Research and Publications

# Ultima - Last News

• Wavelets-MF (v1.81), the C++ software for wavelet-based analysis of multifractal processes on very large datasets of regularly and irregularly spaced data, is released. Related research papers are following.

# Research Interests

• Time series,
• Long-memory and multifractal processes, change-point detection,
• Financial econometrics, volatility modeling,
• Financial markets with interacting agents, financial bubbles,
• Wavelet signal processing,
• Computational statistics.

# Publications

1. D. Surgailis, G. Teyssière and M. Vaičiulis. The increment ratio statistic.
Journal of Multivariate Analysis (2008) vol 99, 510-541. DOI. MR2396977. Pdf file (Supplementary Material Pdf).
Abstract

We introduce a new statistic written as a sum of certain ratios of second order increments of partial sums process $S_n = \sum_{t=1}^n X_t$ of observations, which we call the Increment Ratio (IR) statistic. The IR statistic can be used for testing nonparametric hypotheses for $d-$integrated ($-1/2 \lt d \lt 3/2$) behavior of time series $X_t$, including short memory ($d=0$), (stationary) long-memory $(0 \lt d \lt 1/2)$ and unit roots ($d=1$). If $S_n$ behaves asymptotically as an (integrated) fractional Brownian motion with parameter $H =d + 1/2$, the IR statistic converges to a monotone function $\Lambda (d)$ of $d \in (-1/2,3/2)$ as both the sample size $N$ and the window parameter $m$ increase so that $N/m \to \infty$. For Gaussian observations $X_t$, we obtain a rate of decay of the bias $\mathrm{E} IR - \Lambda (d)$ and a central limit theorem $(N/m)^{1/2}(IR - \mathrm{E} IR) \rightarrow {\cal N}(0, \sigma^2(d))$, in the region $-1/2 \lt d \lt 5/4$. Graphs of the functions $\Lambda (d)$ and $\sigma (d)$ are included. A simulation study shows that the IR test for short memory ($d=0$) against stationary long-memory alternatives $(0 \lt d \lt 1/2)$ has good size and power properties and is robust against changes in mean, slowly varying trends and nonstationarities. We apply this statistic to sequences of squares of returns on financial assets and obtain a nuanced picture of the presence of long-memory in asset price volatility.

2. 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 and A. Kirman editors, 173-238, Springer (2007). DOI. MR2265060. Pdf file.
Abstract

We present and study the performance of the semiparametric wavelet estimator for the long-memory parameter devised by Veitch and Abry (1999). We compare this estimator with two semiparametric estimators in the spectral domain, the local Whittle (LW) estimator developed by Robinson (1995a) and the log-periodogram (LP) estimator by Geweke and Porter-Hudak (1983). The wavelet estimator performs well for a wide range of nonlinear long-memory processes in the conditional mean and the conditional variance, and is reliable for discriminating between change-points and long-range dependence in volatility. We also address the issue of selection of the range of octaves used as regressors by the weighted least squares estimator. We will see that using the feasible optimal bandwidths for either the LW and LP estimators, respectively studied by Henry and Robinson (1996) and Henry (2001), is a useful rule of thumb for selecting the lowest octave. We apply the wavelet estimator to volatility series of high frequency (intra-day) Foreign Exchange (FX) rates, and to the volatility and volume of stocks of the Dow Jones Industrial Average Index.

3. M. Lavielle and G. Teyssière. Adaptive detection of multiple change-points in asset price volatility.
In Long-Memory in Economics. G. Teyssière and A. Kirman editors, 129-156, Springer (2007). DOI. 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.

4. 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 and A. Kirman editors, 239-261, Springer (2007). DOI. MR2265061. Pdf file.
Abstract

Let $f$ be a given function on the unit circle such that $\displaystyle f(e^{i\theta})=\mid 1-e^{i\theta}\mid^{2\alpha} f_1(e^{i\theta})$ with $\mid \alpha \mid \lt \frac{1}{2}$ and $f_1$ a strictly positive function that will be supposed to be sufficiently smooth. We give the asymptotic behavior of the first column of the inverse of $T_N(f)$, the $(N+1)\times (N+1)$ Toeplitz matrix with elements $(f_{i-j})_{0\le i,j \le N}$ where $\displaystyle f_k=\frac{1}{2\pi}\int_0^{2\pi} f(e^{i\theta})e^{-ik\theta}~d\theta$. We shall compare our numerical results with those given by the Durbin-Levinson algorithm, with particular emphasis on problems of predicting either stationary stochastic long-range dependent processes, or processes with a long-range dependent component.

5. M. Lavielle and G. Teyssière. Detection of multiple change-points in multivariate time series.
Lithuanian Mathematical Journal (2006) vol 46, 287-306. DOI. 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.
Abstract

Nous considérons le problème de détection de ruptures multiples pour des séries chronologiques multivariées, y compris des processus fortement dépendants, avec un nombre inconnu de ruptures. Nous supposons que la structure de covariance de ces séries chronologiques change de façcon abrupte à des dates inconnues. La méthode adaptative proposée ici est capable de détecter des ruptures dans des séries multivariées indépendantes et identiquement distribuées (i.i.d.), faiblement et fortement dépendantes. Cette méthode adaptative surclasse le critère de Schwartz, principalement dans le cas de données faiblement dépendantes. Nous considérons des applications à des séries chronologiques multivariées de rendements d'indices boursiers journaliers et à des séries générées par un marché financier artificiel.

6. P. Doukhan, G. Teyssière and P. Winant. A LARCH$(\infty)$ vector valued process.
In Dependence in Probability and Statistics. Lecture Notes in Statistics. P. Bertail, P. Doukhan and Ph. Soulier editors, vol 187, 245-258, Springer (2006). DOI. MR2283258. Pdf file.
Abstract

The purpose of this chapter is to propose a unified framework for the study of ARCH$(\infty)$ processes that are commonly used in the financial econometrics literature. We extend the study, based on Volterra expansions, of univariate ARCH$(\infty)$ processes by Giraitis, Kokoszka and Leipus (2000) to the multi-dimensional case.

7. A. Kirman and G. Teyssière. Testing for bubbles and change-points.
Journal of Economic Dynamics and Control (2005) vol 29, 765-799. DOI. MR2129522. Pdf and PostScript files.
Abstract

A model for a financial asset is constructed with two types of agents, who differ in terms of their beliefs. The proportion of the two types changes over time according to stochastic processes which model the interaction between the agents. Agents do not persist in holding wrong'' beliefs and bubble-like phenomena in the asset price occur. We consider tests for detecting bubbles in the conditional mean and multiple changes in the conditional variance of the process. A wavelet analysis of the series generated by our models shows that the strong persistence in the volatility is likely to be the outcome of a mix of changes in regimes and a moderate level of long-range dependence. These results are consistent with what has been observed by Kokoszka and Teyssière (2002) and Teyssière (2003).
Key words: market interactions, bubbles, long-memory heteroskedasticity, pseudo long-memory, change-point, wavelets.

8. 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. DOI. MR2073226. Pdf and PostScript files.
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.

9. 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). DOI. MR2233424. Pdf file.
Abstract

We compare three methods of constructing confidence intervals for sample autocorrelations of squared returns modeled by models from the GARCH family. We compare the residual bootstrap, block bootstrap and subsampling methods. The residual bootstrap based on the standard GARCH(1,1) model is seen to perform best.

Volume for the Workshop on Computational Methods in Finance and Insurance, Kraków, Poland, June 2004. Slides.
10. 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. DOI. MR2024032. Pdf and PostScript files. (Special Issue for the 8th Vilnius Conference on Probability Theory and Mathematical Statistics), Vilnius, Lithuania.
Abstract

The paper deals with the power and robustness of the $R/S$ type tests under “contiguous” alternatives. We briefly review some long memory models in levels and volatility, and describe the $R/S$-type tests used to test for the presence of long memory. The empirical power of the tests is investigated when replacing the fractional difference operator $(1 − L)^d$ by the operator $(1 − rL)^d$, with $r \lt 1$ close to 1, in the FARIMA, LARCH and ARCH time series models. We also investigate the Gegenbauer process with a pole of the spectral density at frequency close to zero.
Key words: long memory, Gegenbauer process, ARCH processes, linear ARCH, semi-long memory, modified $R/S$ statistic, KPSS statistic, $V/S$ statistic.

11. 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 and PostScript files.
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.
12. 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. DOI. MR1951145. Pdf file.
Abstract

This paper studies properties of tests for long memory for general fourth order stationary sequences. We propose a rescaled variance test based on the $V/S$ statistic which is shown to have a simpler asymptotic distribution and to achieve a somewhat better balance of size and power than Lo's (1991) modified $R/S$ test and the KPSS test of Kwiatkowski et al. (1992). We investigate theoretical performance of $R/S$, KPSS and $V/S$ tests under short memory hypotheses and long memory alternatives, providing a Monte Carlo study and a brief empirical example. Assumptions of the same type are used in both short and long memory cases, covering all persistent dependence scenarios. We show that the results naturally apply and the assumptions are well adjusted to linear sequences (levels) and to squares of linear ARCH sequences (volatility).
Key words: long memory, modified $R/S$ statistic, KPSS statistic, $V/S$ statistic, linear process, LARCH model.

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. DOI. MR2155635. Pdf file.
13. 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).
Abstract

A model for a financial asset is constructed with two types of agents. The agents differ in terms of their beliefs. The proportions of the two types change over time according to a stochastic process which models the interaction between the agents. Thus, unlike other models, agents do not persist in holding "wrong" beliefs. Bubble-like phenomena in the asset price occur. We consider several tests for detecting long range dependence and change-points in the conditional variance process. Although the model seems to generate long-memory properties of the volatility series, we show that this is due to the switching of regimes which are detected by the tests we propose.
Key words: interaction, bubbles, testing, long-memory, heteroskedasticity, change-point.

14. A. Kirman and G. Teyssière. Microeconomic models for long-memory in the volatility of financial time series.
Studies in Nonlinear Dynamics and Econometrics (2002) vol 5, 281-302. DOI. Pdf and PostScript files.
Abstract

We show that a class of microeconomic behavioral models with interacting agents, derived from Kirman (1991,1993), can replicate the empirical long-memory properties of the two first conditional moments of financial time series. The essence of these models is that the forecasts and thus the desired trades of the individuals in the markets are influenced, directly, or indirectly by those of the other participants. These field effects'' generate herding'' behaviour which affects the structure of the asset price dynamics. The series of returns generated by these models display the same empirical properties as financial returns: returns are $I(0)$, the series of absolute and squared returns display strong dependence, while the series of absolute returns do not display a trend. Furthermore, this class of models is able to replicate the common long-memory properties in the volatility and co-volatility of financial time series, revealed by Teyssière (1997,1998a). These properties are investigated by using various model independent tests and estimators, i.e., semiparametric and nonparametric, introduced by Lo (1991), Kwiatkowski, Phillips, Schmidt and Shin (1992), Robinson (1995), Lobato and Robinson (1998}, Giraitis, Kokoszka, Leipus and Teyssière (2000, 2001). The relative performance of these tests and estimators for long-memory in a non-standard data generating process is then assessed.
Key words: long-memory, microeconomic models, field effects, semiparametric tests, conditional heteroskedasticity.

15. 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. DOI. MR1863965. Pdf and PostScript files.
Abstract

We derive the asymptotic distribution of the sequential empirical process of the squared residuals of an ARCH($p$) sequence. Unlike the residuals of an ARMA process, these residuals do not behave in this context like asymptotically independent random variables, and the asymptotic distribution involves a term depending on the parameters of the model. We show that in certain applications, including the detection of changes in the distribution of the unobservable innovations, our result leads to asymptotically distribution free statistics.
Key words: ARCH model, empirical process, squared residuals.

16. 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). DOI. MR1819290. Pdf and PostScript files.
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.

17. 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 and PostScript files.
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 & Special Issues

Statistical Methods for the Evaluation of the Economic Consequences of Corruption.
J-P. Brun and G. Teyssière (Under preparation).

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

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

# Preprints, Conference Slides & Occasional Papers

• G. Teyssière and P. Abry. Wavelet multifractal analysis of high-frequency financial data (2010), 10th Vilnius Conference on Probability Theory and Mathematical Statistics, Conference Slides (Password required)
• P. Abry and G. Teyssière. Changes in the scaling structure of high frequency financial time series through the wavelet lens (2010). Slides (Password required)
• D. Surgailis and G. Teyssière. The increment ratio test for unit root under linear observations (2009).
• P. Bertrand, G. Teyssière and A. Chamoux. Detection of change-Points in the spectral density. With applications to ECG data. (Occasional paper).
In Proceedings of the EGC 2009 Conference, Workshop "Fouille de données temporelles et analyse de flux de données" (2009) 3-10. Pdf file.
Abstract

We propose a new method for estimating the change-points of heart rate in the orthosympathetic and parasympathetic bands, based on the wavelet transform in the complex domain and the study of the change-points in the moments of the modulus of these wavelet transforms. We observe change-points in the distribution for both bands.

• G. Teyssière. Détection de ruptures multiples sur des séries chronologiques univariées et multivariées. Application à des données de prix de l'énergie (2008). (Research report for 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.
• L. Giraitis, P.M. Robinson and G. Teyssière. Testing for change-point in cyclical and persistent long-memory processes (2005).
• 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 54th 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 8th 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 and PostScript files (Old Version). Under revision/transformation.
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
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.

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 in both Pdf and PostScript formats.