A Numerical Algorithm for the Efficient Estimation of Band-TAR Models
by
Ana-Maria Fuertes
Department of Economics, London Guildhall University, UK
Coauthors: Jerry Coakley (Birkbeck College, University of London, UK), M.Teresa Perez (ETSII, University of Valladolid, Spain)

This paper proposes an efficient estimation method for the class of Band threshold autoregressive (Band-TAR) time series models. It defines the threshold space as the union of a countable number of continuous nonoverlapping intervals called threshold intervals. Givens rotations are employed to update the QR decomposition of the LS problem associated to the first threshold interval. By showing that the residual sum of squares function is a continuous rational function of degree type (4,2) over each threshold interval we propose an algorithm that readily determines the optimal threshold locally in each iteration. An Akaike information type criteria is adopted to find the global optimal threshold over the countable set of local minima, and thus the best fit Band-TAR model. The paper shows via simulations the gain in the ratio of accuracy to computation time of this method over a conventional grid search.

Date received: January 31, 2000