a Department of Accounting, Finance and Management, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK;b Faculty of Finance, Cass Business School, UK;c Departmento de Matemática Aplicada, ETSII, University of Valladolid, Spain
Abstract:
This paper analyses the contribution of various numerical approaches to making the estimation of threshold autoregressive time series more efficient. It relies on the computational advantages of QR factorizations and proposes Givens transformations to update these factors for sequential LS problems. By showing that the residual sum of squares is a continuous rational function over threshold intervals it develops a new fitting method based on rational interpolation and the standard necessary optimality condition. Taking as benchmark a simple grid search, the paper illustrates via Monte Carlo simulations the efficiency gains of the proposed tools.