Numerical issues in threshold autoregressive modeling of time series

Asymmetric adjustment and nonlinear dynamics in real exchange rates

“…20. See Coakley et al (2003) who propose an algorithm with low computational burden but accurate grid search. 21.…”

On the least squares estimation of multiple-regime threshold autoregressive models

“…Tsay (1989) transforms model (2.1) into a change-point model and use the rearranged technique to localize possible positions of threshold parameters. Similarly, using same rearranged technique, Coakley, Fuertes and Pérez (2003) provides an efficient estimation approach which relies on the computational advantages of QR factorizations of matrices. When m is small, the grid-based search algorithm is an easy way to obtain the global minimum of L n (·).…”

Changing-regime volatility: a fractionally integrated SETAR model

“…Ideally, one would like to apply here methods based on maximum likelihood approach (the Whittle estimator), but this is not feasible because, as in the standard SETAR model, the log-likelihood function is not continuously differentiable with respect to the threshold parameters. In the standard SETAR modeling, the estimation methods are generally sequential (see Tong (1990), Tsay (1989) or Hansen (1997 and2000) among others); nevertheless, some recent papers try to develop different methods in order to make a joint estimation of the parameters (by using some factorizations as in Coakley, Fuertes and Pérez (2003), Bayesian method as in So and Chen ( 2003) or genetic algorithm as in Wu and Chang (2002)). The transposition of these methods to our case is, however, not feasible because of the presence of the fractional parameters in the regimes.…”