Statistical Inference for Oscillation Processes

TL;DR

This paper introduces a novel statistical model for oscillation time series, combining a hidden phase process and a nonparametric pattern, with efficient inference methods validated on simulations and ECG data.

Contribution

It develops a new generalized state space model for oscillations, proves its identifiability, and proposes a particle smoother and nonparametric EM algorithm for inference.

Findings

Effective estimation of oscillation patterns and phase processes

Algorithms perform well in simulations and ECG analysis

Model provides a flexible framework for oscillation analysis

Abstract

A new model for time series with a specific oscillation pattern is proposed. The model consists of a hidden phase process controlling the speed of polling and a nonparametric curve characterizing the pattern, leading together to a generalized state space model. Identifiability of the model is proved and a method for statistical inference based on a particle smoother and a nonparametric EM algorithm is developed. In particular, the oscillation pattern and the unobserved phase process are estimated. The proposed algorithms are computationally efficient and their performance is assessed through simulations and an application to human electrocardiogram recordings.