Linear-Regression-Based Models of Nonlinear Processes

Abstract
Classical linear regression methods are applied to the analysis of long multivariate climatic time series by constructing predictive stochastic models of the observed variability. The data-based models so obtained are linear in terms of their propagator's dependence on the (empirically determined) regression parameters, but involve (pre- specified) nonlinear dependence on the climate state vector itself. This presentation will outline a strategy for practical combination of linear regression approach with data compression techniques and regularization methods, and introduce an efficient multi-level algorithm for incorporating, into a regression model, most of the data set's information content. The resulting empirical models produce surrogate time series whose statistical properties mimic closely those of the original data set; examples will include observed and dynamical-model-generated series of mid-latitude geopotential-height anomalies, as well as tropical sea-surface temperature variability associated with ENSO. Analysis of the regression models provides conceptual view for possible dynamical causes behind the observed statistics.

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