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Non-Gaussian autoregressive moving average processes.

K S Lii1, M Rosenblatt

  • 1Department of Statistics, University of California, Riverside, CA 92521, USA.

Proceedings of the National Academy of Sciences of the United States of America
|October 1, 1993
PubMed
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This study introduces efficient methods for estimating coefficients in non-Gaussian autoregressive moving average models. It focuses on nonminimum-phase models, advancing time series analysis for complex data.

Area of Science:

  • Statistics
  • Time Series Analysis
  • Econometrics

Background:

  • Autoregressive moving average (ARMA) models are fundamental in time series analysis.
  • Non-Gaussian and nonminimum-phase models present unique estimation challenges.
  • Accurate coefficient estimation is crucial for reliable time series forecasting and inference.

Purpose of the Study:

  • To develop asymptotically efficient estimation methods for non-Gaussian stationary autoregressive moving average sequences.
  • To address the specific challenges posed by nonminimum-phase models.
  • To provide robust techniques for estimating model coefficients under specified density function conditions.

Main Methods:

  • Consideration of non-Gaussian stationary autoregressive moving average sequences.

Related Experiment Videos

  • Application of estimation methods under conditions of density function smoothness and positivity.
  • Focus on asymptotically efficient techniques for coefficient estimation.

    • Main Results:

    • Development of asymptotically efficient methods for estimating unknown coefficients.
    • Demonstration of applicability to nonminimum-phase models.
    • Establishment of estimation procedures under specific distributional assumptions.

    Conclusions:

    • The proposed methods offer efficient estimation for non-Gaussian ARMA models, particularly nonminimum-phase variants.
    • The findings contribute to advanced statistical inference for complex time series data.
    • The study provides a theoretical framework for robust coefficient estimation in challenging model structures.