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Order flow in the financial markets from the perspective of the Fractional L\'{e}vy stable motion

Vygintas Gontis

posted on 06 May 2021

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It is a challenging task to identify the best possible models
based on given empirical data of real stochastic time series. Though the financial markets provide us with a vast amount of empirical data, the best model selection is still a big challenge for researchers. The widely used long-range memory and self-similarity estimators give varying values of the parameters as these estimators themselves are developed for the specific models of time series. Here we investigate the order disbalance time series constructed from the limit order book data of the financial markets under fractional L\'{e}vy stable motion assumption. Our results suggest that previous findings of persistence in order flow are related to the power-law distribution of order sizes. Still, orders have stable estimates of anti-correlation for the 18 randomly selected stocks, when Absolute value and Higuchi's estimators are implemented. The burst duration analysis based on the first passage problem of time series and implemented in this research gives different estimates of the Hurst parameter more consistent with the uncorrelated increment cases.

Discussion

This manuscript analyzes the order flow in the financial markets data from Fractional Levy's stable motion and ARFIMA time series perspective. Though the financial markets provide us with a vast amount of empirical data, the best model selection is still a big challenge for researchers. The widely used long-range memory and self-similarity estimators give varying values of the parameters as these estimators themselves are developed for the specific models of time series. Here we investigate the order disbalance time series constructed from the limit order book data of the financial markets under fractional Levy stable motion assumption. Our results suggest that previous findings of persistence in order flow are related to the assumption of Gaussian noise. Our results give stable estimates of anti-correlation for the 18 randomly selected stocks when Absolute value and Higuchi's estimators are implemented. The burst duration analysis based on the first passage problem of time series and implemented in this research gives different estimates of the Hurst parameter more consistent with the uncorrelated increment cases.

The proposed manuscript is based on the Time-series and signals analysis; discrete, stochastic dynamics; Fractional dynamics. We seek to interpret the general properties of scaling in socio-economic systems that might value the broad interdisciplinary research community.