Fitting ARMA Time Series Models without Identification: A Proximal Approach

Yin Liu, Sam Davanloo Tajbakhsh

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 nonsmooth hierarchical sparsity-inducing penalty based on two path graphs that allows 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 studies supporting the performance of the proposed method and comparing it with other schemes are presented.