249 – Regularization and Prediction in Time Series and Longitudinal Models
Regression Tree Flow Field Forecasting
Kyle A. Caudle
South Dakota School of Mines and Technology
Patrick Fleming
South Dakota School of Mines and Technology
Michael Frey
Bucknell University
Flow field forecasting is a statistical learning methodology originally devised to forecast a univariate time series. This methodology in essence uses past histories to forecast the future from the current history. This perspective has at least two attractive features: 1) the choice of explanatory variables that defines the structure of the history is wide open (flexibility) and 2) extension to multivariate time series is straightforward. Defining the history structure in flow field forecasting is analogous to variable selection in regression, with the complication that the choice of history structure may change. In other settings classification and regression tree (CART) methodology has been effective for navigating large sets of explanatory variables, doing so by assuming a structured form of the regression function, and thereby finessing the curse of dimensionality. We show how CART methodology can be adapted to support flow field forecasting of multivariate time series. In our application of the CART paradigm, we do not need to grow the entire regression tree; only the tree's branch that is most similar to the current history. This is a significant computational advantage.