Threshold stochastic volatility: Properties and forecasting

Asymmetric stochastic volatility models: Properties and particle filter-based simulated maximum likelihood estimation

“…Asai and McAleer (2011) derive the first and second order moments of returns and Yu (2012a) derives the moments of returns and the conditions for stationarity, strict stationarity and ergodicity in extended specifications of the A-ARSV model. Mao et al (2017) derive the moments of returns when…”

“…When γ 2 = 0 , the specification is similar to the asymmetric SV model proposed by Asai and McAleer (2006) . Finally, when γ 1 = γ 2 = 0 , the specification gives the threshold model where only the constant changes depending on the sign of past returns; see the recent discussion by Mao et al (2017) on Threshold SV models.…”

“…where ( • ) is the Gaussian cumulative distribution function. The expressions of the marginal variance derived by Taylor (1994) for the classical asymmetric SV model of Harvey and Shephard (1996) , by Ruiz and Veiga (2008) for the asymmetric long-memory SV model, by Asai and McAleer (2011) for their general specification and by Mao et al (2017) for a Threshold SV model, can be obtained as particular cases of expression (5) with P (1, φ) defined as in (12) . When ν < 1, we cannot obtain analytical expressions of E (| y t | c ).…”

“…5] . This specification has been previously considered by Asai and McAleer (2006) and it is a restricted version of the Threshold SV model proposed by Breidt (1996) and So et al (2002) ; see Mao et al (2017) for the relevance of this specification when compared to the more general Threshold SV model. Hereafter, we refer to this model as restricted Threshold SV (RT-SV).…”

Data cloning estimation for asymmetric stochastic volatility models

“…Complex parametric stochastic volatility models have been extensively proposed in the literature to cope with the main empirical facts of financial time series. Very recent examples are the models proposed by Mao et al (2015Mao et al ( , 2017 and Asai et al (2017) that accommodate a general asymmetric function for volatility. Asymmetric effects have been traditionally modeled, either by considering a negative correlation between returns and future volatility (Harvey and Shephard, 1996), or by allowing the parameters of the log-volatility equation to differ depending on the sign of the lagged returns (Breidt, 1996;So et al, 2002).…”