Chapter 5 Descriptive Statistics for Financial Data

Updated: May 4, 2021

Copyright © Eric Zivot 2015, 2016, 2020, 2021

In this chapter we use graphical and numerical descriptive statistics to study the distribution and dependence properties of daily and monthly asset returns on a number of representative assets. The purpose of this chapter is to introduce the techniques of exploratory data analysis for financial time series and to document a set of stylized facts for monthly and daily asset returns that will be used in later chapters to motivate probability models for asset returns.

This chapter is organized as follows. Section 5.1 introduces the example data and reviews graphical and numerical descriptive statistics for univariate data. Graphical descriptive statistics include time plots, histograms, QQ-plots and boxplots. Numerical statistics are the sample statistics associated with the analagous characteristics of univariate distributions. For the example data, it is shown that monthly returns are approximately normally distributed but that daily returns have much fatter tails than the normal distribution. Section 5.2 covers univariate time series descriptive statistics including sample autocovariances, autocorrelations and the sample autocorrelation function. For the example data, it is shown that daily and monthly asset returns are uncorrelated but that daily returns exhibit a nonlinear time dependence related to time varying volatility. Section 5.3 presents bivariate descriptive statistics including scatterplots, sample covariance and correlation, and sample cross-lag covariances and correlations. Section 5.5 concludes with a summary of some stylized facts for monthly and daily returns.

The R packages used in this chapter are corrplot, IntroCompFinR, PerformanceAnalytics, sn, tseries, zoo and xts. Make sure these packages are installed and loaded before running the R examples in the chapter.