Matthieu Garcin

@article{garcin_3053,

title = {Nonparametric estimator of the tail dependence coefficient: balancing bias and variance},

author = {Matthieu Garcin and Maxime Nicolas},

url = {https://link.springer.com/article/10.1007/s00362-024-01582-w},

year  = {2024},

date = {2024-06-01},

journal = {Statistical Papers},

volume = {65},

pages = {4875-4913},

abstract = {A theoretical expression is derived for the mean squared error of a nonparametric estimator of the tail dependence coefficient, depending on a threshold that defines which rank delimits the tails of a distribution. We propose a new method to optimally select this threshold. It combines the theoretical mean squared error of the estimator with a parametric estimation of the copula linking observations in the tails. Using simulations, we compare this semiparametric method with other approaches proposed in the literature, including the plateau-finding algorithm.},

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@article{brouty_2818,

title = {Fractal properties, information theory, and market efficiency},

author = {Xavier Brouty and Matthieu Garcin},

url = {https://doi.org/10.1016/j.chaos.2024.114543},

year  = {2024},

date = {2024-03-01},

journal = {Chaos Solitons & Fractals},

volume = {180},

pages = {1-14},

abstract = {Considering that both the entropy-based market information and the Hurst exponent are useful tools for determining whether the efficient market hypothesis holds for a given asset, we study the link between the two approaches. We thus provide a theoretical expression for the market information when log-prices follow either a fractional Brownian motion or its stationary extension using the Lamperti transform. In the latter model, we show that a Hurst exponent close to 1/2 can lead to a very high informativeness of the time series, because of the stationarity mechanism 	extcolor{red}{induced by the Lamperti transform. This result contrasts with the zero information of the fractional Brownian motion for the same value of the Hurst exponent.} In addition, we introduce a multiscale method to get a deeper interpretation of the entropy and of the market information, depending on the size of the information set. Applications to Bitcoin, CAC 40 index, Nikkei 225 index, and EUR/USD FX rate, using daily or intraday data, illustrate the methodological content.},

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@article{garcin_2477,

title = {Estimation of time-varying kernel densities and chronology of the impact of COVID-19 on financial markets},

author = {Matthieu Garcin and Jules Klein and Sana Laaribi},

url = {https://www.tandfonline.com/doi/abs/10.1080/02664763.2023.2272226},

year  = {2023},

date = {2023-12-01},

journal = {Journal Of Applied Statistics},

volume = {51},

number = {11},

pages = {101183},

abstract = {The time-varying kernel density estimation relies on two free parameters: the bandwidth and the discount factor. We propose to select these parameters so as to minimize a criterion consistent with the traditional requirements of the validation of a probability density forecast. These requirements are both the uniformity and the independence of the so-called probability integral transforms, which are the forecast time-varying cumulated distributions applied to the observations. We thus build a new numerical criterion incorporating both the uniformity and independence properties by the mean of an adapted Kolmogorov-Smirnov statistic. We apply this method to financial markets during the onset of the COVID-19 crisis. We determine the time-varying density of daily price returns of several stock indices and, using various divergence statistics, we are able to describe the chronology of the crisis as well as regional disparities. For instance, we observe a more limited impact of COVID-19 on financial markets in China, a strong impact in the US, and a slow recovery in Europe.},

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@article{bernis_2476,

title = {Interest rates term structure models driven by Hawkes processes},

author = {Guillaume Bernis and Matthieu Garcin and Simone Scotti and Carlo Sgarra},

url = {https://epubs.siam.org/doi/10.1137/22M1502604},

year  = {2023},

date = {2023-10-01},

journal = {Siam Journal On Financial Mathematics},

volume = {14},

number = {4},

pages = {1062-1079},

abstract = {This paper includes a marked Hawkes process in the original HJM set-up, and investigates the impact of this assumption on the pricing of the popular vanilla fixed-income derivatives.

Our model exhibits a smile that can fit the implied volatility of swaptions for a given key rate (tenor). We harness on the log-normality of the model, conditionally with respect to jumps, and derive formulae to evaluate both caplets/floorlets and swaptions. Our model exhibits negative jumps on the zero-coupon (hence positive on the rates). Therefore, its behaviour is compatible with the situation where globally low interest rates can suddenly show cluster of positive jumps in case of tensions on the market. One of the main difficulties when dealing with the HJM model is to keep a framework that is Markovian. In particular, it is important to preserve the important features of the Hull and White version, especially the reconstruction formula that provides the zero-coupon bonds in terms of the underlying model factors. In our case, this formula is based on two factors: a classical Gaussian part and a pure jump martingale part based on a Hawkes process.},

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@article{brouty_2325,

title = {A statistical test of market efficiency based on information theory},

author = {Xavier Brouty and Matthieu Garcin},

url = {https://www.tandfonline.com/doi/full/10.1080/14697688.2023.2211108?src=},

year  = {2023},

date = {2023-05-01},

journal = {Quantitative Finance},

volume = {23},

number = {6},

pages = {1003-1018},

abstract = {We determine the amount of information contained in a time series of price returns at a given time scale, by using a widespread tool of the information theory, namely the Shannon entropy, applied to a symbolic representation of this time series. By deriving the exact and the asymptotic distribution of this market information indicator in the case where the efficient market hypothesis holds, we develop a statistical test of market efficiency. We apply it to a real dataset of stock indices, single stocks, and cryptocurrencies, for which we are able to determine at each date whether the efficient market hypothesis is to be rejected, with respect to a given confidence level.},

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@article{garcin_2066,

title = {A multivariate quantile based on Kendall ordering},

author = {Matthieu Garcin and Dominique Guégan and Bertrand Hassani},

url = {https://revstat.ine.pt/index.php/REVSTAT/article/view/397},

year  = {2023},

date = {2023-01-01},

journal = {Revstat-Statistical Journal},

volume = {21},

number = {1},

pages = {77-96},

abstract = {We introduce the Kendall multivariate quantiles, which are a transformation of orthant quantiles by the Kendall function. Each quantile is then a set of vectors with some advantageous properties, compared to the standard orthant quantile: i/ it induces a total order, ii/ the probability level of the quantile is consistent with the probability measure of the set of the dominated vectors, iii/ the multivariate quantiles based on the distribution function or on the survival function have vectors in common which conciliate both upper- and lower-orthant approaches. Definition and properties of the Kendall multivariate quantiles are illustrated using Archimedean copulas.},

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@article{ammy-driss_2069,

title = {Efficiency of the financial markets during the COVID-19 crisis: time-varying parameters of fractional stable dynamics},

author = {Ayoub Ammy-Driss and Matthieu Garcin},

url = {https://www.sciencedirect.com/science/article/pii/S0378437122008937},

year  = {2023},

date = {2023-01-01},

journal = {Physica A-Statistical Mechanics And Its Applications},

volume = {609},

pages = {128335},

abstract = {This paper investigates the impact of COVID-19 on financial markets. It focuses on the evolution of the market efficiency, using two efficiency indicators: the Hurst exponent and the memory parameter of a fractional Lévy-stable motion. The second approach combines, in the same model of dynamic, an alpha-stable distribution and a dependence structure between price returns. We provide a dynamic estimation method for the two efficiency indicators. This method introduces a free parameter, the discount factor, which we select so as to get the best alpha-stable density forecasts for observed price returns. The application to stock indices during the COVID-19 crisis shows a strong loss of efficiency for US indices. On the opposite, Asian and Australian indices seem less affected and the inefficiency of these markets during the COVID-19 crisis is even questionable.},

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@article{garcin_2068,

title = {A comparison of maximum likelihood and absolute moments for the estimation of Hurst exponents in a stationary framework},

author = {Matthieu Garcin},

url = {https://www.sciencedirect.com/science/article/pii/S1007570422002076},

year  = {2022},

date = {2022-11-01},

journal = {Communications In Nonlinear Science And Numerical Simulation},

volume = {114},

pages = {106610},

abstract = {The absolute-moment method is widespread for estimating the Hurst exponent of a fractional Brownian motion $X$. But this method is biased when applied to a stationary version of $X$, in particular an inverse Lamperti transform of $X$, with a linear time contraction of parameter $	heta$. We present an adaptation of the absolute-moment method to this framework and we compare it to the maximum likelihood method, with simulations and an application to a financial time series. While it appears that the maximum-likelihood method is more accurate than the adapted absolute-moment estimation, this last method is not uninteresting for two reasons: it makes it possible to confirm visually that the model is well specified and it is computationally more performing.},

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@article{garcin_2065,

title = {Long versus short time scales: the rough dilemma and beyond},

author = {Matthieu Garcin and Martino Grasselli},

url = {https://link.springer.com/article/10.1007/s10203-021-00358-3},

year  = {2022},

date = {2022-06-01},

journal = {Decisions in Economics and Finance},

volume = {45},

pages = {257-278},

abstract = {Using a large dataset on major FX rates, we test the robustness of the rough fractional volatility model over different time scales, by including smoothing and measurement errors into the analysis. Our findings lead to new stylized facts in the log-log plots of the second moments of realized variance increments against lag which exhibit some convexity in addition to the roughness and stationarity of the volatility. The very low perceived Hurst exponents at small scales are consistent with the rough framework, while the higher perceived Hurst exponents for larger scales lead to a nonlinear behaviour of the log-log plot that has not been described by models introduced so far.},

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@article{garcin_2067,

title = {Forecasting with fractional Brownian motion: a financial perspective},

author = {Matthieu Garcin},

url = {https://www.tandfonline.com/doi/abs/10.1080/14697688.2022.2071758},

year  = {2022},

date = {2022-06-01},

journal = {Quantitative Finance},

volume = {22},

number = {8},

pages = {1495-1512},

abstract = {The fractional Brownian motion (fBm) extends the standard Brownian motion by introducing some dependence between non-overlapping increments. Consequently, if one considers for example that log-prices follow an fBm, one can exploit the non-Markovian nature of the fBm to forecast future states of the process and make statistical arbitrages. We provide new insights into forecasting an fBm, by proposing theoretical formulas for accuracy metrics relevant to a systematic trader, from the hit ratio to the expected gain and risk of a simple strategy. In addition, we answer some key questions about optimizing trading strategies in the fBm framework: Which lagged increments of the fBm, observed in discrete time, are to be considered? If the predicted increment is close to zero, up to which threshold is it more profitable not to invest? We also propose empirical applications on high-frequency FX rates, as well as on realized volatility series, exploring the rough volatility concept in a forecasting perspective.},

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@article{sapina_1658,

title = {Lempel-Ziv complexity of the pNNx statistics - an application to neonatal stress},

author = {Matej ?apina and Chandan Karmakar and Karolina Kramari? and Marcin Kosmider and Matthieu Garcin and Dario Brdari? and Kre?imir Milas and John Yearwood},

url = {https://www.sciencedirect.com/science/article/abs/pii/S0960077921000564},

year  = {2021},

date = {2021-05-01},

journal = {Chaos Solitons & Fractals},

volume = {146},

number = {1},

pages = {110703},

abstract = {Among the existing measures of heart rate variability (HRV), the pNN50 statistics is one of the most commonly reported. However, it is only a single member of a much larger family of HRV measures - the pNN statistics. In this research pNN was further extended, combining it with the Lempel-Ziv complexity (LZ76) in a controlled neonatal stress framework. Two different types of stress stimuli on forty healthy newborns - a routine heel stick blood sampling, and a dull heel pressure stimulation - were considered by recording time intervals between heartbeats. Instead of relying on a single value, the entire spectrum from pNN1 to pNN100 was calculated, along with LZ76 derived from binarized sequences for each NN. The results of this study show a downward shift of the pNN curves when newborns are stressed, with reduced LZ76 complexity when stressed. When ROC curves were utilized for the pNN statistics and LZ76, however, the highest AUC values were observed when both measures were combined, with the highest AUC values of 0.88 (0.80-0.94) and 0.85 (0.74-0.91) for discriminating resting states from stress phases. Combining the widely used pNN statistics with LZ76 extends the existing HRV toolbox, and shows a promising application in recognizing acute neonatal stress.},

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@article{garcin_1204,

title = {Non-parametric new impact curve: a variational approach},

author = {Matthieu Garcin and Clément Goulet},

url = {https://link.springer.com/article/10.1007/s00500-019-04607-x},

year  = {2020},

date = {2020-09-01},

journal = {Soft Computing},

volume = {24},

number = {18},

pages = {13797-13812},

abstract = {In this paper, we propose an innovative algorithm for modelling the news impact curve. The news impact curve provides a nonlinear relation between past returns and current volatility and thus enables to forecast volatility. Our news impact curve is the solution of a dynamic optimization problem based on variational calculus. Consequently, it is a non-parametric and smooth curve. The technique we propose is directly inspired from noise removal techniques in signal theory. To our knowledge, this is the first time that such a method is used for volatility modelling. Applications on simulated heteroskedastic processes as well as on financial data show a better accuracy in estimation and forecast for this approach than for standard parametric (symmetric or asymmetric ARCH) or non-parametric (Kernel-ARCH) econometric techniques.},

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@article{sapina_1197,

title = {The Hurst Exponent of Heart Rate Variability in Neonatal Stress, Based on a Mean-Reverting Fractional Lévy Stable Motion},

author = {Matej ?apina and Matthieu Garcin and Karolina Kramari? and Kre?imir Milas and Dario Brdari? and Marko Piri?},

url = {https://www.worldscientific.com/doi/abs/10.1142/S0219477520500261},

year  = {2020},

date = {2020-08-17},

journal = {Fluctuation And Noise Letters},

volume = {19},

number = {3},

pages = {2050026},

abstract = {We aim at detecting stress in newborns by observing heart rate variability (HRV). The HRV features nonlinearities. Fractal dynamics is a usual way to model them and the Hurst exponent summarizes the fractal information. In our framework, we have observations of short duration, for which usual estimators of the Hurst exponent, like detrended °uctuation analysis (DFA), are not adapted. Moreover, we observe that the Hurst exponent does not vary much between stress and rest phases, but its decomposition in memory and underlying properties of the probability distribution leads to satisfactory diagnostic tools. This decomposition of the Hurst exponent is in addition embedded in a mean-reverting model. The resulting model is a mean-reverting fractional L
evy stable motion (FLSM). We estimate it and use its parameters as diagnostic tools of neonatal stress. Indeed, the value of the speed of reversion parameter is a signi¯cant indicator of stress. The evolution of both parameters in which the Hurst exponent is decomposed provides us with signi¯cant indicators as well. On the contrary, the Hurst exponent itself does not bear useful information.},

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@article{garcin_1372,

title = {Fractal analysis of the multifractality of foreign exchange rates},

author = {Matthieu Garcin},

url = {https://www.unive.it/pag/31137/},

year  = {2020},

date = {2020-01-01},

journal = {Mathematical Methods in Economics and Finance},

volume = {13-14},

number = {1},

pages = {49-73},

abstract = {x},

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@article{garcin_945,

title = {Hurst Exponents and Delampertized Fractional Brownian Motions},

author = {Matthieu Garcin},

url = {https://www.worldscientific.com/doi/abs/10.1142/S0219024919500249},

year  = {2019},

date = {2019-07-31},

journal = {International Journal of Theoretical and Applied Finance},

volume = {22},

number = {5},

pages = {1950024},

abstract = {The inverse Lamperti transform of a fractional Brownian motion (fBm) is a stationary process. We determine the empirical Hurst exponent of such a composite process with the help of a regression of the log absolute moments of its increments, at various scales, on the corresponding log scales. This perceived Hurst exponent underestimates the Hurst exponent of the underlying fBm. We thus encounter some time series having a perceived Hurst exponent lower than 1/2, but an underlying Hurst exponent higher than 1/2. This paves the way for short- and medium-term forecasting. Indeed, in such series, mean reversion predominates at high scales, whereas persistence is overriding at lower scales. We propose a way to characterize the Hurst horizon, namely a limit scale between these opposite behaviors. We show that the delampertized fBm, which mixes persistence and mean reversion, is relevant for financial time series, in particular for high-frequency foreign exchange rates. In our sample, the empirical Hurst horizon is always above 1h and 23min.},

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@article{kramaric_1071,

title = {Heart rate asymmetry as a new marker for neonatal stress},

author = {Karolina Kramari? and Matej ?apina and Matthieu Garcin and Kre?imir Milas and Marko Piri? and Dario Brdari? and Gordana Luki? and Vesna Milas and Silvija Pu?elji?},

url = {https://www.sciencedirect.com/science/article/pii/S1746809418302258},

year  = {2019},

date = {2019-01-01},

journal = {Biomedical Signal Processing And Control},

volume = {47},

pages = {219-223},

abstract = {The autocorrelation of the heart rate variability is presented by various methods and models, but Poincaré plots remain valuable analytic tools. Heart rate asymmetry analysis (HRA) is used for the quantification of unevenly distributed points above and below the line of identity. The aim of this work is to implement HRA analysis in newborns, to use it as a marker for acute stress. Forty healthy term newborn infants were included in the study. The protocol included two baseline phases, and two stress phases (heel stimulation and heel stick blood sampling), during which the heart rate was measured. Additionally, to the standard HRA indices, a new index (SKG) related to the first differences of the RR interval time series is introduced. A ROC curve analysis was applied to test the diagnostic properties of the asymmetry indices. With AUC significantly different from 0.5, the results show that HRA indices may be used as clinical markers. With higher AUC values (0.906 and 0.785), accuracy (87.5% and 81.3%) and sensitivity (87.5% and 81.3%), the SKG index outperformed the traditional indices. This novel application of HRA shows potential benefit in stress assessment of newborns, and in nonverbal patients in general.},

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@article{garcin_1654,

title = {Estimation of time-dependent Hurst exponents with variational smoothing and application to forecasting foreign exchange rates},

author = {Matthieu Garcin},

url = {https://www.sciencedirect.com/science/article/abs/pii/S037843711730434X},

year  = {2017},

date = {2017-10-01},

journal = {Physica A-Statistical Mechanics And Its Applications},

volume = {483},

number = {1},

pages = {462-479},

abstract = {Hurst exponents depict the long memory of a time series. For human-dependent phenomena, as in finance, this feature may vary in the time. It justifies modelling dynamics by multifractional Brownian motions, which are consistent with time-dependent Hurst exponents. We improve the existing literature on estimating time-dependent Hurst exponents by proposing a smooth estimate obtained by variational calculus. This method is very general and not restricted to the sole Hurst framework. It is globally more accurate and easier than other existing non-parametric estimation techniques. Besides, in the field of Hurst exponents, it makes it possible to make forecasts based on the estimated multifractional Brownian motion. The application to high-frequency foreign exchange markets (GBP, CHF, SEK, USD, CAD, AUD, JPY, CNY and SGD, all against EUR) shows significantly good forecasts. When the Hurst exponent is higher than 0.5, what depicts a long-memory feature, the accuracy is higher.},

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@article{garcin_1655,

title = {Wavelet shrinkage of a noisy dynamical system with non-linear noise impact},

author = {Matthieu Garcin and Dominique Guégan},

url = {https://www.sciencedirect.com/science/article/abs/pii/S0167278916301105},

year  = {2016},

date = {2016-06-01},

journal = {Physica D-Nonlinear Phenomena},

volume = {325},

number = {1},

pages = {126-145},

abstract = {By filtering wavelet coefficients, it is possible to construct a good estimate of a pure signal from noisy data. Especially, for a simple linear noise influence, Donoho and Johnstone (1994) have already defined an optimal filter design in the sense of a minimization of the error made when estimating the pure signal. We set here a different framework where the influence of the noise is non-linear. In particular, we propose a method to filter the wavelet coefficients of a discrete dynamical system disrupted by a weak noise, in order to construct good estimates of the pure signal, including Bayes' estimate, minimax estimate, oracular estimate or thresholding estimate. We present the example of a logistic and a Lorenz chaotic dynamical system as well as an adaptation of our technique in order to show empirically the robustness of the thresholding method in presence of leptokurtic noise. Moreover, we test both the hard and the soft thresholding and also another kind of smoother thresholding which seems to have almost the same reconstruction power as the hard thresholding. Finally, besides the tests on an estimated dataset, the method is tested on financial data: oil prices and NOK/USD exchange rate.},

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@article{garcin_1656,

title = {Probability density of the empirical wavelet coefficients of a noisy chaos},

author = {Matthieu Garcin and Dominique Guégan},

url = {https://www.sciencedirect.com/science/article/abs/pii/S0167278914000542},

year  = {2014},

date = {2014-05-01},

journal = {Physica D-Nonlinear Phenomena},

volume = {276},

number = {1},

pages = {28-47},

abstract = {We are interested in the random empirical wavelet coefficients of a noisy signal when this signal is a unidimensional or multidimensional chaos. More precisely we provide an expression of the conditional probability density of such coefficients, given a discrete observation grid. The noise is assumed to be described by a symmetric alpha-stable random variable. If the noise is a dynamic noise, then we present the exact expression of the probability density of each wavelet coefficient of the noisy signal. If we face a measurement noise, then the noise has a non-linear influence and we propose two approximations. The first one relies on a Taylor expansion whereas the second one, relying on an Edgeworth expansion, improves the first general Taylor approximation if the cumulants of the noise are defined. We give some illustrations of these theoretical results for the logistic map, the tent map and a multidimensional chaos, the Hénon map, disrupted by a Gaussian or a Cauchy noise.},

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@article{garcin_1657,

title = {Extreme values of random or chaotic discretization steps and connected networks},

author = {Matthieu Garcin and Dominique Guégan},

url = {http://www.m-hikari.com/ams/ams-2012/ams-117-120-2012/index.html},

year  = {2012},

date = {2012-01-01},

journal = {Applied Mathematical Sciences},

volume = {6},

number = {119},

pages = {5901 - 5926},

abstract = {x},

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}