Articlegold2017

Time averaging, ageing and delay analysis of financial time series

Andrey G. Cherstvy · Deepak Vinod · Erez Aghion · Aleksei V. Chechkin · Ralf Metzler

57 citations0/0 files storedNew Journal of Physics

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Complex Systems and Time Series Analysis Stochastic processes and financial applications Statistical Mechanics and Entropy

Abstract

We introduce three strategies for the analysis of financial time series based on time averaged observables. These comprise the time averaged mean squared displacement (MSD) as well as the ageing and delay time methods for varying fractions of the financial time series. We explore these concepts via statistical analysis of historic time series for several Dow Jones Industrial indices for the period from the 1960s to 2015. Remarkably, we discover a simple universal law for the delay time averaged MSD. The observed features of the financial time series dynamics agree well with our analytical results for the time averaged measurables for geometric Brownian motion, underlying the famed Black–Scholes–Merton model. The concepts we promote here are shown to be useful for financial data analysis and enable one to unveil new universal features of stock market dynamics.

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References

1973The Pricing of Options and Corporate Liabilities 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1965The Behavior of Stock-Market Prices 1985A Theory of the Term Structure of Interest Rates 1971Optimum consumption and portfolio rules in a continuous-time model 1976Option pricing when underlying stock returns are discontinuous 2016Numerical solution of stochastic differential equations 1963The Variation of Certain Speculative Prices

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