A time deformation model and its time-varying autocorrelation: An application to US unemployment data

A G-Lambda model is characterized by a constant mean, a finite variance and a covariance that is a function of both time and lags. The Box–Cox transformation of the time scale transforms a non-stationary G-Lambda model into a stationary model. This paper explores the time-varying behavior of the G-Lambda model. Simulation results indicate that it is possible to distinguish between the G-Lambda model and other better-known models such as the ARIMA, ARFIMA and STAR models. Applying the model to US unemployment data, the performance of the G-Lambda model varies as the start of the forecast periods changes. However, the results of the sign test and the Diebold–Mariano test indicate that the G-Lambda model has significantly better long-term forecasts than other models.