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Financial Time Operator for random walk markets

Author

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  • Gialampoukidis, I.
  • Gustafson, K.
  • Antoniou, I.

Abstract

Based on previous work on non-equilibrium statistical mechanics, and the recent extensions of Time Operators to observations and financial processes, we construct a general Time Operator for non-stationary Bernoulli Processes. The Age and the innovation probabilities are defined and discussed in detail and a formula is presented for the special case of random walks. The formulas reduce the computations to variance estimations. Assuming that a stock market price evolves according to a random walk, we illustrate a financial application. We provide an Age estimator from historical stock market data. As an illustration we compute the Age of Greek financial market during elections and we compare with the Age of another period with less irregular events. The Age of a process is a new statistical index, assessing the average level of innovations during the observation period, resulting from the underlying complexity of the system.

Suggested Citation

  • Gialampoukidis, I. & Gustafson, K. & Antoniou, I., 2013. "Financial Time Operator for random walk markets," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 62-72.
    • Handle: RePEc:eee:chsofr:v:57:y:2013:i:c:p:62-72
    DOI: 10.1016/j.chaos.2013.08.010
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    References listed on IDEAS

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    1. Parkinson, Michael, 1980. "The Extreme Value Method for Estimating the Variance of the Rate of Return," The Journal of Business, University of Chicago Press, vol. 53(1), pages 61-65, January.
    2. Misra, B. & Prigogine, I. & Courbage, M., 1979. "From deterministic dynamics to probabilistic descriptions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 98(1), pages 1-26.
    3. Garman, Mark B & Klass, Michael J, 1980. "On the Estimation of Security Price Volatilities from Historical Data," The Journal of Business, University of Chicago Press, vol. 53(1), pages 67-78, January.
    4. Antoniou, I. & Gustafson, K., 1999. "Wavelets and stochastic processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 49(1), pages 81-104.
    5. Yang, Dennis & Zhang, Qiang, 2000. "Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices," The Journal of Business, University of Chicago Press, vol. 73(3), pages 477-491, July.
    6. Courbage, M., 1983. "Intrinsic irreversibility of Kolmogorov dynamical systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 122(3), pages 459-482.
    7. Courbage, M. & Misra, B., 1980. "On the equivalence between Bernoulli dynamical systems and stochastic Markov processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 104(3), pages 359-377.
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    Cited by:

    1. Gialampoukidis, I. & Gustafson, K. & Antoniou, I., 2014. "Time operator of Markov chains and mixing times. Applications to financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 141-155.
    2. Gialampoukidis, Ilias & Antoniou, Ioannis, 2015. "Age, Innovations and Time Operator of Networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 140-155.

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