Characterization of Financial Time Series

This paper provides an exhaustive review of the literature on the characterization of financial time series. A stylized fact is a term in economics used to refer to empirical findings that are so consistent across markets that they are accepted as truth. Financial time series may be characterized by the following stylized facts. The autocorrelation of returns is largely insignificant. The distribution of returns is non-stationary (clustered volatility) and approximately symmetric with increasingly positive kurtosis as the time interval decreases and has a power law or Pareto-like tail. There are non-linearities in the mean and (especially) the variance of returns. Markets exhibit non-trivial scaling properties. Volatility exhibits positive autocorrelation, long-range dependence of autocorrelation, scaling, has a non-stationary log-normal distribution and exhibits non-linearities. Volume exhibits calendar effects and has a distribution that decays as a power law. Regarding calendar effects, intraday effects exist, the weekend effect seems to have all but disappeared, intramonth effects were found in most countries, the January effect has halved and holiday effects exist in some countries. There is about a 30% chance that stock market returns exhibit long memory, a 50% chance that foreign exchange returns exhibit long memory and an 80% chance that market volatility exhibits long memory. There is little evidence of lowdimensional chaos in financial markets. This note also includes a summary of the important literature on market microstructure and the order book. UCL DEPARTMENT OF COMPUTER SCIENCE Characterization of Financial Time Series Martin Sewell