Fabienne Comte

Long Memory in Continuous Time Stochastic Volatility Models

This paper studies a classical extension of the Black and Scholes model of option pricing, often known as the Hull and White model. Our specificity is that the volatility process is assumed not only to be stochastic, but also to have long memory features and properties. We study here the implications of this long memory continuous time modelization, on the volatility process itself, as well as on the global asset pricing model.

Asymptotic theory for multivariate GARCH processes

We provide in this paper asymptotic theory for the multivariate GARCH(p, q) process. Strong consistency of the quasi-maximum likelihood estimator (MLE) is established by appealing to conditions given by Jeantheau (Econometric Theory 14 (1998), 70) in conjunction with a result given by Boussama (Ergodicity, mixing and estimation in GARCH models, Ph.D. Dissertation, University of Paris 7, 1998) concerning the existence of a stationary and ergodic solution to the multivariate GARCH(p, q) process. We prove asymptotic normality of the quasi-MLE when the initial state is either stationary or fixed.

Long memory continuous time models

This paper presents a new family of long memory models: the continuous time moving average fractional process. The continuous time framework allows to reconcile two competitive types of modelling: fractional integration of ARMA processes and fractional Brownian Motion. A comparison with usual discrete time ARFIMA models is lead. Some well-known empirical evidence on macroeconomic and financial time series, such as variability of forward rates, aggregation of responses across heterogeneous agents, are well-captured by this continuous time modelling. Moreover, the usual statistical tools for long memory series and for Stochastic Differential Equations can be jointly applied in this setting.

Second‐Order Noncausality in Multivariate GARCH Processes

Typical multivariate economic time series may exhibit co-behavior patterns not only in the conditional means, but also in the conditional variances. In this paper we give two new definitions of variance noncausality in a multivariate setting a Granger-type noncausality and a linear Granger noncausality through projections on Hilbert spaces. Both definitions are related to a previous second-order noncausality concept defined by Granger et al. in a bivariate setting. The implications of second-order noncausality on multivariate ARMA processes with GARCH-type errors are investigated. We derive exact testable restrictions on the parameters of the processes considered, implied by this type of noncausality. Conditions for the finiteness of the fourth-order moment of the multivariate GARCH process are derived and related to earlier results in the univariate framework. We include an illustration of second-order noncausality in a trivariate model of daily financial returns.

Estimation for Lévy processes from high frequency data within a long time interval

In this paper, we study nonparametric estimation of the Levy density for Levy processes, first without then with Brownian component. For this, we consider 2n (resp. 3n) discrete time observations with step

Penalized nonparametric mean square estimation of the coefficients of diffusion processes

\Delta

Adaptive functional linear regression

. The asymptotic framework is: n tends to infinity,

A new algorithm for fixed design regression and denoising

\Delta=\Delta_n

Adaptive estimation of mean and volatility functions in (auto-)regressive models

tends to zero while

Noncausality in Continuous Time Models

n\Delta_n