Revisiting inference for ARMA models: Improved fits and superior confidence intervals

Area of Science:

• Statistics
• Time Series Analysis

Background:

• Autoregressive Moving Average (ARMA) models are standard tools for time series data analysis.
• Current likelihood-based inference methods for ARMA models can lead to suboptimal parameter estimates due to local optima in maximization algorithms.

Purpose of the Study:

• To address the limitations of existing ARMA model inference methods.
• To introduce a novel algorithm for overcoming local optima in ARMA likelihood maximization.
• To demonstrate the superiority of profile likelihoods for confidence intervals.

Main Methods:

• Development of a novel random initialization algorithm tailored to the ARMA likelihood function structure.
• Comparison of profile likelihoods with Fisher information matrix-based confidence intervals.
• Validation through a data analysis example and simulation studies.

Main Results:

• The proposed random initialization algorithm effectively overcomes local optima in ARMA parameter estimation.
• Profile likelihoods yield superior confidence intervals compared to those derived from the Fisher information matrix.
• The methodology demonstrates improved accuracy and reliability in ARMA model analysis.

Conclusions:

• Existing ARMA model inference procedures have under-recognized shortcomings that impact scientific and industrial applications.
• The novel random initialization algorithm and profile likelihood approach offer significant improvements for ARMA model analysis.
• This work enhances statistical practice by providing robust solutions for common ARMA modeling challenges.