The functional form used in regression may be generalized by the Box-Cox transformation. We adopt the generalized information criterion (GIC) approach to determine a need for Box-Cox (J. Roy. Statist. Soc. Ser. B 26 (1964) 211) transformation of the response variable. The utilization of the...

Wavelets are applied to identify the time delay and thresholds in open-loop threshold autoregressive models. Based on Truong and Stone's lemma, the empirical wavelet coefficients of the data are defined. The time delay and thresholds are detected and then estimated by checking the variation of...