Gaussian Likelihood Estimation for Nearly Nonstationary AR(1) Processes.

Abstract

An asymptotic analysis is presented for estimation in the three parameter first order autoregressive model, where the parameters are the mean, autoregressive coefficient, and variance of the shocks. The nearly nonstationary asymptotic model is considered wherein the autoregressive coefficient tends to 1 as sample size tends to infinity. Three different estimators are considered: the exact gaussian maximum likelihood estimator, the conditional maximum likelihood or least squares estimator, and some naive estimators. It is shown that the estimators converge in distribution to analogous estimators for a continuous time Ornstein-Uhlenbeck process. Simulation results show that the MLE has smaller asymptotic mean squared error than the other two, and that the conditional maximum likelihood estimator gives a very poor estimator of the process mean. Keywords: Likelihood estimation; Autoregressive processes; Nearly nonstationary time series; Ornstein Uhlenbeck process.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1987
Accession Number
ADA183534

Entities

People

  • Dennis D. Cox

Organizations

  • University of Washington

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Coefficients
  • Convergence
  • Data Science
  • Differential Equations
  • Equations
  • Estimators
  • Information Science
  • Mathematics
  • Probability
  • Random Variables
  • Simulations
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics
  • Stochastic Processes
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Statistical inference.