A Novel Neural Network Estimator for the AR(1) Model

• Activity Number: 114 - Time Series Methods and Applications
• Type: Contributed
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Angela Folz* and Mary Gregg and Lucas Koepke and Michael Frey
• Companies: National Institute of Standards and Technology/University of Colorado Boulder and National Institute of Standards and Technology and National Institute of Standards and Technology and National Institute of Standards and Technology
• Keywords: artificial neural network; AR(1) process; parameter estimation; training data generation; estimator architecture; machine learning estimator

Abstract

The class of autoregressive moving average (ARMA) models are archetypal statistical models for stationary time series. ARMA model parameters are usually estimated by classical approaches such as maximum likelihood, maximum entropy (the Burg method), method of moments, or Bayesian methods. We focus on the simplest member of this class, the AR(1) model, and propose a machine learning estimator for its primary parameter based around the architecture of a neural network (NN). The architecture of this NN estimator includes many weights (hyperparameters) that can be tuned to the given time series data set. Tuning (or training) the NN requires a training data set with many time series samples labelled by the model parameter(s) that created them. In practice, though, only the original time series data are available. We overcome this problem by sampling from a data-driven distribution to artificially generate training data. This novel data generation scheme can produce training data sets of any size. The performance (bias, standard error, and mean squared error) of the NN estimator is compared with those of some of the classical approaches.