DELAY PARAMETER OF TRANSITION VARIABLE IN THE SMOOTH TRANSITION AUTOREGRESSIVE (STAR) MODEL: IMPORTANT DETERMINANT

Abstract

This study investigates some determinant of appropriate delay parameter of the transition variable in the Smooth Transition Autoregressive (STAR) models, with emphasize on the model type and data characteristics through a refine method.  Daily share price data were sourced from the Nigerian Exchange Limited, covering 10 years (January 2, 2014 to December 29, 2023), comprising 2,472 observations for each of the selected stocks: GTCO and STANBIC from the financial sector, and DANGCEM, BETAGLASS, and WAPCO from the industrial sector. Linearity tests demonstrated that DANGCEM, GTCO, and STANBIC share returns exhibit nonlinear characteristic of financial time series (FTS), whereas WAPCO returns remain linear and the most suitable delay parameter for each stock returns was determined. The Escribano-Jorda procedure was employed to select appropriate transition function. An asymmetric transition function was specified for DANGCEM and GTCO stock returns, while a symmetric transition function was identified for STANBIC and BETAGLASS returns. Consequently, asymmetric STAR models were fitted to DANGCEM and GTCO, and symmetric STAR models were fitted to BETAGLASS and STANBIC, using delay lengths within the range (1≤d≤p). The results indicated that the APLSTAR, LSTAR, and SPLSTAR models with the initially chosen delay lengths were optimal for DANGCEM, GTCO, and BETAGLASS stock returns, respectively. However, for STANBIC returns, the optimal SPLSTAR model was associated with a delay length different from the initially selected delay parameter. This study concludes that while the delay parameter of the transition variable is typically determined from the characteristics of the FTS, STAR model type also significantly influences the selection of an appropriate delay parameter.