In theory, it is often assumed that random variables follow a normal distribution. However, in practice, this is often not the case. ETH returns during the time period from 2015 to the beginning of 2022 are bullish and follow a skewed distribution with heavy tails. The Tukey's g- and h- transformation provides a way to model this non-normality via the modification of standard normal random variables.
In this courselet, we will cover the theoretical background on the Tukey gh transformations, show examples and illustrate limitations. Furthermore, we estimate the parameters g and h based on return data.
As a result, the participants will get a deeper understanding of non-normality and the modification possibilities of already existing distributions. In addition, people will learn about skewness and heavy tails which can come in handy when dealing with financial return data.