Fractional integration: an overview and results on mining sector time series

Many empirically observed time series, even when behaving as stationary processes (eventually after differencing), exhibit characteristics of extremely high persistence. Unit root tests and autocorrelation functions do not always provide unequivocal indications regarding long-run dynamic properties of these variables. This paper sets off by considering theoretical and applied developments in this field. Log-spectrum regressions, complemented with alternative estimation techniques, is applied to analyse variables of concern to the mining sector in South Africa, covering different periods and frequencies. Most of the variables are found to be fractionally integrated, with the order tending to be higher than one, thus bearing implications for the analysis of persistence, non-stationarity and cointegration.

Keywords: fractional integration, mineral resources, time series analysis