The use of scaling properties to detect relevant changes in financial time series: A new visual warning tool

Antoniades, Ioannis P.; Brandi, Giuseppe; Magafas, L.; Matteo, Tiziana Di

doi:10.1016/j.physa.2020.125561

Cited by 20 publications

(9 citation statements)

References 36 publications

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“…[10] shows the results for the S&P 500 index, as discussed above. 2 There is a notable rising trend for 𝐻 1 in the period ~1955 -~1970 followed by a dropping trend in the period ~1970 -~2010. This was first observed by Alvarez-Ramirez et al in (Alvarez-Ramirez 2008) and was also confirmed by the calculations performed for this study.…”

Section: Sandp 500 Stock Marketmentioning

confidence: 95%

“…Since financial timeseries are generally fattailed, the choice of q is relevant for the two measures of multiscaling, the width W and the depth B. One possible choice, that was suggested recently by Antoniades et al in (Antoniades, 2020), is to pick a narrow range of 𝑞-𝑞′ values for B and a wide range for W. This way, the value of B is not so much biased by the extreme edges of the difference distributions, but is rather affected by the small and medium differences. W, on the other hand, is deliberately allowed to be affected by the extreme tail data, which in financial timeseries are potentially important.…”

Section: Generalized Hurst Exponent (Hq)mentioning

confidence: 99%

“…In this direction, Stosic et al (Stosic, 2019) studied the non-extensivity of price volatilities for 34 major stock market indices between 2010 and 2019 by the estimation of q-triplet of Tsallis statistics. The distances between q-triplets [2] indicated that some stock markets might share similar non-extensive dynamics, while others are widely different. The study concentrated in comparing non-extensive statistics between major stock markets for a particular time-period only.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dynamical characteristics of global stock markets based on time dependent Tsallis non-extensive statistics and generalized Hurst exponents

Antoniades

Karakatsanis²,

Pavlos³

2021

Physica A: Statistical Mechanics and its Applications

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Section: Sandp 500 Stock Marketmentioning

confidence: 95%

Section: Generalized Hurst Exponent (Hq)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical characteristics of global stock markets based on time dependent Tsallis non-extensive statistics and generalized Hurst exponents

Antoniades

Karakatsanis²,

Pavlos³

2021

Physica A: Statistical Mechanics and its Applications

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“…it is a non-Markovian process. 2 In order to compute the Hurst exponent from sample data, in this paper we use the method of that is based on Generalized Hurst Exponent method (GHE), see (Di Matteo, 2007;Kantelhardt et al, 2002;Di Matteo et al, 2003, 2005Buonocore et al, 2016Buonocore et al, , 2017Antoniades et al, 2021). This methodology relies on the measurement of the direct scaling of the qthorder moments of the distribution of the increments (described in Section 4).…”

Section: Fractional Brownian Motionmentioning

confidence: 99%

Multiscaling and rough volatility: an empirical investigation

Brandi¹,

Matteo²

2022

Preprint

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Pricing derivatives goes back to the acclaimed Black and Scholes model. However, such a modeling approach is known not to be able to reproduce some of the financial stylized facts, including the dynamics of volatility. In the mathematical finance community, it has therefore emerged a new paradigm, named rough volatility modeling, that represents the volatility dynamics of financial assets as a fractional Brownian motion with Hurst exponent very small, which indeed produces rough paths. At the same time, prices' time series have been shown to be multiscaling, characterized by different Hurst scaling exponents. This paper assesses the interplay, if present, between price multiscaling and volatility roughness, defined as the (low) Hurst exponent of the volatility process. In particular, we perform extensive simulation experiments by using one of the leading rough volatility models present in the literature, the rough Bergomi model. A real data analysis is also carried out in order to test if the rough volatility model reproduces the same relationship. We find that the model is able to reproduce multiscaling features of the prices' time series when a low value of the Hurst exponent is used but it fails to reproduce what the real data say. Indeed, we find that the dependency between prices' multiscaling and the Hurst exponent of the volatility process is diametrically opposite to what we find in real data, namely a negative interplay between the two.

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“…Since they provide important information to risk and asset managers, they need to be properly addressed and analyzed. The (multi)scaling property of time series is particularly important in risk management and has been recently employed as a warning tool for financial events (Antoniades et al 2021). In particular, models that implicitly or explicitly assume independence of asset returns should be tested against long-term dependence alternatives.…”

Section: Introductionmentioning

confidence: 99%

On the statistics of scaling exponents and the multiscaling value at risk

Brandi

Matteo

2021

The European Journal of Finance

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Research on scaling analysis in finance is vast and still flourishing. We introduce a novel statistical procedure based on the generalized Hurst exponent, the Relative Normalized and Standardized Generalized Hurst Exponent (RNSGHE), to robustly estimate and test the multiscaling property. Furthermore, we introduce a new tool to estimate the optimal aggregation time used in our methodology which we name Autocororrelation Segmented Regression. We numerically validate this procedure on simulated time series by using the Multifractal Random Walk and we then apply it to real financial data. We present results for times series with and without anomalies and we compute the bias that such anomalies introduce in the measurement of the scaling exponents. We also show how the use of proper scaling and multiscaling can ameliorate the estimation of risk measures such as Value at Risk (VaR). Finally, we propose a methodology based on Monte Carlo simulation, which we name Multiscaling Value at Risk (MSVaR), that takes into account the statistical properties of multiscaling time series. We mainly show that by using this statistical procedure in combination with the robustly estimated multiscaling exponents, the one year forecasted MSVaR mimics the VaR on the annual data for the majority of the stocks.

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The use of scaling properties to detect relevant changes in financial time series: A new visual warning tool

Cited by 20 publications

References 36 publications

Dynamical characteristics of global stock markets based on time dependent Tsallis non-extensive statistics and generalized Hurst exponents

Dynamical characteristics of global stock markets based on time dependent Tsallis non-extensive statistics and generalized Hurst exponents

Multiscaling and rough volatility: an empirical investigation

On the statistics of scaling exponents and the multiscaling value at risk

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