Author: Stanford University. Department of Statistics
Publisher:
ISBN:
Category : Time-series analysis
Languages : en
Pages : 318
Book Description
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.
Asymptotic Properties of Some Estimators in Moving Average Models
Author: Stanford University. Department of Statistics
Publisher:
ISBN:
Category : Time-series analysis
Languages : en
Pages : 318
Book Description
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.
Publisher:
ISBN:
Category : Time-series analysis
Languages : en
Pages : 318
Book Description
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.
Asymptotic Properties of Some Preliminary Estimators for Autoregressive Moving Average Time Series Models
Author: Pentti Saikkonen
Publisher:
ISBN: 9789514532917
Category :
Languages : en
Pages : 31
Book Description
Publisher:
ISBN: 9789514532917
Category :
Languages : en
Pages : 31
Book Description
Asymptomatic Properties of the Maximum Likelihood and Non-linear Least Squares Estimators for Noninvertible Moving Average Models
Author: Katsuto Tanaka
Publisher:
ISBN: 9780868311517
Category : Econometric models
Languages : en
Pages : 38
Book Description
Publisher:
ISBN: 9780868311517
Category : Econometric models
Languages : en
Pages : 38
Book Description
Asymptotically Efficient Estimates of the Parameters of a Moving Average Time Series
Author: M. Lawrence Clevenson
Publisher:
ISBN:
Category : Time-series analysis
Languages : en
Pages : 212
Book Description
The thesis is concerned with the estimation of the parameters of a moving average time series, (x sub t, t= 0, plus or minus 1, plus or minus 2 ...), of order M. By definition, such a series has the representation x sub t = (eta sub t) + (b sub 1)(eta sub (t-1)) + (b sub 2)(eta sub (t-2)) + ... + (b sub M)(eta sub (+-M)) for some series of uncorrelated, identically distributed random variables eta sub t, t = 0, plus or minus 1, plus or minus 2 ...). It is assumed that the process has mean zero and is a Gaussian process; hence eta sub t has a normal distribution with mean and some unknown variance (sigma sub n) squared. The goal is to find asymptotically normal and efficient estimates of the parameters of the model. (Author).
Publisher:
ISBN:
Category : Time-series analysis
Languages : en
Pages : 212
Book Description
The thesis is concerned with the estimation of the parameters of a moving average time series, (x sub t, t= 0, plus or minus 1, plus or minus 2 ...), of order M. By definition, such a series has the representation x sub t = (eta sub t) + (b sub 1)(eta sub (t-1)) + (b sub 2)(eta sub (t-2)) + ... + (b sub M)(eta sub (+-M)) for some series of uncorrelated, identically distributed random variables eta sub t, t = 0, plus or minus 1, plus or minus 2 ...). It is assumed that the process has mean zero and is a Gaussian process; hence eta sub t has a normal distribution with mean and some unknown variance (sigma sub n) squared. The goal is to find asymptotically normal and efficient estimates of the parameters of the model. (Author).
Asymptotic properties of tests in autoregressive moving average models
Optimal Asymptotic Properties of Maximum Likelihood Estimators of Parameters of Some Econometric Models
Author: Mary Kathleen Vickers
Publisher:
ISBN:
Category : Asymptotes
Languages : en
Pages : 312
Book Description
Four theorems are proven, which simplify the application to econometric models of Weiss's theorem on asymptotic properties of maximum likelihood estimators in nonstandard cases. The theorems require, roughly: the uniform convergence in any compact sets of the unknown parameters of the expection of the Hessian matrix of the log likelihood function; and the uniform convergence to 0 in the same sense of the variance of the same quantities. The fourth theorem allows one to conclude that the optimal properties hold on an image set of the parameters when the map satisfies certain smoothness conditions, and the first three theorems are satisfied for the original parameter set. These four theorems are applied to autoregressive models, nonlinear models, systems of equations, and probit and logit models to infer optimal asymptotic properties. (Author).
Publisher:
ISBN:
Category : Asymptotes
Languages : en
Pages : 312
Book Description
Four theorems are proven, which simplify the application to econometric models of Weiss's theorem on asymptotic properties of maximum likelihood estimators in nonstandard cases. The theorems require, roughly: the uniform convergence in any compact sets of the unknown parameters of the expection of the Hessian matrix of the log likelihood function; and the uniform convergence to 0 in the same sense of the variance of the same quantities. The fourth theorem allows one to conclude that the optimal properties hold on an image set of the parameters when the map satisfies certain smoothness conditions, and the first three theorems are satisfied for the original parameter set. These four theorems are applied to autoregressive models, nonlinear models, systems of equations, and probit and logit models to infer optimal asymptotic properties. (Author).
Some Asymptotic Properties of the Sample Covariances of Gaussian Autoregressive Moving Average Processes
Scientific and Technical Aerospace Reports
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1460
Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1460
Book Description
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Asymptotic Properties and Computation of Maximum Likelihood Estimates in the Mixed Model of the Analysis of Variance
Author: Stanford University. Department of Statistics
Publisher:
ISBN:
Category : Analysis of variance
Languages : en
Pages : 556
Book Description
The problem considered is the estimation of the parameters in the mixed model of the analysis of variance, assuming normality of the random effects and errors. Both asymptotic properties of such estimates as the size of the design increases and numerical procedures for their calculation are discussed. Estimation is carried out by the method of maximum likelihood. It is shown that there is a sequence of roots of the likelihood equations which is consistent, asymptotically normal and asymptotically efficient in the sense of attaining the Cramer-Rao lower bound for the covariance matrix as the size of the design increases. This is accomplished using a Taylor series expansion of the log-likelihood. (Modified author abstract).
Publisher:
ISBN:
Category : Analysis of variance
Languages : en
Pages : 556
Book Description
The problem considered is the estimation of the parameters in the mixed model of the analysis of variance, assuming normality of the random effects and errors. Both asymptotic properties of such estimates as the size of the design increases and numerical procedures for their calculation are discussed. Estimation is carried out by the method of maximum likelihood. It is shown that there is a sequence of roots of the likelihood equations which is consistent, asymptotically normal and asymptotically efficient in the sense of attaining the Cramer-Rao lower bound for the covariance matrix as the size of the design increases. This is accomplished using a Taylor series expansion of the log-likelihood. (Modified author abstract).