Statistical Time Series Prediction with Deep Learning Methodology

Abstract

The objective of this study is to develop methodology for the modelling and forecasting of multivariate time series. We propose three models with trend functions and/or time- dependent coefficients in the best linear predictor, which is assumed to involve past values up to a finite lag p. The trend and time-varying parameters are generated from LSTM networks and optimised using the associated deep learning methodology. Our network training adheres to the sound principle of exact maximum likelihood estimation. Once the network is trained, optimal forecasts can be derived from each fitted model. We also enforce the causality condition on the VAR coefficients to ensure the stability of each model and its interpretability as a prediction model. In our first model, DeepVARwT, we allow the presence of a trend in the time series, while the dependence is modelled by a VAR(p) model with fixed parameters. The second model, DeepTVAR, allows the time series to have time-dependent coefficients in its best linear predictor. The third model, DeepTVARwT, contains both a trend and time dependent coefficients in its best linear predictor. This most general model includes DeepVARwT and DeepTVAR as special cases. We demonstrate the effectiveness of the proposed models and estimation methods through simulation studies and real data applications.

Date of Award	1 Aug 2024
Original language	English
Awarding Institution	The University of Manchester
Supervisor	Jingsong Yuan (Supervisor) & Georgi Boshnakov (Supervisor)