Cross-Sectional Universalities in Financial Time Series

Abstract

When estimating process on financial time series, the usual method is to postulate the equations for the process and to estimate the parameter values for each time series. The implicit assumption is that the equations are universal (i.e. identical for all assets), while the parameters are specific (i.e. depending on the peculiarities of each asset). In this paper, we show that the parameter values can also be taken as universal. Two sets of time series are used for the study, one taken from the stock market and one generated by an ARCH process with fixed parameters. Both sets have the same number of time series and lengths. A broad panel of 40 statistical estimators is used to extract the properties of the data over 9 time horizons ranging from 1 day to 1 year, covering the known stylized facts. The total of 360 statistics constitutes a very stringent sieve for processes. The Kolmogorov-Smirnov test applied to the cross-sectional distribution for each of the statistics shows that the distributions are very similar, and only the mean volatility is found to have a component depending on the time series. This shows that the same data generating process can be used for all stocks.

Keywords: ARCH processes, stylized facts, universality, time series statistics, cross-sectional statistics, Kolmogorov-Smirnov test, long memory volatility, leverage effect

JEL Classification: C21, C22, C31, C32