02 - A novel artificial neural network estimator for AR(1) time series parameters

The class of ARMA(p,q) models are archetypal statistical models for stationary time series. ARMA model parameters are usually estimated by the classical methods of maximum likelihood, maximum entropy (the Burg method), ordinary least squares, or moments. 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 an artificial neural network (ANN). The architecture of this ANN estimator includes many weights (hyperparameters) that can be tuned to the given time series data set. Tuning (or training) the ANN 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 the parameter's posterior distribution to artificially generate training data. This novel Bayesian data generation scheme can produce training data sets of any size. The performance (bias and standard error) of the ANN estimator is compared with those of some of the classical approaches.

artificial neural network

AR(1) process

parameter estimation

Bayesian data generation

estimator architecture

machine learning estimator 

Mid-Level

Knowledge

Women in Statistics and Data Science 2022