title: Long memory mean and volatility models of platinum and palladium price return series under heavy tailed distributions.
abstract: South Africa is a cornucopia of the platinum group metals particularly platinum and palladium. These metals have many unique physical and chemical characteristics which render them indispensable to technology and industry, the markets and the medical field. In this paper we carry out a holistic investigation on long memory (LM), structural breaks and stylized facts in platinum and palladium return and volatility series. To investigate LM we employed a wide range of methods based on time domain, Fourier and wavelet based techniques while we attend to the dual LM phenomenon using ARFIMA-FIGARCH type models, namely FIGARCH, ARFIMA-FIEGARCH, ARFIMA-FIAPARCH and ARFIMA-HYGARCH models. Our results suggests that platinum and palladium returns are mean reverting while volatility exhibited strong LM. Using the Akaike information criterion (AIC) the ARFIMA-FIAPARCH model under the Student distribution was adjudged to be the best model in the case of platinum returns although the ARCH-effect was slightly significant while using the Schwarz information criterion (SIC) the ARFIMA-FIAPARCH under the Normal Distribution outperforms all the other models. Further, the ARFIMA-FIEGARCH under the Skewed Student distribution model and ARFIMA-HYGARCH under the Normal distribution models were able to capture the ARCH-effect. In the case of palladium based on both the AIC and SIC, the ARFIMA-FIAPARCH under the GED distribution model is selected although the ARCH-effect was slightly significant. Also, ARFIMA-FIEGARCH under the GED and ARFIMA-HYGARCH under the normal distribution models were able to capture the ARCH-effect. The best models with respect to prediction excluded the ARFIMA-FIGARCH model and were dominated by the ARFIMA-FIAPARCH model under Non-normal error distributions indicating the importance of asymmetry and heavy tailed error distributions.
authors.affiliation: Department of Statistics, University of South Africa, Cnr Christiaan de Wet and Pioneer Avenue, Florida Park, Roodepoort, 1710 South Africa.
authors.forename: Edmore
authors.initials: E
authors.lastname: Ranganai
authors.affiliation: Department of Statistics, University of South Africa, Cnr Christiaan de Wet and Pioneer Avenue, Florida Park, Roodepoort, 1710 South Africa.
authors.forename: Sihle Basil
authors.initials: SB
authors.lastname: Kubheka
keywords: ARFIMA–FIGARCH type models; Heavy tailed distribution; Heteroskedasticity; Long memory; Palladium; Platinum; Structural breaks; Volatility