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Modeling non-stationarities in high-frequency financial time series

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  • Linda Ponta
  • Mailan Trinh
  • Marco Raberto
  • Enrico Scalas
  • Silvano Cincotti

Abstract

We study tick-by-tick financial returns belonging to the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We can confirm previously detected non-stationarities. However, scaling properties reported in the previous literature for other high-frequency financial data are only approximately valid. As a consequence of the empirical analyses, we propose a simple method for describing non-stationary returns, based on a non-homogeneous normal compound Poisson process. We test this model against the empirical findings and it turns out that the model can approximately reproduce several stylized facts of high-frequency financial time series. Moreover, using Monte Carlo simulations, we analyze order selection for this model class using three information criteria: Akaike's information criterion (AIC), the Bayesian information criterion (BIC) and the Hannan-Quinn information criterion (HQ). For comparison, we also perform a similar Monte Carlo experiment for the ACD (autoregressive conditional duration) model. Our results show that the information criteria work best for small parameter numbers for the compound Poisson type models, whereas for the ACD model the model selection procedure does not work well in certain cases.

Suggested Citation

  • Linda Ponta & Mailan Trinh & Marco Raberto & Enrico Scalas & Silvano Cincotti, 2012. "Modeling non-stationarities in high-frequency financial time series," Papers 1212.0479, arXiv.org, revised Feb 2017.
    • Handle: RePEc:arx:papers:1212.0479
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    2. Elżbieta Szaruga & Elżbieta Załoga, 2022. "Environmental Management from the Point of View of the Energy Intensity of Road Freight Transport and Shocks," IJERPH, MDPI, vol. 19(21), pages 1-22, November.
    3. Kreer, Markus & Kizilersu, Ayse & Thomas, Anthony W., 2022. "Censored expectation maximization algorithm for mixtures: Application to intertrade waiting times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    4. Arias-Calluari, Karina & Najafi, Morteza. N. & Harré, Michael S. & Tang, Yaoyue & Alonso-Marroquin, Fernando, 2022. "Testing stationarity of the detrended price return in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    5. Eom, Cheoljun & Kaizoji, Taisei & Livan, Giacomo & Scalas, Enrico, 2021. "Limitations of portfolio diversification through fat tails of the return Distributions: Some empirical evidence," The North American Journal of Economics and Finance, Elsevier, vol. 56(C).
    6. Eom, Cheoljun & Kaizoji, Taisei & Scalas, Enrico, 2019. "Fat tails in financial return distributions revisited: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    7. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.
    8. Héctor Raúl Olivares-Sánchez & Carlos Manuel Rodríguez-Martínez & Héctor Francisco Coronel-Brizio & Enrico Scalas & Thomas Henry Seligman & Alejandro Raúl Hernández-Montoya, 2022. "An empirical data analysis of “price runs” in daily financial indices: Dynamically assessing market geometric distributional behavior," PLOS ONE, Public Library of Science, vol. 17(7), pages 1-25, July.
    9. Binghui Wu & Tingting Duan, 2019. "Nonlinear Dynamics Characteristic of Risk Contagion in Financial Market Based on Agent Modeling and Complex Network," Complexity, Hindawi, vol. 2019, pages 1-12, June.

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