An Empirical Method to Measure Stochasticity and Multifractality in Nonlinear Time Series

摘要

An empirical algorithm is used here to study the stochastic and multifractalnature of nonlinear time series. A parameter can be defined to quantitativelymeasure the deviation of the time series from a Wiener process so that thestochasticity of different time series can be compared. The local volatility ofthe time series under study can be constructed using this algorithm and themultifractal structure of the time series can be analyzed by using this localvolatility. As an example, we employ this method to analyze financial timeseries from different stock markets. The result shows that while developedmarkets evolve very much like an Ito process, the emergent markets are far fromefficient. Differences about the multifractal structures and leverage effectsbetween developed and emergent markets are discussed. The algorithm used herecan be applied in a similar fashion to study time series of other complexsystems.