Measuring market efficiency: The Shannon entropy of high-frequency financial time series

Shternshis, Andrey; Mazzarisi, Piero; Marmi, Stefano

doi:10.1016/j.chaos.2022.112403

Cited by 30 publications

(18 citation statements)

References 45 publications

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“…In our previous work,[29] we found that the degree of inefficiency for the U.S. ETF market is about 0.11 for monthly time intervals and the 3-symbols discretization only.…”

mentioning

confidence: 82%

“…2∆ and erf (x) is the Gaussian error function; d is a tick size 4 , ∆ is a time step 5 , P is a rounded price, and σ is an estimation of volatility [29]. It is obtained by considering the probability that a price following a Geometric Brownian Motion moves less than one tick size, assuming that price increments are normally distributed.…”

Section: Estimation Of Price Stalenessmentioning

confidence: 99%

“…According to our methodology of filtering out excess 0-returns presented in [29], we save 0-returns proportionally to the probability in Eq. 3 and set other 0-returns as missing values.…”

Section: Estimation Of Price Stalenessmentioning

confidence: 99%

“…See [31] for the proof of the consistency of this estimator and [29] for the case of missing values. Since the sequence is finite, the estimation of entropy is underestimated.…”

Section: Let X Nmentioning

confidence: 99%

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Efficiency of the Moscow Stock Exchange before 2022

Shternshis¹,

Mazzarisi²,

Marmi³

2022

Preprint

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This paper investigates the degree of efficiency for the Moscow Stock Exchange. A market is called efficient if prices of its assets fully reflect all available information. We show that the degree of market efficiency is significantly low for most of the months from 2012 to 2021. We calculate the degree of market efficiency by (i) filtering out regularities in financial data and (ii) computing the Shannon entropy of the filtered return time series. We have developed a simple method for estimating volatility and price staleness in empirical data, in order to filter out such regularity patterns from return time series. The resulting financial time series of stocks' returns are then clustered into different groups according to some entropy measures. In particular, we use the Kullback-Leibler distance and a novel entropy metric capturing the co-movements between pairs of stocks. By using Monte Carlo simulations, we are then able to identify the time periods of market inefficiency for a group of 18 stocks. The inefficiency of the Moscow Stock Exchange that we have detected is a signal of the possibility of devising profitable strategies, net of transaction costs. The deviation from the efficient behavior for a stock strongly depends on the industrial sector it belongs.

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“…In our previous work,[29] we found that the degree of inefficiency for the U.S. ETF market is about 0.11 for monthly time intervals and the 3-symbols discretization only.…”

mentioning

confidence: 82%

Section: Estimation Of Price Stalenessmentioning

confidence: 99%

“…According to our methodology of filtering out excess 0-returns presented in [29], we save 0-returns proportionally to the probability in Eq. 3 and set other 0-returns as missing values.…”

Section: Estimation Of Price Stalenessmentioning

confidence: 99%

“…See [31] for the proof of the consistency of this estimator and [29] for the case of missing values. Since the sequence is finite, the estimation of entropy is underestimated.…”

Section: Let X Nmentioning

confidence: 99%

See 2 more Smart Citations

Efficiency of the Moscow Stock Exchange before 2022

Shternshis¹,

Mazzarisi²,

Marmi³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Moreover, we consider any time gap without trading more than 2 h as the closure of the market. We set the time step to be equal to 1 min for these gaps);

is a rounded price;

is an estimation of volatility [ 36 ]. It is obtained by considering the probability that a price following a Geometric Brownian Motion moves less than one tick size, assuming that price increments are normally distributed.…”

Section: Materials and Methodsmentioning

confidence: 99%

Efficiency of the Moscow Stock Exchange before 2022

Shternshis

Mazzarisi

Marmi

2022

Entropy

Self Cite

View full text Add to dashboard Cite

This paper investigates the degree of efficiency for the Moscow Stock Exchange. A market is called efficient if prices of its assets fully reflect all available information. We show that the degree of market efficiency is significantly low for most of the months from 2012 to 2021. We calculate the degree of market efficiency by (i) filtering out regularities in financial data and (ii) computing the Shannon entropy of the filtered return time series. We developed a simple method for estimating volatility and price staleness in empirical data in order to filter out such regularity patterns from return time series. The resulting financial time series of stock returns are then clustered into different groups according to some entropy measures. In particular, we use the Kullback–Leibler distance and a novel entropy metric capturing the co-movements between pairs of stocks. By using Monte Carlo simulations, we are then able to identify the time periods of market inefficiency for a group of 18 stocks. The inefficiency of the Moscow Stock Exchange that we have detected is a signal of the possibility of devising profitable strategies, net of transaction costs. The deviation from the efficient behavior for a stock strongly depends on the industrial sector that it belongs to.

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Extreme Events and Stock Market Efficiency: The Modified Shannon Entropy Approach

Olbrys

2024

Applied Economic Research and Trends

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Measuring market efficiency: The Shannon entropy of high-frequency financial time series

Cited by 30 publications

References 45 publications

Efficiency of the Moscow Stock Exchange before 2022

Efficiency of the Moscow Stock Exchange before 2022

Efficiency of the Moscow Stock Exchange before 2022

Extreme Events and Stock Market Efficiency: The Modified Shannon Entropy Approach

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