Modelling conditional moments and correlation with the continuous hidden-threshold-skew-normal distribution

Rachid Belhachemi, Pierre Rostan*, François Éric Racicot

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A key issue in modelling conditional densities of returns of financial assets is the time-variation of conditional volatility. The classic econometric approach models volatility of returns with the generalized autoregressive conditional heteroscedasticity (GARCH) models where the conditional mean and the conditional volatility depend only on historical prices. We propose a new family of distributions in which the conditional distribution depends on a latent continuous factor with a continuum of states. The distribution has an interpretation in terms of a mixture distribution with time-varying mixing probabilities. The distribution parameters have economic interpretations in terms of conditional volatilities and correlations of the returns with the hidden continuous state. We show empirically that this distribution outperforms its main competitor, the mixed normal conditional distribution, in terms of capturing the stylized facts known for stock returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence.

Original languageEnglish
Pages (from-to)5461-5475
Number of pages15
JournalApplied Economics
Issue number51
Publication statusPublished - 2 Nov 2015


  • conditional kurtosis
  • conditional skewness
  • conditional volatility
  • continuous hidden threshold
  • leverage effect
  • regime dependence


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