Optimal Recursive Estimation of Dynamic Models

Abstract

This article checks, using both real and simulated data, the effectiveness of modern adaptive techniques to track the parameters of time-varying dynamic models. The real case studies concern a bone marrow transplant data set published by Tong, the gas furnace model of Box and Jenkins, and two series of West German interest rates. Simulation studies focus on ARX models with smoothly and suddenly changing parameters. The general approach is to compare the fitting-forecasting performance of classical and adaptive methods, holding fixed the order of the models. At the methodological level, the basic step is taken by unifying known estimators, such as recursive least squares and Kalman filter, into a general algorithm. Next, the problem of optimal design of the tracking coefficients (such as discounting factors and learning rates), is solved by optimizing a quadratic functional based on one-step-ahead prediction errors. All applications show that adaptive modeling, based on the design and the optimization of recursive algorithms, leads to significant improvements of the forecasting performance.

Key Words:

• Bone marrow transplant data
• Extended Kalman filter
• Gas furnace data set
• Recursive least squares
• Transfer function models
• West German interest rates