Hidden truncation model with heteroskedasticity: S&P 500 index returns reexamined

Purpose This paper aims to introduce a heteroskedastic hidden truncation normal (HTN) model that allows for conditional volatilities, skewness and kurtosis, which evolve over time and are linked to economic dynamics and have economic interpretations. Design/methodology/approach The model consists of the HTN distribution introduced by Arnold et al. (1993) coupled with the NGARCH type (Engle and Ng, 1993). The HTN distribution nests two well-known distributions: the skew-normal family (Azzalini, 1985) and the normal distributions. The HTN family of distributions depends on a hidden truncation and has four parameters having economic interpretations in terms of conditional volatilities, kurtosis and correlations between the observed variable and the hidden truncated variable. Findings The model parameters are estimated using the maximum likelihood estimator. An empirical application to market data indicates the HTN-NGARCH model captures stylized facts manifested in financial market data, specifically volatility clustering, leverage effect, conditional skewness and kurtosis. The authors also compare the performance of the HTN-NGARCH model to the mixed normal (MN) heteroskedastic MN-NGARCH model. Originality/value The paper presents a structure dynamic, allowing us to explore the volatility spillover between the observed and the hidden truncated variable. The conditional volatilities and skewness have the ability at modeling persistence in volatilities and the leverage effects as well as conditional kurtosis of the S&P 500 index.