Abstract— We apply an approach for estimating Value-at-Risk (VaR) describing the tail of the conditional distribution of a heteroscedastic financial return series. The method combines quasi-maximum-likelihood fitting of AR(1)-GARCH(1,1) model to estimate the current mean as well as volatility, and extreme value theory (EVT) to estimate the tail of the adjusted standardized return series. We employ the approach to investigate the existence and significance of the calendar anomalies: seasonal effect and day-of- the-week effect in Americas Indexes VaR. We also examine the statistical properties and made a comprehensive set of diagnostic checks on the one decade of considered Americas Indexes returns. Our results suggest that the lowest VaR of considered Americas Indexes negative log returns occurs on the fourth season among all seasons. Moreover, comparatively low Wednesday VaR is captured among all weekdays during the test period.
Keywords— Risk Measures, Value-at-Risk, GARCH models, Extreme value theory, Generalized Pareto Distribution, Day-of-the-week effect, Seasonal effect.