Indirect TARCH-CAViaR Model and Its Parameter Estimation by MCMC Method with an Application

Indirect TARCH-CAViaR model is proposed to explain asymmetric impacts from lagged returns on its current quantiles. The nonlinearity and discrete gradient inherited in CAViaR model form a conundrum for parameter estimation. By introducing asymmetric Laplace distribution with parameterized scale parameter to be the error distribution in quantile regression, Bayesian inference joined with Markov chain Monte Carlo simulation is successfully used to estimate the model. In an example of measuring dynamic market risk of Shanghai Composite Index, news impact curves reveal significant asymmetric impacts from good or bad news on current market risk, and the impact intensities change with confidence levels of value at risk. Dynamic quantile test and back testing of value at risk also prove that the new model is effective in out-of-sample forecasting especially in extreme quantiles.