Looking for skewness in financial time series

Abstract

In this paper marginal and conditional skewness of financial return time series is studied, by means of testing procedures and suitable models, for nine major international stock indexes. To analyze time-varying conditional skewness a new GARCH-type model with dynamic skewness and kurtosis is proposed. Results indicate that there are no evidences of marginal asymmetry in the nine series, but there are clear findings of significant time-varying conditional skewness. The economic significance of conditional skewness is analyzed and compared by considering Value-at-Risk, Expected Shortfall and Market Risk Capital Requirements set by the Basel Accord.

Effects of risk aversion on securities portfolio performance in underdeveloped capital markets: the case of the capital market of Bosnia and Herzegovina

“…According to Grigoletto and Lisi (2009), and from a financial perspective, skewness is crucial since it may be considered as a measure of risk. Positive skewness means that the distribution has a long right tail, whilst negative skewness implies that the distribution has a long left tail.…”

Value-at-Risk Prediction by Higher Moment Dynamics

“…An analysis of the one-day-ahead 1% VaR for these series and models can be found in Grigoletto and Lisi (2006). They compared nominal and observed VaR coverages and showed, by using the Kupiec LR test (Kupiec, 1995), that only for the GARCHDSK models they are not significantly different, at the 5% significance level.…”

“…Within this context, we consider nine time series of stock index returns for which the significance of the conditional asymmetry and kurtosis was studied in Grigoletto and Lisi (2006). For these series we analyze -in terms of VaR -the performances of two Gaussian models (a Gaussian GARCH and the Riskmetrics model), of a non-Gaussian symmetric model (a GARCH with Student's t innovations), and of a non-Gaussian asymmetric model (the GARCHDSK, introduced by Grigoletto and Lisi, 2006).…”

“…For these series we analyze -in terms of VaR -the performances of two Gaussian models (a Gaussian GARCH and the Riskmetrics model), of a non-Gaussian symmetric model (a GARCH with Student's t innovations), and of a non-Gaussian asymmetric model (the GARCHDSK, introduced by Grigoletto and Lisi, 2006). The GARCHDSK model, in particular, allows to describe skewness and kurtosis of the conditional return distributions, both when they are assumed constant and when they are time-varying.…”

“…In Grigoletto and Lisi (2006) the analyses were limited to an in-sample context for shorter time series. Furthermore, the focus was on studying performances connected to Market Risk Capital Requirements (MRCR) as a function of past VaRs and of their violations, as defined by the guidelines of the Basel Accord on Banking Supervision.…”