Estimation of predictive loss distributions by particle filtering

We model an observed time series of stock market returns by a stochastic volatility model with unknown parameters. We are interested in exploiting the model for sequential estimation of the predictive distributions of returns, or more precisely, the predictive distributions of losses. The obtained distributions allow for computation of various risk-metrics including quantiles and conditional moments. For estimation of the desired distributions, we apply particle filtering. Simultaneously, we may use the particle filtering method for assessing the applied models. We demonstrate the proposed approach using univariate returns of the S&P500 stock index over a large swath of history.