In this article we derive conditions which ensure the non-negativity of the conditional variance in the Hyperbolic GARCH(p, d, q) (HYGARCH) model of Davidson (2004). The conditions are necessary and sufficient for p ≤ 2 and sufficient for p > 2 and emerge as natural extensions of the inequality constraints derived in Nelson and Cao (1992) for the GARCH model and in Conrad and Haag (2006) for th...

GARCH-type models have been highly developed since Engle [1982] presented ARCH process 30 years ago. Different kinds of GARCH-type models are applicable to different kinds of research purposes. As documented by many literatures that short-memory processes with level shifts will exhibit properties that make standard tools conclude long-memory is present. Therefore, in this paper, we want to fore...

This paper develops a bivariate Markov Switching FIGARCH (MS-FIGARCH) process with constant and time varying transition probabilities as a way of modeling spot futures dynamics. An application of the model illustrates that the S&P500 and its futures exhibit long memory in volatility and structural breaks that are driven by changes in the cost of carry. The model with constant transition probabi...

We analyze the S&P 500 index data for the 13-year period, from January 1, 1984 to December 31, 1996, with one data point every 10 min. For this database, we study the distribution and clustering of volatility return intervals, which are defined as the time intervals between successive volatilities above a certain threshold q. We find that the long memory in the volatility leads to a clustering ...

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 ret...

A new sufficient condition for the existence of a stationary causal solution of an ARCH(∞) equation is provided. This condition allows to consider coefficients with power-law decay, so that it can be applied to the so-called FIGARCH processes, whose existence is thus proved.

This paper identifies the best models for forecasting the volatility of daily exchange returns of developing countries. An emerging consensus in the recent literature focusing on industrialised counties has noted the superior performance of the FIGARCH model in the case of industrialised countries, a result that is reaffirmed here. However, we show that when dealing with developing countries’ d...