in this new Second Edition, covers the importantadvances of recent years, including nonstationary models, nonlinearestimation, multivariate models, state space representations, andempirical model identification. New sections have also been addedon the Wold decomposition, partial autocorrelation, long memoryprocesses, and the Kalman filter. Major topics include: * Moving average and autoregressive processes * Introduction to Fourier analysis * Spectral theory and filtering * Large sample theory * Estimation of the mean and autocorrelations * Estimation of the spectrum * Parameter estimation * Regression, trend, and seasonality * Unit root and explosive time series To accommodate a wide variety of readers, review material,especially on elementary results in Fourier analysis, large samplestatistics, and difference equations, has been included.
Download or read book The Asymptotic Distribution of Differentiable Functions of Standardised Least Squares Residuals from Stochastic Processes written by Richard M. Huggins and published by . This book was released on 1989 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conditions are given under which the asymptotic distribution of a function of the standardised residuals from fitting a model to a stochastic process is normal. The results are illustrated by an application to a first order autoregressive process with independently and identically distributed errors.
Download or read book On the Finite Sample Distribution of a Least Square Estimator in a First Order Autoregressive Model written by Albert Ka-Cheng Tsui and published by . This book was released on 1989 with total page 918 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Sequential Estimation of Parameters in a First Order Autoregressive Model written by Tharuvai Narayanaswami Sriram and published by . This book was released on 1986 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotics for Stationary Very Nearly Unit Root Processes written by Donald W.K. Andrews and published by . This book was released on 2007 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Econometrics written by Takeshi Amemiya and published by Harvard University Press. This book was released on 1985 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main features of this text are a thorough treatment of cross-section models—including qualitative response models, censored and truncated regression models, and Markov and duration models—and a rigorous presentation of large sample theory, classical least-squares and generalized least-squares theory, and nonlinear simultaneous equation models.
Download or read book Higher Order Asymptotic Theory for Time Series Analysis written by Masanobu Taniguchi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: The initial basis of this book was a series of my research papers, that I listed in References. I have many people to thank for the book's existence. Regarding higher order asymptotic efficiency I thank Professors Kei Takeuchi and M. Akahira for their many comments. I used their concept of efficiency for time series analysis. During the summer of 1983, I had an opportunity to visit The Australian National University, and could elucidate the third-order asymptotics of some estimators. I express my sincere thanks to Professor E.J. Hannan for his warmest encouragement and kindness. Multivariate time series analysis seems an important topic. In 1986 I visited Center for Mul tivariate Analysis, University of Pittsburgh. I received a lot of impact from multivariate analysis, and applied many multivariate methods to the higher order asymptotic theory of vector time series. I am very grateful to the late Professor P.R. Krishnaiah for his cooperation and kindness. In Japan my research was mainly performed in Hiroshima University. There is a research group of statisticians who are interested in the asymptotic expansions in statistics. Throughout this book I often used the asymptotic expansion techniques. I thank all the members of this group, especially Professors Y. Fujikoshi and K. Maekawa foItheir helpful discussion. When I was a student of Osaka University I learned multivariate analysis and time series analysis from Professors Masashi Okamoto and T. Nagai, respectively. It is a pleasure to thank them for giving me much of research background.
Download or read book The Approximate Moments of the Least Squares Estimator for the Stationary Autoregressive Model Under a General Error Distribution 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: I derive the approximate bias and mean squared error of the least squares estimator of the autoregressive coefficient in a stationary first-order dynamic regression model, with or without an intercept, under a general error distribution. It is shown that the effects of nonnormality on the approximate moments of the least squares estimator come into play through the skewness and kurtosis coefficients of the nonnormal error distribution.
Download or read book Econometrics written by Bruce Hansen and published by Princeton University Press. This book was released on 2022-06-28 with total page 1081 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most authoritative and up-to-date core econometrics textbook available Econometrics is the quantitative language of economic theory, analysis, and empirical work, and it has become a cornerstone of graduate economics programs. Econometrics provides graduate and PhD students with an essential introduction to this foundational subject in economics and serves as an invaluable reference for researchers and practitioners. This comprehensive textbook teaches fundamental concepts, emphasizes modern, real-world applications, and gives students an intuitive understanding of econometrics. Covers the full breadth of econometric theory and methods with mathematical rigor while emphasizing intuitive explanations that are accessible to students of all backgrounds Draws on integrated, research-level datasets, provided on an accompanying website Discusses linear econometrics, time series, panel data, nonparametric methods, nonlinear econometric models, and modern machine learning Features hundreds of exercises that enable students to learn by doing Includes in-depth appendices on matrix algebra and useful inequalities and a wealth of real-world examples Can serve as a core textbook for a first-year PhD course in econometrics and as a follow-up to Bruce E. Hansen’s Probability and Statistics for Economists
Download or read book Fixed Accuracy Estimation of an Autoregressive Parameter written by STANFORD UNIV CA DEPT OF STATISTICS. and published by . This book was released on 1982 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: For a first order non-explosive autoregressive process with unknown parameter beta epsilon (1,1), it is shown that if data are collected according to a particular stopping rule, the least squares estimator of beta is asymptotically normally distributed uniformly in beta. In the case of normal residuals, the stopping rule may be interpreted as sampling until the observed Fisher information reaches a preassigned level. The situation is contrasted with the fixed sample size case, where the estimator has a non-normal limiting distribution when (beta) = 1. (Author).
Download or read book Asymptotic Approximations in the Near Integrated Model with a Non Zero Initial Condition written by Pierre Perron and published by . This book was released on 2001 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers various asymptotic approximations in the near-integrated first-order autoregressive model with a non-zero initial condition. We first extend the work of Knight and Satchell (1993), who considered the random walk case with a zero initial condition, to derive the expansion of the relevant joint moment generating function in this more general framework. We also consider, as alternative approximations, the stochastic expansion of Phillips (1987c) and the continuous-time approximation of Perron (1991a). We assess, via a Monte Carlo simulation study, the extent to which these alternative methods provide adequate approximations to the finite sample distribution of the least-squares estimator in a first-order autoregressive model. The results show that, when the initial condition is non-zero, Perron's (1991a) continuous-time approximation performs very well while the others only offer improvements when the initial condition is zero.
Download or read book Asymptotic Distribution of Maximum Likelihood Estimators in Linear Models with Autoregressive Disturbances written by Clifford G. Hildreth and published by . This book was released on 1966 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hildreth and Lu proposed a method for obtaining maximum likelihood estimates of linear model coefficients whose disturbances are generated by a stationary linear first-order autoregressive process with unknown autoregression coefficient. Until the present study was performed, consistency was the only property that had been shown for these estimates. This memorandum shows that the estimates of coefficients of independent variables and the estimate of the autoregression coefficient have a limiting joint multivariate-normal distribution, with the estimate of autoregression distributed independently of the estimates of coefficients of independent variables. This asymptotic covariance matrix of these latter estimates is the same as that of the best linear unbiased estimates for a model in which the autoregression coefficient is known. (Author).
Download or read book Asymptotics for LS GLS and Feasible GLS Statistics in an AR 1 Model with Conditional Heteroskedaticity written by Donald W. K. Andrews and published by . This book was released on 2008 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper considers a first-order autoregressive model with conditionally heteroskedastic innovations. The asymptotic distributions of least squares (LS), infeasible generalized least squares (GLS), and feasible GLS estimators and t statistics are determined. The GLS procedures allow for misspecification of the form of the conditional heteroskedasticity and, hence, are referred to as quasi-GLS procedures. The asymptotic results are established for drifting sequences of the autoregressive parameter and the distribution of the time series of innovations. In particular, we consider the full range of cases in which the autoregressive parameter rho_n satisfies (i) n(1 - rho_n) -gt; infinity and (ii) n(1 - rho_n) -gt; h_1 lt; infinity as n -gt; infinity, where n is the sample size. Results of this type are needed to establish the uniform asymptotic properties of the LS and quasi-GLS statistics.
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.
