Record statistics of financial time series and geometric random walks

Abstract

The study of record statistics of correlated series is gaining momentum. In this work, we study the records statistics of the time series of select stock market data and the geometric random walk, primarily through simulations. We show that the distribution of the age of records is a power law with the exponent $\alpha$ lying in the range $1.5\le \alpha \le 1.8$. Further, the longest record ages follow the Fréchet distribution of extreme value theory. The records statistics of geometric random walk series is in good agreement with that from the empirical stock data.

arXiv comment4 pages, 5 figures

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• Record statistics for random walks and Lévy flights with resetting
• Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit
• Universal framework for record ages under restart
• Exploring the Gillis model: a discrete approach to diffusion in logarithmic potentials
• Statistical properties of avalanches via the c-record process
• Time since maximum of Brownian motion and asymmetric Levy processes
• Extreme Event Statistics in a Drifting Markov Chain
• Continuous Gated First-Passage Processes