This paper aims to statistically model the serial dependence in the first and second moments of a univariate time series using copulas, bridging the gap between theory and applications, which are the focus of risk managers.
The appealing feature of the method is that it captures not just the linear form of dependence (a job usually accomplished by ARIMA linear models), but also the non‐linear ones, including tail dependence, the dependence occurring only among extreme values. In addition it investigates the changes in the mean modeling after whitening the data through the application of GARCH type filters. A total 62 US stocks are selected to illustrate the methodologies.
The copula based results corroborate empirical evidences on the existence of linear and non‐linear dependence at the mean and at the volatility levels, and contributes to practice by providing yet a simple but powerful method for capturing the dynamics in a time series. Applications may follow and include VaR calculation, simulations based derivatives pricing, and asset allocation decisions. The authors recall that the literature is still inconclusive as to the most appropriate value‐at‐risk computing approach, which seems to be a data dependent decision.
This paper uses a conditional copula approach for modeling the time dependence in the mean and variance of a univariate time series.
