Simulation Evidence on Long Memory and Regime Switching in the Second Moment for Modelling of Financial Returns

Abstract: It is well-known that long memory and regime switching in the first moment of a stochastic process are easily confused. But the relation between long memory in the second moment and regime switching in the second moment is less well understood. We perform a simulation study in which we assess the possibility to distinguish the two properties in the case that data with long memory in the second moment is generated as a FIGARCH(0,d,0)-process, and when regime switching is modelled by HMM with switching variance. Those model specifications are common in the modelling of financial returns, and conform to several well-known stylised facts of financial data. The simulation study lends evidence to the risk of confusing long memory and regime switching in the case studied.