\( \newcommand{\bm}[1]{\boldsymbol{#1}} \newcommand{\textm}[1]{\textsf{#1}} \newcommand{\textnormal}[1]{\textsf{#1}} \def\T{{\mkern-2mu\raise-1mu\mathsf{T}}} \newcommand{\R}{\mathbb{R}} % real numbers \newcommand{\E}{{\rm I\kern-.2em E}} \newcommand{\w}{\bm{w}} % bold w \newcommand{\bmu}{\bm{\mu}} % bold mu \newcommand{\bSigma}{\bm{\Sigma}} % bold mu \newcommand{\bigO}{O} %\mathcal{O} \renewcommand{\d}[1]{\operatorname{d}\!{#1}} \)

2.6 Summary

Financial data display unique characteristics known as stylized facts, with the most prominent ones including:

• Lack of stationarity: The statistics of financial data change over time significantly and any attempt at modeling will have to continuously adapt.

• Volatility clustering: This is perhaps the most visually apparent aspect of financial time series. There are a myriad models in the literature that can be utilized for forecasting (covered in Chapter 4).

• Heavy tails: The distribution of financial data is definitely not Gaussian and this constitutes a significant departure from many traditional modeling approaches (covered in Chapter 3).

• Strong asset correlation: The goal in investing is to discover assets that are not strongly correlated, which is a daunting task due to the naturally occurring strong asset correlation.