Fitting ARMA Time Series Models without Identification: A Proximal Approach

TL;DR

This paper introduces a novel proximal approach for fitting ARMA time series models that simultaneously performs model identification and parameter estimation, avoiding traditional offline methods.

Contribution

It proposes a regularized optimization framework with hierarchical sparsity penalties and an efficient proximal algorithm for ARMA model fitting.

Findings

Method effectively performs model identification and estimation simultaneously.

Ensures stationarity and invertibility conditions are satisfied.

Numerical results demonstrate the approach's efficiency and accuracy.

Abstract

Fitting autoregressive moving average (ARMA) time series models requires model identification before parameter estimation. Model identification involves determining the order of the autoregressive and moving average components which is generally performed by inspection of the autocorrelation and partial autocorrelation functions or other offline methods. In this work, we regularize the parameter estimation optimization problem with a non-smooth hierarchical sparsity-inducing penalty based on two path graphs that allow performing model identification and parameter estimation simultaneously. A proximal block coordinate descent algorithm is then proposed to solve the underlying optimization problem efficiently. The resulting model satisfies the required stationarity and invertibility conditions for ARMA models. Numerical results supporting the proposed method are also presented.