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A Bayesian ARMA Probability Density Estimator.

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  • 1Department of Statistics, Texas A&M University, College Station, TX 77843, USA.

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Summary
This summary is machine-generated.

This study introduces a Bayesian method for creating Autoregressive Moving Average (ARMA) probability density estimators. This new approach offers improved efficiency and parsimony compared to traditional Fourier series methods.

Keywords:
BICKullback–Leibler discrepancyLaplace approximationidentifiabilityimportance samplingintegrated squared errorprobability bandssingle-component Metropolis–Hastings algorithmtruncated Fourier series

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Area of Science:

  • Statistics
  • Time Series Analysis
  • Probability Theory

Background:

  • Traditional methods for probability density estimation, such as Fourier series estimators, have limitations in parsimony and efficiency.
  • Autoregressive Moving Average (ARMA) models are widely used for time series analysis.

Purpose of the Study:

  • To propose a novel Bayesian approach for constructing ARMA probability density estimators.
  • To demonstrate the advantages of these Bayesian estimators over existing methods, particularly Fourier series estimators.

Main Methods:

  • A Bayesian framework is employed for estimator construction.
  • Markov Chain Monte Carlo (MCMC) methods are utilized to implement the Bayesian approach.
  • The proposed estimators are characterized as ratios of trigonometric polynomials.

Main Results:

  • The Bayesian ARMA estimators exhibit greater parsimony and efficiency under common conditions.
  • MCMC output facilitates the calculation of probability intervals for parameters and the underlying density.
  • Simulation studies assess finite sample efficiency and smoothing parameter selection.

Conclusions:

  • The proposed Bayesian approach provides a robust and efficient method for ARMA probability density estimation.
  • These estimators offer practical advantages for analyzing time series data, as illustrated with a wine attribute dataset.