Adaptive Estimation and Structural Change in Regression and Time Series Models

Heuristic and model-based approaches to adaptive estimation in regression models are reviewed in this chapter. We describe a model-based approach that introduces time-varying coefficients explicitly and assumes that the coefficients follow certain autoregressive integrated moving average time series processes. We show how these time-varying coefficient models can be written in state space form, we illustrate how the Kalman filter approach can be used to update the coefficient estimates and forecasts, and we discuss why the resulting estimates are more responsive to structural change than the standard least squares estimates. The parameters in the underlying stochastic processes that generate the time-varying coefficients are needed to update the coefficient estimates. It is shown how these parameters can be estimated from historic observations. These parameters determine how adaptive the resulting coefficient estimates are to changes in the coefficients.