Fitting ARMA Time Series Models without Identification: A Proximal Approach
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Fitting autoregressive moving average (ARMA) time series models requires model identification before parameter estimation. Model identification involves determining the order for the autoregressive and moving average components which is generally performed by visual inspection of the autocorrelation and partial autocorrelation functions, or by other offline methods. In many of today's big data regime applications of time series models, however, there is a need to model one or multiple streams of data in an iterative fashion. Hence, the offline model identification step is significantly prohibitive. In this work, we regularize the objective of the optimization behind the ARMA parameter estimation problem with a nonsmooth hierarchical sparsity inducing penalty based on two path graphs that allows incorporating the identification into the estimation step. A proximal block coordinate descent algorithm is then proposed to solve the underlying optimization problem. The resulting model satisfies the required stationarity and invertibility conditions for ARMA models. Numerical results supporting the proposed method are presented.
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