A1109
Title: Logistic regression with GAS dynamics
Authors: Michal Cerny - University of Economics Prague (Czech Republic) [presenting]
Martin Konopasek - Prague University of Economics and Business (Czech Republic)
Abstract: The aim is to deal with a logistic binary choice model with time-varying regression coefficients, where the dynamics in the regression coefficients is introduced via the generalized autoregressive score (GAS) methodology. The GAS equation for the dynamics consists of an autoregressive component and a score-driven component, formalizing the intuition that "when observed data is not well predicted by the model, then for the next period, it is reasonable to make an update in the direction of the gradient of the log-likelihood (in the parameter space)." Plotting the paths of the estimated time-varying coefficients can serve as a natural diagnostic tool for changepoints or for changes in the significance of regressors. Some hypotheses, such as "a regression coefficient is constant in time," can be tested explicitly in this model. The main challenge is computational: estimating the model amounts to optimizing a complex likelihood function, the formula of which has an exponential length w.r.t. the number of observations. It follows that standard tools used in optimization, such as the gradient or hessian, are hard to express. Some theoretical challenges associated with this model are presented, such as identification conditions or an algorithm for fitting the model.
