Comparison of Value-at-Risk forecasting performance of Markov-Switching GARCH models, namely symmetric GARCH, Exponential GARCH, and GJR-GARCH, based on stock markets universe.
The data considered here are 5,000 daily percentage log returns of each stock indices: DAX, S&P500, and Nikkei.
The first 3,000 daily log returns are fit univariately to 2-state-Markov-switching GARCH-type models as mentioned above, each with 2 innovation assumptions: Normal and Student's t distributions.
Model estimation is done by MCMC, using a robust adaptive random-walk Metropolis algorithm proposed by Vihola (2012). The forecasting horizons used here are 1, 3, 10 and 22, and the VaR is calculated at 1% shortfall probability.
For a fixed rolling-window length of 3,000, the experiment is repeated 2,000 times, providing the 2,000 out-of-sample data, which later on used for evaluating the forecasting performance of each model setting.
The goodness of in-sample fit is evaulated based on:
- The Akaike information criterion (AIC) and
- The Bayesian information criterion (BIC).
The forecasting performance is evaluated based on
- Backtesting:
- Unconditional coverage test by Kupiec (1995),
- Independence test by Christoffersen (1998),
- Conditional coverage test by Christoffersen (1998),
- Dynamic quantile test of Engle and Mangenelli (2004), and
- Model confidence set by Hansen et al. (2011), with the VaR-based loss function defined by González-Rivera et al (2004).
- MSGARCH: https://github.com/keblu/MSGARCH
- data.table: https://CRAN.R-project.org/package=data.table
- MCS: https://CRAN.R-project.org/package=MCS
- MASS: https://CRAN.R-project.org/package=MASS
- plyr: https://cran.r-project.org/package=plyr
- expm: https://CRAN.R-project.org/package=expm
- dplyr: https://cran.r-project.org/package=dplyr