Download or read book Asymptotic Bias of the Least Squares Estimator for Multivariate Autoregressive Models written by Stanford University. Institute for Mathematical Studies in the Social Sciences and published by . This book was released on 1982 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymtotic Bias of Ordinary Least Squares Estimator for Multivariate Autoregressive Models written by Taku Yamamoto and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Distribution of the Bias Corrected Least Squares Estimators in Measurement Error Linear Regression Models Under Long Memory written by Hira Koul and published by . This book was released on 2020 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article derives the consistency and asymptotic distribution of the bias corrected least squares estimators (LSEs) of the regression parameters in linear regression models when covariates have measurement error (ME) and errors and covariates form mutually independent long memory moving average processes. In the structural ME linear regression model, the nature of the asymptotic distribution of suitably standardized bias corrected LSEs depends on the range of the values of where ,, and are the LM parameters of the covariate, ME and regression error processes respectively. This limiting distribution is Gaussian when and non-Gaussian in the case . In the former case some consistent estimators of the asymptotic variances of these estimators and a log()-consistent estimator of an underlying LM parameter are also provided. They are useful in the construction of the large sample confidence intervals for regression parameters. The article also discusses the asymptotic distribution of these estimators in some functional ME linear regression models, where the unobservable covariate is non-random. In these models, the limiting distribution of the bias corrected LSEs is always a Gaussian distribution determined by the range of the values of )-)
Download or read book Asymptotic Normality of Least Squares Estimators in Autoregressive Linear Regression Models written by B. B. van der Genugten and published by . This book was released on 1985 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elements of Multivariate Time Series Analysis written by Gregory C. Reinsel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of methods of time series analysis in the study of multivariate time series has become of increased interest in recent years. Although the methods are rather well developed and understood for univarjate time series analysis, the situation is not so complete for the multivariate case. This book is designed to introduce the basic concepts and methods that are useful in the analysis and modeling of multivariate time series, with illustrations of these basic ideas. The development includes both traditional topics such as autocovariance and auto correlation matrices of stationary processes, properties of vector ARMA models, forecasting ARMA processes, least squares and maximum likelihood estimation techniques for vector AR and ARMA models, and model checking diagnostics for residuals, as well as topics of more recent interest for vector ARMA models such as reduced rank structure, structural indices, scalar component models, canonical correlation analyses for vector time series, multivariate unit-root models and cointegration structure, and state-space models and Kalman filtering techniques and applications. This book concentrates on the time-domain analysis of multivariate time series, and the important subject of spectral analysis is not considered here. For that topic, the reader is referred to the excellent books by Jenkins and Watts (1968), Hannan (1970), Priestley (1981), and others.
Download or read book Studies in Econometrics Time Series and Multivariate Statistics written by Samuel Karlin and published by Academic Press. This book was released on 2014-05-10 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Econometrics, Time Series, and Multivariate Statistics covers the theoretical and practical aspects of econometrics, social sciences, time series, and multivariate statistics. This book is organized into three parts encompassing 28 chapters. Part I contains studies on logit model, normal discriminant analysis, maximum likelihood estimation, abnormal selection bias, and regression analysis with a categorized explanatory variable. This part also deals with prediction-based tests for misspecification in nonlinear simultaneous systems and the identification in models with autoregressive errors. Part II highlights studies in time series, including time series analysis of error-correction models, time series model identification, linear random fields, segmentation of time series, and some basic asymptotic theory for linear processes in time series analysis. Part III contains papers on optimality properties in discrete multivariate analysis, Anderson’s probability inequality, and asymptotic distributions of test statistics. This part also presents the comparison of measures, multivariate majorization, and of experiments for some multivariate normal situations. Studies on Bayes procedures for combining independent F tests and the limit theorems on high dimensional spheres and Stiefel manifolds are included. This book will prove useful to statisticians, mathematicians, and advance mathematics students.
Download or read book Higher order Asymptotic Expansions of the Least squares Estimation Bias in First order Dynamic Regression Models written by Jan F. Kiviet and published by . This book was released on 1987 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Higher order Asymptotic Expansions of the Least squares Estimation Bias in First order Regression Models written by J. F. Kiviet and published by . This book was released on 1996 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book ARMA Model Identification written by ByoungSeon Choi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last two decades, considerable progress has been made in statistical time series analysis. The aim of this book is to present a survey of one of the most active areas in this field: the identification of autoregressive moving-average models, i.e., determining their orders. Readers are assumed to have already taken one course on time series analysis as might be offered in a graduate course, but otherwise this account is self-contained. The main topics covered include: Box-Jenkins' method, inverse autocorrelation functions, penalty function identification such as AIC, BIC techniques and Hannan and Quinn's method, instrumental regression, and a range of pattern identification methods. Rather than cover all the methods in detail, the emphasis is on exploring the fundamental ideas underlying them. Extensive references are given to the research literature and as a result, all those engaged in research in this subject will find this an invaluable aid to their work.
Download or read book Asymptotic Properties of Some Estimators in Moving Average Models written by Stanford University. Department of Statistics and published by . This book was released on 1975 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author considers estimation procedures for the moving average model of order q. Walker's method uses k sample autocovariances (k> or = q). Assume that k depends on T in such a way that k nears infinity as T nears infinity. The estimates are consistent, asymptotically normal and asymptotically efficient if k = k (T) dominates log T and is dominated by (T sub 1/2). The approach in proving these theorems involves obtaining an explicit form for the components of the inverse of a symmetric matrix with equal elements along its five central diagonals, and zeroes elsewhere. The asymptotic normality follows from a central limit theorem for normalized sums of random variables that are dependent of order k, where k tends to infinity with T. An alternative form of the estimator facilitates the calculations and the analysis of the role of k, without changing the asymptotic properties.
Download or read book Higher Order Asymptotic Expansions of the Least Squares Estimation Bias in Firsts Order Dynamic Regression Models written by Jan F. Kiviet and published by . This book was released on 1996 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotics for the Conditional Sum Of Squares Estimator in Multivariate Fractional Time Series Models written by Morten Ørregaard Nielsen and published by . This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This article proves consistency and asymptotic normality for the conditional-sum-of-squares estimator, which is equivalent to the conditional maximum likelihood estimator, in multivariate fractional time-series models. The model is parametric and quite general and, in particular, encompasses the multivariate non-cointegrated fractional autoregressive integrated moving average (ARIMA) model. The novelty of the consistency result, in particular, is that it applies to a multivariate model and to an arbitrarily large set of admissible parameter values, for which the objective function does not converge uniformly in probability, thus making the proof much more challenging than usual. The neighbourhood around the critical point where uniform convergence fails is handled using a truncation argument.
Download or read book Multivariate Least Squares Forecasting Averaging by Vector Autoregressive Models written by Jen-Che Liao and published by . This book was released on 2016 with total page 47 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper proposes a multivariate least squares Mallows averaging approach to the issue of forecast combination by vector autoregressive (VAR) model fitting. Our approach extends the current literature on frequentist least squares model/forecast averaging methods, in particular Hansen (2008), to multivariate time series models. We provide a theoretical foundation of our approach by presenting the relation between the proposed multivariate Mallows averaging criterion and the in-sample mean squared error and out-of-sample mean squared forecast error. We also establish the asymptotic properties such as unbiasedness and optimality of our approach. In a simulation experiment, the proposed approach performs well in finite samples relative to other selection and averaging methods. For an empirical illustration, we apply our methodology to forecasting U.S. macroeconomic dynamic systems based on small-scale and medium-scale VARs fitted to the datasets that were previously studied by Sims (1980) and Stock and Watson (2009).
Download or read book Biases in GLS Estimators for Dynamic Panel Data Models Allowing Cross Sectional Heteroscedasticity written by Muhammad Abdullah and published by . This book was released on 2017 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: The inclusion of lagged dependent variable in the list of explanatory variables introduces the specific estimation problems even the generalized least squares estimator for the dynamic panel data models allowing cross sectional heteroscedasticity becomes biased and inconsistent. In this study, the analytical expressions for the inconsistency have been derived in the first order autoregressive case. A comparison between asymptotic bias and small sample simulated bias has also been carried out. The analytical biases emerged coincident with or a little above the small sample simulated biases. The closeness of the two types of biases mainly depends on coefficient of lagged dependent variable (y) and the number of cross sectional units N.
Download or read book Asymptotic Theory of the Least Squares Estimators of Sinusoidal Signal written by and published by . This book was released on 1997 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: The consistency and the asymptotic normality of the least squares estimators are derived of the sinusoidal model under the assumption of stationary random error. It is observed that the model does not satisfy the standard sufficient conditions of Jennrich (1969) Wu (1981) or Kundu (1991). Recently the consistency and the asymptotic normality are derived for the sinusoidal signal under the assumption of normal error (Kundu; 1993) and under the assumptions of independent and identically distributed random variables in Kundu and Mitra (1996). This paper will generalize them. Hannan (1971) also considered the similar kind of model and establish the result after making the Fourier transform of the data for one parameter model. We establish the result without making the Fourier transform of the data. We give an explicit expression of the asymptotic distribution of the multiparameter case, which is not available in the literature. Our approach is different from Hannan's approach. We do some simulations study to see the small sample properties of the two types of estimators.
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 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.
