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May, 1978 On Conditional Least Squares Estimation for Stochastic Processes
Lawrence A. Klimko, Paul I. Nelson
Ann. Statist. 6(3): 629-642 (May, 1978). DOI: 10.1214/aos/1176344207


An estimation procedure for stochastic processes based on the minimization of a sum of squared deviations about conditional expectations is developed. Strong consistency, asymptotic joint normality and an iterated logarithm rate of convergence are shown to hold for the estimators under a variety of conditions. Special attention is given to the widely studied cases of stationary ergodic processes and Markov processes with are asymptotically stationary and ergodic. The estimators and their limiting covariance matrix are worked out in detail for a subcritical branching process with immigration. A brief Monte Carlo study of the performance of the estimators is presented.


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Lawrence A. Klimko. Paul I. Nelson. "On Conditional Least Squares Estimation for Stochastic Processes." Ann. Statist. 6 (3) 629 - 642, May, 1978.


Published: May, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0383.62055
MathSciNet: MR494770
Digital Object Identifier: 10.1214/aos/1176344207

Primary: 62M05
Secondary: 62F10 , 62M10

Keywords: asymptotic normality , branching process with immigration , consistency , ergodic Markov processes , estimation , iterated logarithm , Stationary processes , time series

Rights: Copyright © 1978 Institute of Mathematical Statistics


Vol.6 • No. 3 • May, 1978
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