Empirical Mug Shots

Abstract

The statistics which reveal the most interesting pieces of information are collected in a “mug shot”. The mug shots give a summary of the most salient properties of a time series, where the time series can be generated by a process or obtained from the financial market. The most important statistics relate to the volatility clustering (the heteroscedasticity), the long memory of the volatility (the slow decrease of the lagged correlation), and the distributional properties for the returns (the fat tails). This chapter contains the mug shots for the most important FX rates. They serve as a benchmark for the subsequent analysis of the processes. For this set of FX rates, they show in an informal way the regularities and variability in the statistics. For the processes studied in the following chapter, the mug shots will give a convenient summary of the statistical properties that need to be reproduced.