Modern Strategies for Time Series Regression

Abstract

This paper discusses several modern approaches to regression analysis involving time series data where some of the predictor variables are also indexed by time. We discuss classical statistical approaches as well as methods that have been proposed recently in the machine learning literature. The approaches are compared and contrasted, and it will be seen that there are advantages and disadvantages to most currently available approaches. There is ample room for methodological developments in this area. The work is motivated by an application involving the prediction of water levels as a function of rainfall and other climate variables in an aquifer in eastern Australia.

Forecasting Multiple Groundwater Time Series with Local and Global Deep Learning Networks

“…The best and most reliable predictions, particularly for the longer term, will result from models that incorporate a rich and relevant set of additional features. In [10], results obtained through this type of classic statistical time series modelling were compared with those obtained through the application of machine learning strategies.…”

“…By including the month-within-year v with extractions, the model has the flexibility to create an interaction that all tion of an annual dip and recovery, with the depth of the dip dependent on t ber of extractions for that year. More detail can be found in [10], along with sion about how MLPs compare and contrast with more classical statistical me such an approach may sometimes work reasonably well, the literature in rec moved towards more sophisticated ways to extend neural networks to appl for time series prediction. In the MLP, each connection between nodes has an associated weight, or parameter, to be estimated.…”

“…In a recent project sponsored by the NSW Department of Planning and Environment (DPIE) in New South Wales (NSW), Australia, we compared machine learning approaches based on neural network models with classic time series methods to model the level of groundwater in an aquifer in the Richmond River catchment, in the northeast part of the state [10]. We found that, while each approach has some unique advantages and disadvantages, both did a remarkably good job at capturing changing patterns over time.…”

“…Neither approach gives a perfect prediction, but both do very well in terms of capturing the key features of how the aquifer levels changed over time. See [10] for more detail.…”

Erratum

“…In Clark et al (2020), errors in the sizing and resolution resulted in a lack of clarity in some of the figures.…”