Copulas

What are copula functions and why do we need themA 3D Gaussian Copula (Image by Author)Copulas are functions that model the dependency among several distributions.They are mostly used in financial applications like portfolio risk assessment and hedge fund management. They came to prominence in 2008, when it was discovered that quantitative scientists had misused copulas in their calculations, failing to predict significant events.Nonetheless, copulas are still great mathematical tools. One compelling reason for studying…

It’s all fun and games until your time-series is not Normal anymorePhoto by Heather Zabriskie on UnsplashARMA (AutoRegressive — Moving Average) models are arguably the most popular approach to time-series forecasting. Unfortunately, plain ARMA is made for Gaussian distributed data only. On the one hand, you can often still use ARMA by transforming the raw data. On the other hand, this typically makes probabilistic forecasts quite tedious.One approach to apply ARMA to non-Normal data are Copula models. Roughly, the latter…