Markov switch smooth transition HYGARCH model: Stability and estimation

Application of fractional exponential feature to GARCH model variants for improvement in value-at-risk prediction

“…Since this research concentrates on the combination between asymmetry GARCH and fractional exponential GARCH models, the combinations between models in literature are reviewed. For the combination between Markov switching Asymmetric Power ARCH (APARCH) (Ding et al, 1993) FIAPARCH (Tse, 1998) FIGARCH (Baillie et al, 1996) GJR-GARCH (Glosten et al, 1993) Figure 4 The literature gap as seen from Basatini and Rezakhah (2019) to Basatini and Rezakhah (2020) As seen in Figure 4, the way to MSST-HYGARCH model in the literatures comes in order of smooth transition before the Markov process. However, there is an alternative way that the Markov process might apply to the HYGARCH model before smooth transition that Basatini and Rezakhah (2020) did not cover.…”

“…Different from Basatini and Rezakhah (2020), Bildirici and Ersin (2014) made use of Markov switching process to the fractional exponential FIAPARCH model combining with the autoregressive moving average (ARMA) model. However, the MS-ARMA-FIAPARCH model was not the main player in the research.…”

“…This concept of using GARCH models under the more complicated neural network is interesting. However, when the neural network with GARCH noises is in use, the perspective is too close to the accuracy of the model, not the quantitative parameter estimated from HYGARCH (Davidson, 2004) Smooth Transition HYGARCH (ST-HYGARCH) (Basatini and Rezakhah, 2019) Markov Switching ST-HYGARCH (MSST-HYGARCH) (Basatini and Rezakhah, 2020)…”

“…Generalizedprocess and fractional exponential GARCH models,Basatini and Rezakhah (2020) proposed the way to apply the Markov process to the smooth transition HYGARCH (ST-HYGARCH) model fromBasatini and Rezakhah (2019) as the Markov switching smooth transition HYGARCH (MSST-HYGARCH) model Basatini and Rezakhah (2020). also demonstrated how better the MSST-HYGARCH model can do than the ST-HYGARCH model and HYGARCH model from the case study of daily VaR prediction on S&P 500 and DJIA indices.…”

“…Figure4The literature gap as seen fromBasatini and Rezakhah (2019) toBasatini and Rezakhah (2020) ..........................................................................................................Figure 5 S&P 500 daily logarithmic returns, January 13 th , 1956 -December 31 st , ......................................................................................................................................Figure 6 S&P 500 cumulative daily logarithmic returns, January 13 th , 1956 -December 31 st , 1999 ....................................................................................................…”