M-Estimation for Nearly Non-Stationary Autoregressive Time Series.

Abstract

The nearly nonstationary first order autoregression is a sequence of processes where the autoregressive coefficient tends to 1 as n approaches infinity. M-estimates of the autoregressive coefficient are considered. The process is allowed to be nongaussian, but a 2 + delta moment condition is assumed. The limiting distribution is not the usual normal limit but is characterized as a ratio of two stochastic integrals. The asymptotically most efficient M-estimate is not given by maximum likelihood. However, it is shown that the loss of efficiency in using maximum likelihood is no worse than about 20% whereas the usual least squares estimator can have arbitrarily low efficiency. Keywords: M estimation; time series, autoregressive; non stationary.

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1987
Accession Number
ADA181184

Entities

People

  • Dennis D. Cox
  • Isabel Llatas

Organizations

  • University of Washington

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Brownian Motion
  • Coefficients
  • Differential Equations
  • Equations
  • Estimators
  • Integrals
  • Mathematics
  • New York
  • Numerical Integration
  • Probability
  • Random Variables
  • Sequences
  • Stationary
  • Statistical Algorithms
  • Statistics
  • Stochastic Processes
  • Three Dimensional

Fields of Study

  • Mathematics

Readers

  • Statistical inference.