Maximum likelihood estimation for a fractionally differenced autoregressive model on a two-dimensional lattice

Sankara N Sethuraman, I. V. Basawa

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A two-dimensional time series model with long-memory dependence is introduced. The model is based on a fractionally differenced autoregressive process (long-memory) combined with a standard pth order stationary autoregressive process (short-memory). The maximum likelihood estimators for the parameters in the model are derived and their asymptotic distributions are obtained. A novel feature of the derivations is that a new two-dimensional martingale representation is used.

Original languageEnglish (US)
Pages (from-to)219-235
Number of pages17
JournalJournal of Statistical Planning and Inference
Volume44
Issue number2
DOIs
StatePublished - Apr 1 1995

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Maximum likelihood estimation
Long Memory
Autoregressive Process
Autoregressive Model
Maximum Likelihood Estimation
Martingale Representation
Data storage equipment
Time Series Models
Stationary Process
Maximum Likelihood Estimator
Asymptotic distribution
Maximum likelihood
Time series
Model
Autoregressive model
Autoregressive process
Long memory
Standards
Time series models
Maximum likelihood estimator

Keywords

  • 62M05
  • 62M10
  • Asymptotic inference
  • Lattice processes
  • Long-memory dependence
  • Maximum likelihood estimation
  • Time series

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

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AB - A two-dimensional time series model with long-memory dependence is introduced. The model is based on a fractionally differenced autoregressive process (long-memory) combined with a standard pth order stationary autoregressive process (short-memory). The maximum likelihood estimators for the parameters in the model are derived and their asymptotic distributions are obtained. A novel feature of the derivations is that a new two-dimensional martingale representation is used.

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