Robust Two-Step Wavelet-Based Inference for Time Series Models

Area of Science:

• Statistics
• Time Series Analysis
• Signal Processing

Background:

• Latent time series models, including Autoregressive Moving Average (ARMA) models, are vital in biology, ecology, engineering, and economics.
• Challenges in analyzing these models include data outliers, high computational costs for large datasets, and complex model selection.
• Existing methods often fail to address these issues simultaneously.

Purpose of the Study:

• To propose a general framework for robust two-step estimation of latent time series models.
• To jointly address challenges of outliers, computational complexity, and model selection.
• To provide a practical and efficient method for analyzing complex time series data.

Main Methods:

• Development of a bounded influence M-estimator for wavelet variance to handle outliers.
• Establishment of conditions for the joint asymptotic normality of the wavelet variance estimator for inference.
• Application of the generalized method of wavelet moments (GMWM) for robust two-step estimation.

Main Results:

• The proposed robust two-step estimation framework effectively handles outliers and reduces computational complexity.
• Asymptotic properties of the robust estimators are derived using the GMWM framework.
• Simulation studies demonstrate the good finite sample performance of the robust GMWM estimator.

Conclusions:

• The developed framework offers a simultaneous solution to common challenges in latent time series analysis.
• The robust GMWM estimator is practically relevant and performs well in simulations.
• This approach enhances the reliability and efficiency of time series analysis in diverse scientific domains.