Integrated nested Laplace approximations for threshold stochastic volatility models

The aim of the paper is to implement the integrated nested Laplace (INLA) approximations,known to be very fast and efficient, for a threshold stochastic volatility model. INLAreplaces MCMC simulations with accurate deterministic approximations. We use properal though not very informative priors and Penalizing Complexity (PC) priors. The simulation results favor the use of PC priors, specially when the sample size varies from small to moderate. For these sample sizes, they provide more accurate estimates of the model'sparameters, but as sample size increases both type of priors lead to reliable estimates of the parameters. We also validate the estimation method in-sample and out-of-sample by applying it to six series of returns including stock market, commodity and crypto currency returns and by forecasting their one-day-ahead volatilities, respectively. Our empirical results support that the TSV model does a good job in forecasting the one-day-ahead volatility of stock market and gold returns but faces difficulties when the volatility of returns is extreme, which occurs in the case of cryptocurrencies.