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Distribution Of The Least Squares Estimator In A First Order Autoregressive Model
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Book Synopsis Distribution of the Least Squares Estimator in a First-Order Autoregressive Model by : Mukhtar M. Ali
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.
Book Synopsis Asymptotic Distribution of the Least Squares Estimator in the First-order Autoregressive Process by : Mithat Gonen
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:
Book Synopsis On the Finite Sample Distribution of a Least Square Estimator in a First Order Autoregressive Model by : Albert Ka-Cheng Tsui
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:
Book Synopsis Moment Approximation for Least-Squares Estimator in First-Order Regression Models with Unit Root and Nonnormal Errors by : Yong Bao
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.
Book Synopsis The Approximate Moments of the Least Squares Estimator for the Stationary Autoregressive Model Under a General Error Distribution by : Yong Bao
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.
Book Synopsis Seemingly Unrelated Regression Equations Models by : Virendera K. Srivastava
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.
Book Synopsis Series Expansions for the Lower Order Moments of the Least Squares Estimator in a First Order Stationary Autoregressive Model by : Albert Tsui
Download or read book Series Expansions for the Lower Order Moments of the Least Squares Estimator in a First Order Stationary Autoregressive Model written by Albert Tsui and published by . This book was released on 1990 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Autoregressive Models by : Kelly Wade
Download or read book Autoregressive Models written by Kelly Wade and published by . This book was released on 2012 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consider a sequence of random variables which obeys a first order autoregressive model with unknown parameter alpha. Under suitable assumptions on the error structure of the model, the limiting distribution of the normalized least squares estimator of alpha is discussed. The choice of the normalizing constant depends on whether alpha is less than one, equals one, or is greater than one in absolute value. In particular, the limiting distribution is normal provided that the absolute value of alpha is less than one, but is a function of Brownian motion whenever the absolute value of alpha equals one. Some general remarks are made whenever the sequence of random variables is a first order moving average process.
Book Synopsis Computational Methods in Statistics and Econometrics by : Hisashi Tanizaki
Download or read book Computational Methods in Statistics and Econometrics written by Hisashi Tanizaki and published by CRC Press. This book was released on 2004-01-21 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reflecting current technological capacities and analytical trends, Computational Methods in Statistics and Econometrics showcases Monte Carlo and nonparametric statistical methods for models, simulations, analyses, and interpretations of statistical and econometric data. The author explores applications of Monte Carlo methods in Bayesian estimation, state space modeling, and bias correction of ordinary least squares in autoregressive models. The book offers straightforward explanations of mathematical concepts, hundreds of figures and tables, and a range of empirical examples. A CD-ROM packaged with the book contains all of the source codes used in the text.
Book Synopsis Introduction to Statistical Time Series by : Wayne A. Fuller
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.
Book Synopsis MULTIPERIOD PREDICTIONS FROM AN AUTOREGRESSIVE MODEL USING EMPIRICAL BAYES METHODS by : R.W. ANDREWS
Download or read book MULTIPERIOD PREDICTIONS FROM AN AUTOREGRESSIVE MODEL USING EMPIRICAL BAYES METHODS written by R.W. ANDREWS and published by . This book was released on 1976 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Sample Econometrics by : Aman Ullah
Download or read book Finite Sample Econometrics written by Aman Ullah and published by Oxford University Press. This book was released on 2004-05-20 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides a comprehensive treatment of finite sample statistics and econometrics. Within this framework, the book discusses the basic analytical tools of finite sample econometrics and explores their applications to models covered in a first year graduate course in econometrics.
Book Synopsis Approximation of the Bias of the Least Squares Estimator of [sigma]2 in the Case of a First-order Autoregressive Process and Two Correlated Predictors by : Wilfried R. Vanhonacker
Download or read book Approximation of the Bias of the Least Squares Estimator of [sigma]2 in the Case of a First-order Autoregressive Process and Two Correlated Predictors written by Wilfried R. Vanhonacker and published by . This book was released on 1981 with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Ying Zhang Publisher :National Library of Canada = Bibliothèque nationale du Canada ISBN 13 :9780612771260 Total Pages :292 pages Book Rating :4.7/5 (712 download)
Book Synopsis Topics in Autoregression [microform] by : Ying Zhang
Download or read book Topics in Autoregression [microform] written by Ying Zhang and published by National Library of Canada = Bibliothèque nationale du Canada. This book was released on 2002 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: An overview of the thesis is given in Chapter 1. Chapter 2 discusses a symbolic form for the exact maximum likelihood estimator in the stationary normal AR(1) process. We derive the finite sample inference properties of the exact maximum likelihood estimator. We establish its consistency and its empirical cumulative distribution for a random walk case. The power of our one-tail unit root test overall outperforms that of previous proposals in the unknown mean AR(1) model. Chapter 3 provides a general technique to describe the shape of the admissible region of AR(p). As applications, we have visualized the admissible regions for AR(3) and AR(4). For the AR(4) process, all possible subset admissible regions for the model re-parametrized in terms of partial autocorrelations are obtained and it is demonstrated that these regions are quite complex and hence this re-parameterization is not so useful in the subset case. Chapter 4 develops an algorithm for computing the expectations of time series products given the autocovariance function. Using it as our tool, we evaluate the bias and variance of the Burg estimate to order n-1 in the first order autoregressive model and find that Burg estimate and the least-squares estimate have the same bias and variance to order n-1 in that case. We also obtain explicit formulae for the large sample bias of Burg estimates in the second order cases. Both simulations and theory indicates that Burg estimates have biases similar to the least-squares estimates in the second order cases. The advantages of the Burg estimates over the least-squares estimates are briefly indicated. Chapter 5 is an extension of Chapter 3. A new more computationally efficient general purpose algorithm for computing the exact maximum likelihood estimates in an AR(p) model is developed. Then this algorithm is used to develop a new approach to subset autoregression modelling in which the subsets are obtained by containing some of the zeta parameters to zero. After the exact maximum likelihood estimation algorithm for the subset models is presented, it is shown how a tentative identification of possible subset AR models can be accomplished using the AIC or BIC criterion and the partial autocorrelation function. The distribution of the residual autocorrelations for subset AR models is also derived and appropriate diagnostic checks for model adequacy are discussed. Several illustrative examples are presented.
Book Synopsis The Finite Sample Analysis of Least Squares Estimators in Dynamic Econometric Models [microform] by : Thomas Armstrong Peters
Download or read book The Finite Sample Analysis of Least Squares Estimators in Dynamic Econometric Models [microform] written by Thomas Armstrong Peters and published by National Library of Canada. This book was released on 1986 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: The least squares estimator of the autoregressive parameter, LS((gamma)), in a first-order stochastic difference equation with independent, identically distributed random innovations is known to be asymptotically unbiased, efficient and consistent (as T ( -->) (INFIN) or (sigma) ( -->) 0) under the proper model specification. Further, LS((gamma)) has a limiting normal distribution around the true parameter, (gamma), if the random innovations are drawn from a normal population. These properties are not observed, however, in sample sizes that are typical of economic time series.
Book Synopsis Advanced Econometrics by : Takeshi Amemiya
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.
Book Synopsis Sequential Estimation of Parameters in a First Order Autoregressive Model by : Tharuvai Narayanaswami Sriram
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:
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