Title: Big machine learning models that learn to estimate and forecast a class of autoregressive processes
Authors: Pablo Montero Manso - University of Sydney (Australia) [presenting]
Abstract: Machine Learning/AI models are complex enough to learn not only how to predict a single individual autoregressive process, but the whole class of autoregressive models. For example, suppose that a given class of autoregressive models of fixed order is optimally estimated by ordinary linear least squares; that is, all potential processes within the class are linear autoregressive of a fixed order, and the 'optimal' estimation in terms of mean squared error is to fit the parameters by least squares. A machine learning model that has been trained from a large set of time series of that class can learn an estimation algorithm, potentially replicating the least squares algorithm itself. We will present: 1) An analytical result that shows how a whole class or linear autoregressive models can be optimally estimated and predicted by a nonlinear model that does not require fit to each individual time series. 2) Specific machine learning models that are trained on millions of simulated time series (AR and VAR) that learn an `optimal' estimation procedure for the time series of that class. 3) Then compare the predictive performance of these models on new time series (without fitting them to data) against traditional estimation methods, such as the Box-Jenkins methodology.