ABSTRACT

The forecast performance of a smooth transition autoregressive (STAR) model is affected by the choice of transition function. In this study, the well-known logistic function is modified, leading to power logistic family of transition functions. Two special cases of this family, namely, the symmetric power logistic function and asymmetric power logistic function are defined. Each of the functions is approximated by using the Taylor series expansion up to the third order. Certain properties of the functions are determined following the approximations. The two functions are used to formulate the symmetric and asymmetric STAR models. The former and the latter are justifiably fitted to monthly exchange rate of naira to United States dollar and Euro, respectively, over the period, January, 2004 to April, 2021. On the basis of each of the economic time series, the fit of the appropriate power logistic STAR model is compared with the fits of the competing (comparable) models. It is observed that symmetric power logistic STAR model is the most suitable for exchange rate of naira to United States dollar, while asymmetric power logistic STAR model fits exchange rate of naira to Euro better than the other models. Residuals from each of the models fitted to each series are subjected to the Lagrange Multiplier test for autoregressive conditional heteroscedastic (ARCH) effects. There is no substantial evidence to reject the presence of ARCH effects in the sets of residuals. Hence, I adopt hybrid smooth transition autoregressive-generalized ARCH (STAR-GARCH) models. The STAR-GARCH models are compared using forecasts evaluation criteria. On balance SPLSTAR-GARCH (1, 1) model is the best for exchange rate of naira to United States dollar, while APLSTAR-GARCH (0, 1) model is the best for exchange rate of naira to Euro.