Time-varying Hurst–Hölder exponents and the dynamics of (in)efficiency in stock markets

Market inefficiency is a latent concept, and it is difficult to be measured by means of a single indicator. In this paper, following both the adaptive market hypothesis (AMH) and the fractal market hypothesis (FMH), we develop a new time-varying measure of stock market inefficiency. The proposed measure, called composite efficiency index (CEI), is estimated as the synthesis of the most common efficiency measures such as the returns’ autocorrelation, liquidity, volatility, and a new measure based on the Hurst exponent, called the Hurst efficiency index (HEI). To empirically validate the indicator, we compare different European stock markets in terms of efficiency over time.

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“…In this paper, we propose to estimate h t with the AMBE method of Bianchi et al [31] and Bianchi and Pianese [44] that works as follows.…”

Section: A New Hurst-based Efficiency Measurementioning

confidence: 99%

A Composite Index for Measuring Stock Market Inefficiency

2022

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“…Note that fractional Brownian motion and other fractional models were also considered as asset price models in the mathematical finance literature, often in the context of long-range dependence; see the seminal work of [48] but also [14,15,16], for example. In those works, it is typically the behavior of the kernel g at t = ∞ that is of primary interest, as this determines whether the resulting process has short or long memory.…”

Section: Modelmentioning

confidence: 99%

When Frictions are Fractional: Rough Noise in High-Frequency Data

Chong¹,

Delerue²,

Li³

2021

Preprint

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We consider the problem of estimating volatility for high-frequency data when the observed process is the sum of a continuous Itô semimartingale and a noise process that locally behaves like fractional Brownian motion with Hurst parameter H. The resulting class of processes, which we call mixed semimartingales, generalizes the mixed fractional Brownian motion introduced by Cheridito [Bernoulli 7 (2001) 913-934] to time-dependent and stochastic volatility. Based on central limit theorems for variation functionals, we derive consistent estimators and asymptotic confidence intervals for H and the integrated volatilities of both the semimartingale and the noise part, in all cases where these quantities are identifiable. When applied to recent stock price data, we find strong empirical evidence for the presence of fractional noise, with Hurst parameters H that vary considerably over time and between assets.

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“…The methods presented in the previous sections are based on the development of a linear log-log type graph that only outputs a unique H value. These methods are insufficient when estimating the locally time-dependent Hurst exponent, H(t) [30], [31].…”

Section: Time-scale Analysis (Tsa)mentioning

confidence: 99%

Time Series Analysis of Computer Network Traffic in a Dedicated Link Aggregation

Millán¹,

Lefranc²,

Osorio-Comparán³

et al. 2021

Preprint

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Fractal behavior and long-range dependence are widely observed in measurements and characterization of traffic flow in high-speed computer networks of different technologies and coverage levels. This paper presents the results obtained when applying fractal analysis techniques on a time series obtained from traffic captures coming from an application server connected to the Internet through a high-speed link. The results obtained show that traffic flow in the dedicated high-speed network link have fractal behavior when the Hurst exponent is in the range of 0.5, 1, the fractal dimension between 1, 1.5, and the correlation coefficient between –0.5, 0. Based on these results, it is ideal to characterize both the singularities of the traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyses, the fact that the traffic flows of current computer networks exhibit fractal behavior with a long-range dependency is reaffirmed.

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Time-varying Hurst–Hölder exponents and the dynamics of (in)efficiency in stock markets

Cited by 33 publications

References 38 publications

A Composite Index for Measuring Stock Market Inefficiency

A Composite Index for Measuring Stock Market Inefficiency

When Frictions are Fractional: Rough Noise in High-Frequency Data

Time Series Analysis of Computer Network Traffic in a Dedicated Link Aggregation

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