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Academic Archives

Research Archives

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, 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, Austria, May 2004.
P. Kokoszka and G. Teyssière. Change-point detection in GARCH models: asymptotic and bootstrap tests, PostScript .

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, Berlin, 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). (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, 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

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.

Teaching Archives

2009: Aarhus University, PhD lectures, based on the draft version of the book Large Sample Inference for Long Memory Processes (2012) Imperial College Press. In 2013, I reviewed this book for Mathematical Reviews®; MathSciNet subscribers can read this review from my author profile.
Additional material, not covered in that book, on Long–Memory and Change–Points in Volatility Processes, Slides.
2006-2007: Ensae, lectures (in French) on Long-range dependence and change-points, Applications to univariate and multivariate financial time series: Leçon 1 : Processus fortement dépendants, Transparents ; Leçon 2 : Tests de détection de longue portée et estimateurs du paramètre de longue portée, Transparents; Leçon 3 : Tests de détection de ruptures, Transparents; Leçon 4 : Méthodes statistiques robustes aux ruptures, Transparents.
1993-1996: University of London, Lectures on optimization techniques with Maple. I have typed a 200 pages document.