The Annals of Statistics

On Conditional Least Squares Estimation for Stochastic Processes

Lawrence A. Klimko and Paul I. Nelson

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 6, Number 3 (1978), 629-642.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344207

Digital Object Identifier
doi:10.1214/aos/1176344207

Mathematical Reviews number (MathSciNet)
MR494770

Zentralblatt MATH identifier
0383.62055

JSTOR
links.jstor.org

Subjects
Primary: 62M05: Markov processes: estimation
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62F10: Point estimation

Keywords
Estimation ergodic Markov processes stationary processes consistency asymptotic normality iterated logarithm branching process with immigration time series

Citation

Klimko, Lawrence A.; Nelson, Paul I. On Conditional Least Squares Estimation for Stochastic Processes. Ann. Statist. 6 (1978), no. 3, 629--642. doi:10.1214/aos/1176344207. https://projecteuclid.org/euclid.aos/1176344207


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