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.

4 pages, 5 figures

References in corpus (10)

• Power-law distributions in empirical data
• Universal Record Statistics of Random Walks and Lévy Flights
• Record statistics for biased random walks, with an application to financial data
• Record statistics and persistence for a random walk with a drift
• Record dynamics and the observed temperature plateau in the magnetic creep rate of type II superconductors
• Records in a changing world
• Record Statistics for Multiple Random Walks
• A record-driven growth process
• Record Statistics of Continuous Time Random Walk
• Universal statistics of longest lasting records of random walks and Lévy flights

Cited by in corpus (6)

• Extreme events in dynamical systems and random walkers: A review
• 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
• Statistical properties of avalanches via the c-record process
• Continuous Gated First-Passage Processes