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Research & Publications

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Research Interests

Machine learning, computational statistics,
Long-memory and multifractal processes, change-point detection,
Wavelet signal processing of scaling processes,
Artificial intelligence and complexity in financial markets.

Publications

D. Surgailis, G. Teyssière and M. Vaičiulis. The increment ratio statistic.
Journal of Multivariate Analysis (2008) vol 99, 510-541. MR2396977. Pdf file (Supplementary Material Pdf).
M. Lavielle and G. Teyssière. Adaptive detection of multiple change-points in asset price volatility.
In Long-Memory in Economics. G. Teyssière et al. editors, 129-156, Springer (2007). MR2265058. Pdf file.

Abstract

This chapter considers the multiple change-point problem for time series, including strongly dependent processes, with an unknown number of change-points. We propose an adaptive method for finding the segmentation, i.e., the sequence of change-points \(\boldsymbol{\tau}\) with the optimal level of resolution. This optimal segmentation \(\hat{\boldsymbol{\tau}}\) is obtained by minimizing a penalized contrast function \(J(\boldsymbol{\tau},\boldsymbol{y}) + \beta {\rm pen}(\boldsymbol{\tau})\). For a given contrast function \(J(\boldsymbol{\tau},\boldsymbol{y})\) and a given penalty function \({\rm pen}(\boldsymbol{\tau})\), the adaptive procedure for automatically choosing the penalization parameter \(\beta\) is such that the segmentation \(\hat{\boldsymbol{\tau}}\) does not strongly depend on \(\beta\). This algorithm is applied to the problem of detection of change-points in the volatility of financial time series, and compared with Vostrikova's (1981) binary segmentation procedure.
G. Teyssière and P. Abry. Wavelet analysis of nonlinear long-range dependent processes. Applications to financial time series.
In Long-Memory in Economics. G. Teyssière et al. editors, 173-238, Springer (2007). MR2265060. Pdf file.
D. Kateb, A. Seghier and G. Teyssière. Prediction, orthogonal polynomials and Toeplitz matrices: a fast and reliable approximation to the Durbin-Levinson algorithm,
In Long-Memory in Economics. G. Teyssière et al. editors, 239-261, Springer (2007). MR2265061.
M. Lavielle and G. Teyssière. Detection of multiple change-points in multivariate time series.
Lithuanian Mathematical Journal (2006) vol 46, 287-306. MR2285348. Pdf file.

Abstract

We consider the multiple change-point problem for multivariate time series, including strongly dependent processes, with an unknown number of change-points. We assume that the covariance structure of the series changes abruptly at some unknown common change-point times. The proposed adaptive method is able to detect changes in multivariate i.i.d., weakly and strongly dependent series. This adaptive method outperforms the Schwarz criteria, mainly for the case of weakly dependent data. We consider applications to multivariate series of daily stock indices returns and series generated by an artificial financial market.
Key words: adaptive methods, multivariate time series, change-point detection, heteroskedasticity.

M. Lavielle and G. Teyssière. Détection de ruptures multiples dans des séries temporelles multivariées (French version of this paper).
Lietuvos Matematikos Rinkinys (2006) vol 46, 351-376. Pdf file.
P. Doukhan, G. Teyssière and P. Winant. A LARCH\((\infty)\) vector valued process.
In Dependence in Probability and Statistics. Lecture Notes in Statistics,, vol 187, 245-258, Springer (2006). MR2283258.
A. Kirman and G. Teyssière. Testing for bubbles and change-points.
Journal of Economic Dynamics and Control (2005) vol 29, 765-799. MR2129522. Pdf file.
L. Horváth, P. Kokoszka and G. Teyssière. Bootstrap misspecification tests for ARCH based on the empirical process of squared residuals.
Journal of Statistical Computation and Simulation (2004) vol 74, 469-485. MR2073226. Pdf file.

Abstract

We propose and study by means of simulations and graphical tools a class of goodness-of-fit tests for ARCH models. The tests are based on the empirical distribution function of squared residuals and smooth (parametric) bootstrap. We examine empirical size and power by means of a simulation study. While the tests have overall correct size, their power strongly depends on the type of alternative and is particularly high when the assumption of Gaussian innovations is violated. As an example, the tests are applied to returns on Foreign Exchange rates.
Key words: ARCH model, empirical process, goodness-of-fit tests, size-power curves, smooth bootstrap, squared residuals.
P. Kokoszka, G. Teyssière and A. Zhang. Confidence intervals for the autocorrelations of the squares of GARCH sequences.
In Computational Science - ICCS 2004. Lecture Notes in Computer Science. M. Bubak et al. editors, vol 3039, 827-834, Springer (2004). MR2233424. Pdf file. Volume for the Workshop on Computational Methods in Finance and Insurance, Kraków, Poland, June 2004. Slides.
L. Giraitis, P. Kokoszka, R. Leipus and G. Teyssière. On the power of \(R/S\)-type tests under contiguous and semi long-memory alternatives.
Acta Applicandae Mathematicae (2003) vol 78, 285-299. MR2024032. Pdf file. (Special Issue for the 8^th Vilnius Conference on Probability Theory and Mathematical Statistics), Vilnius, Lithuania.
G. Teyssière. Interaction models for common long-range dependence in asset price volatilities.
Invited chapter in Processes with Long Range Correlations: Theory and Applications. Lecture Notes in Physics. G. Rangarajan and M. Ding editors, vol 621, 251-269, Springer (2003). DOI. Pdf file.

Abstract

We consider a class of microeconomic models with interacting agents which replicate the main properties of asset prices time series: non-linearities in levels and common degree of long-memory in the volatilities and co-volatilities of multivariate time series. For these models, long-range dependence in asset price volatility is the consequence of swings in opinions and herding behavior of market participants, which generate switches in the heteroskedastic structure of asset prices. Thus, the observed long-memory in asset prices volatility might be the outcome of a change-point in the conditional variance process, a conclusion supported by a wavelet analysis of the volatility series. This explains why volatility processes share only the properties of the second moments of long-memory processes, but not the properties of the first moments.
Key words: long-memory, field effects, interaction models, change-points, wavelets.

Invited lecture to the International Conference on Long-Range Dependent Stochastic Processes and their Applications, Bangalore, India, January 2002.
L. Giraitis, P. Kokoszka, R. Leipus and G. Teyssière. Rescaled variance and related tests for long memory in volatility and levels.
Journal of Econometrics (2003) vol 112, 265-294. MR1951145. Pdf file. See also L. Giraitis, P. Kokoszka, R. Leipus and G. Teyssière, Corrigendum to "Rescaled variance and related tests for long memory in volatility and levels",
Journal of Econometrics (2005) vol 126, 571-572. MR2155635. Pdf file.
A. Kirman and G. Teyssière. Bubbles and Long Range Dependence in Asset Prices Volatilities.
In Equilibrium, Markets and Dynamics. C.H. Hommes, R. Ramer and C. Withagen editors, 307-327, Springer (2002).
DOI.
G. Teyssière and A. Kirman. Microeconomic models for long-memory in the volatility of financial time series.
SNDE (2002) vol 5, 281-302. DOI.
L. Horváth, P. Kokoszka and G. Teyssière. Empirical process of the squared residuals of an ARCH sequence.
The Annals of Statistics (2001) vol 29, 445-469. MR1863965. Pdf file.
L. Giraitis, P. Kokoszka, R. Leipus and G. Teyssière. Semiparametric estimation of the intensity of long-memory in conditional heteroskedasticity.
Statistical Inference for Stochastic Processes (2000) vol 3, 113-128. (Special Issue on Limit Theorems and Long-Range Dependence). MR1819290. Pdf file.

Abstract

The paper is concerned with the estimation of the long memory parameter in a conditionally heteroskedastic model proposed by Giraitis et al. (1999b). We consider estimation methods based on the partial sums of the squared observations, which are similar in spirit to the classical \(R / S\) analysis, as well as spectral domain approximate maximum likelihood estimators. We review relevant theoretical results and present an empirical simulation study.
Key words: long memory, ARCH models, semiparametric estimation, modified \(R/S\), KPSS and \(V/S\) statistics, periodogram.
G. Teyssière. Multivariate long-memory ARCH modelling for high frequency foreign exchange rates.
In Proceedings of the Second High Frequency Data in Finance (HFDF-II) Conference, Olsen & Associates, Zurich, (1998). Pdf file.

Abstract

We estimate here several trivariate FIGARCH models on three series of intra-day FX rates returns: USD/DEM, USD/GBP, and USD/JPY. We consider the trivariate constant conditional correlation CCC-FIGARCH, the unrestricted trivariate FIGARCH, and a trivariate double long-memory model combining an ARFIMA regression function with an unrestricted trivariate FIGARCH skedastic function. Estimation results show that: (i) the three series are anti-persistent and share a common degree of short-range dependence, (ii) the series USD/DEM and USD/JPY have the same regression function, (iii) the three series share the same degree of long-memory in their conditional variance, (iv) the conditional covariances \(\mbox{Cov}_t(\mbox{USD/DEM, USD/JPY})\) and \(\mbox{Cov}_t(\mbox{USD/DEM,USD/GBP})\) have a common degree of persistence, although this degree is different from the degree of long-memory of the conditional variances, (v) the unrestricted FIGARCH model dominates the CCC-FIGARCH model, although (vi) the seasonality in the volatility of these series cannot be captured by FIGARCH models.
Key words: intra-day data, long-memory, antipersistence, heteroskedasticity, multivariate models, multivariate unconstrained FIGARCH model, double long-memory, multivariate ARFIMA-FIGARCH models, second generation models.

Books

Long-Memory in Economics
G. Teyssière and A. Kirman editors, Springer (2007).
MR2263582
ISBN (Hardcover): 978-3540226949
ISBN (Paperback): 978-3642061547
ISBN (eBook): 978-3540346258

Dependence in Probability and Statistics, Lecture Notes in Statistics, Vol 200.
G. Lang, D. Surgailis and G. Teyssière editors, Springer (2010).
MR2741808
ISBN (Paperback): 978-3642141034
ISBN (eBook): 978-3642141041

Preprints & Conference Slides

G. Teyssière and P. Abry. Wavelet multifractal analysis of high-frequency financial data (2010), 10^th Vilnius Conference on Probability Theory and Mathematical Statistics
G. Teyssière. Détection de ruptures multiples sur des séries chronologiques univariées et multivariées. Application à des données de prix de l'énergie (2008). (Rapport de recherche pour EDF).
G. Teyssière. Long-range dependence and multiple change-points in multivariate time series (2007). Slides
Invited presentation to the International Conference on Statistical Models for Financial Data II, organized by István Berkes and Lajos Horváth at the Institute of Statistics, Graz University of Technology, Graz, Austria, 23-26 May 2007.
G. Teyssière. Bubbles, non-stationarity and double long memory (2004).
Invited presentation to the International Conference on Statistical Models for Financial Data, organized by István Berkes and Lajos Horváth at the Institute of Statistics, Graz University of Technology, Graz, Austria, May 2004.
P. Kokoszka and G. Teyssière. Change-point detection in GARCH models: asymptotic and bootstrap tests, PostScript file.

Abstract

Two classes of tests designed to detect changes in volatility are proposed. Procedures based on squared model residuals and on the likelihood ratio are considered. The tests are applicable to parametric nonlinear models like GARCH. Both asymptotic and bootstrap tests are investigated by means of a simulation study and applied to returns data. The tests based on the likelihood ratio are shown to be generally preferable. A wavelet based estimator of long memory is applied to returns data to shed light on the interplay of change points and long memory.
Key words: GARCH model, change-point, likelihood ratio, parametric bootstrap, squared residuals, size-power curves, wavelets.

Presented to the Invited Paper Meeting of the 54^th Session of the International Statistical Institute, August 2003. Slides. Under revision.
G. Teyssière. Nonlinear and semiparametric long-memory ARCH (2001).
Part of the material of this paper appeared in L. Giraitis, P. Kokoszka, R. Leipus and G. Teyssière On the power of R/S-Type tests under contiguous and semi long-memory alternatives, Acta Applicandae Mathematicae (2003), (Special Issue for the 8^th Vilnius Conference on Probability Theory and Mathematical Statistics) vol 78, 285-299. DOI. The remainder of this paper has been inserted in others papers.
G. Teyssière. Modelling exchange rates volatility with multivariate long-memory ARCH processes (1997). Pdf file (Old Version).

Abstract

We propose two multivariate long-memory ARCH models: we first consider a long-memory extension of the restricted constant conditional correlations (CCC) model introduced by Bollerslev (1990), and we propose a new unrestricted conditional covariance matrix model which models the conditional covariances as long-memory ARCH processes. We apply these two models to two daily returns on foreign exchanges (FX) rates series, the Pound-US dollar, and the Deutschmark-US dollar. The estimation results for both models show: (\(i\)) that the unrestricted model outperforms the restricted CCC model, and (\(ii\)) that all the elements of the conditional covariance matrix share the same degree of long-memory for the period April 1979-January 1997, i.e., after the European Monetary System inception in March 1979. However, this result does not hold for the period September 1971-January 1997, and the floating period before March 1979. Semiparametric methods confirm that the volatilities and co-volatility of the two FX rates share the same long-range component, and that the break in the long-term structure is likely to be caused by the European Monetary System inception.
Key words: long-memory processes, conditional heteroskedasticity, multivariate long-memory ARCH models, multivariate FIGARCH models, semiparametric estimators.
G. Teyssière. Double long-memory financial time series (1996), Preprint
Presented in the 1997 Econometric Society European Meeting, the 1997 Society for Economic Dynamics conference Oxford, the 28^th Workshop of the Euro Working Group on Financial Modelling, Vilnius, May 2001, Slides.
In 1996, I pioneered the class of double long memory processes with the ARFIMA-FIGARCH; this was my first paper in time series analysis. My 1998 paper on multivariate (trivariate) ARFIMA-FIGARCH, published in the proceedings of the High Frequency Data in Finance-II conference organized by Olsen & Associates (see above in the list of publications) is available here Pdf.

Abstract

Researchers have been investigating the long-memory properties of financial time series either in the mean or in the conditional variance. We show that some financial time series display long-memory in both their conditional mean and their conditional variance: we refer to such time series as double long-memory time series. We model these series by combining a fractionally integrated regression function and a fractionally integrated skedastic function. We examine the case of a double long-memory model, the ARFIMA-FIGARCH, and we propose an estimation procedure by QML which requires pre-sample values. We show, by using Monte Carlo simulations, that the QML estimator of this model has some nice properties: it is root-\(n\) consistent, asymptotically normal, and the level of bias is negligible. We study for this model some specification tests, i.e., the Ljung-Box statistics based on standardized residuals, squared standardized residuals and absolute standardized residuals. Disregarding the long-memory component in the regression function, even for moderate values of the degree of long-memory which are not detected by appropriate statistical tests, results in (\(i\)) an over-parameterization of the regression function, (\(ii\)) a bias in the estimation of the ARCH parameters of the conditional variance function, whilst the long-memory parameter of the conditional variance is unaffected by this misspecification, and (\(iii\)) a rejection of the null hypothesis of the Ljung-Box statistic based on standardized residuals, whilst the Ljung-Box statistics based on absolute and squared standardized residuals are unaffected.
Key words: fractionally integrated processes, double long-memory, heteroskedasticity, second generation models, Monte Carlo methods.

Co-Authors

Patrice Abry, Jean-Pierre Brun, Lajos Horváth, Casey King, Piotr Kokoszka, Marc Lavielle
My Erdös number is 3. (Path: Paul Erdös \( \longrightarrow\) Endre Csáki \( \longrightarrow\) Lajos Horváth \( \longrightarrow\) Gilles Teyssière)

Academic Service

Reviewer for Mathematical Reviews (MathSciNet®), with over 90 reviews and counting. Mathematical Reviews is edited by the American Mathematical Society, of which I'm a member.
Referee for: IEEE Transactions on Signal Processing, Annals of Statistics, Bernoulli, Stochastic Processes and their Applications, Journal of Statistical Planning and Inference, Canadian Journal of Statistics/ Revue Canadienne de Statistique, Statistica Sinica, Computational Statistics and Data Analysis, Lithuanian Mathematical Journal, Comptes Rendus de l'Académie des Sciences - Mathématiques, Lecture Notes in Statistics, Lecture Notes in Computer Science, Quantitative Finance, Journal of Economic Dynamics and Control, Journal of Financial Econometrics, etc.