GAS or GARCH: A comparison of density and VaR forecasts in Turkish FX and stock markets

Abstract

This paper compares the renowned GARCH model with a novel one, the Generalized Autoregressive Score (GAS) model in terms of forecasting performance. Considering the gap in the literature, this study focuses on the Turkish stock and FX markets. The analysis covers 25 years (1999-2023), of which the last 12 constitute the out-of-sample period. The selected indexes largely represent the finance (XBANK) and industry (XUSIN) sectors and the entire (XUTUM) economy, while the fourth (XU100) is the market benchmark. Likewise, FX rates are the leading factors that dominate Turkish foreign trade. Rolling density forecasts from the standard versions of the models are compared via Diebold-Mariano (DM) test with the two popular scoring rules. The GARCH model generally outperforms GAS when the conditional distribution is the Normal or its skewed version. We find some evidence for the reverse with Student-t and skewed version, but this lacks statistical support, except for the definite superiority of GAS in USD returns coupled with skewed Student-t. A deeper analysis attributed GAS’s underperformance to its treatment of shocks that are more likely to occur in developing markets. We also report similar findings with DM tests using two loss functions for VaR forecasts, whereas the results of the backtesting procedures are inconsistent across risk levels.

Keywords

• GARCH model
• GAS model
• Density forecast
• Density score function
• Forecast evaluation
• Value-at-risk

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