The aim is to implement the integrated nested Laplace approximations (INLA), known to be very fast and efficient, for estimating the parameters of the threshold stochastic volatility (TSV) model. INLA replaces Markov chain Monte Carlo (MCMC) simulations with accurate
deterministic approximations. Weakly informative proper priors are used, as well as 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, PC priors provide more
accurate estimates of the model parameters. However, as sample size increases, both types of priors lead to similar estimates of the parameters. The estimation method is applied to six series of returns, including stock market, commodity and cryptocurrency returns, and its performance is assessed, by means of in-sample and out-of-sample approaches; the forecasting of one-day-ahead volatilities is also carried out. The empirical results support that the TSV is the model that generally fits the best to the series of returns and most of the times ranks the first in terms of forecasting one-day-ahead volatility, when compared to the symmetric stochastic volatility model.
We thank two anonymous referees for their careful and constructive comments that helped to improve the paper, and Professor Maria Antónia Amaral Turkman, Centro de Estatística e Aplicações, Faculdade de Ciências, Universidade de Lisboa, Lisbon, Portugal, for the careful
reading of the manuscript and for all the very useful comments and suggestions. We also thank Professor John McDermott for correcting the English. The first author was partially financed by national funds through FCT - Fundação para a Ciência e a Tecnologia under the
projects PTDC/MAT-STA/28649/2017 and UIDB/00006/2020. The fourth author acknowledges financial support from the Spanish Ministry of Science, Innovation and Universities, research project PGC2018-096977-B-l00, from the Agencia Estatal de Investigación PID2019-108079GBC21/AIE/10.13039/501100011033 and from Fundação para a Ciência e a Tecnologia, grant UIDB/00315/2020.