arXiv subjects

Bruno Saussereau

Publications and source records attributed to Bruno Saussereau.

10 recordsLinked to original sources

arXiv2024

Diagnostic Checking in Multivariate ARMA Models With Dependent Errors Using Normalized Residual Autocorrelations

In this paper we derive the asymptotic distribution of normalized residual empirical autocovariances and autocorrelations under weak assumptions on the noise. We propose new portmanteau statistics for vector autoregressive moving-average (VARMA) models with uncorrelated but non-independent innovations by using a self-normalization approach. We establish the asymptotic distribution of the proposed statistics. This asymptotic distribution is quite different from the usual chi-squared approximation used under the independent and identically distributed assumption on the noise, or the weighted sum of independent chi-squared random variables obtained under nonindependent innovations. A set of Monte Carlo experiments and an application to the daily returns of the CAC40 is presented.

math.ST↗

arXiv2024

Portmanteau test for a class of multivariate asymmetric power GARCH model

We establish the asymptotic behaviour of the sum of squared residuals autocovariances and autocorrelations for the class of multi-variate power transformed asymmetric models. We then derive a portmanteau test. We establish the asymptotic distribution of the proposed statistics. These asymptotic results are illustrated by Monte Carlo experiments. An application to a bivariate real financial data is also proposed.

math.ST↗

arXiv2021

Diagnostic checking in FARIMA models with uncorrelated but non-independent error terms

This work considers the problem of modified portmanteau tests for testing the adequacy of FARIMA models under the assumption that the errors are uncorrelated but not necessarily independent (i.e. weak FARIMA). We first study the joint distribution of the least squares estimator and the noise empirical autocovariances. We then derive the asymp-totic distribution of residual empirical autocovariances and autocorrelations. We deduce the asymptotic distribution of the Ljung-Box (or Box-Pierce) modified portmanteau statistics for weak FARIMA models. We also propose another method based on a self-normalization approach to test the adequacy of FARIMA models. Finally some simulation studies are presented to corroborate our theoretical work. An application to the Standard \& Poor's 500 and Nikkei returns also illustrate the practical relevance of our theoretical results. AMS 2000 subject classifications: Primary 62M10, 62F03, 62F05; secondary 91B84, 62P05.

stat.AP↗

arXiv2021

Estimating FARIMA models with uncorrelated but non-independent error terms

In this paper we derive the asymptotic properties of the least squares estimator (LSE) of fractionally integrated autoregressive moving-average (FARIMA) models under the assumption that the errors are uncorrelated but not necessarily independent nor martingale differences. We relax considerably the independence and even the martingale difference assumptions on the innovation process to extend the range of application of the FARIMA models. We propose a consistent estimator of the asymptotic covariance matrix of the LSE which may be very different from that obtained in the standard framework. A self-normalized approach to confidence interval construction for weak FARIMA model parameters is also presented. All our results are done under a mixing assumption on the noise. Finally, some simulation studies and an application to the daily returns of stock market indices are presented to corroborate our theoretical work.

stat.AP↗

arXiv2019

Estimation of multivariate asymmetric power GARCH models

It is now widely accepted that volatility models have to incorporate the so-called leverage effect in order to to model the dynamics of daily financial returns.We suggest a new class of multivariate power transformed asymmetric models. It includes several functional forms of multivariate GARCH models which are of great interest in financial modeling and time series literature. We provide an explicit necessary and sufficient condition to establish the strict stationarity of the model. We derive the asymptotic properties of the quasi-maximum likelihood estimator of the parameters. These properties are established both when the power of the transformation is known or is unknown. The asymptotic results are illustrated by Monte Carlo experiments. An application to real financial data is also proposed.

math.ST↗

arXiv2018

Portmanteau test for the asymmetric power GARCH model when the power is unknown

It is now widely accepted that, to model the dynamics of daily financial returns, volatility models have to incorporate the so-called leverage effect. We derive the asymptotic behaviour of the squared residuals autocovariances for the class of asymmetric power GARCH model when the power is unknown and is jointly estimated with the model's parameters. We then deduce a portmanteau adequacy test based on the autocovariances of the squared residuals. These asymptotic results are illustrated by Monte Carlo experiments. An application to real financial data is also proposed.

math.ST↗

arXiv2014

Nonparametric inference for fractional diffusion

A non-parametric diffusion model with an additive fractional Brownian motion noise is considered in this work. The drift is a non-parametric function that will be estimated by two methods. On one hand, we propose a locally linear estimator based on the local approximation of the drift by a linear function. On the other hand, a Nadaraya-Watson kernel type estimator is studied. In both cases, some non-asymptotic results are proposed by means of deviation probability bound. The consistency property of the estimators are obtained under a one sided dissipative Lipschitz condition on the drift that insures the ergodic property for the stochastic differential equation. Our estimators are first constructed under continuous observations. The drift function is then estimated with discrete time observations that is of the most importance for practical applications.

math.PR↗

arXiv2012

A new numerical scheme for the Zakaï equation

The aim of this paper is to propose a new method for numerical approximations of the solution of the linear stochastic partial differential equation arising in non-linear filtering problems: the Zakaï equation. The approximation scheme is based on a representation of the solution of the Zakaï equation involving a stochastic part arising from the observation process and a deterministic partial differential equation in which are involved only the parameters of the signal process. We may then employ a dynamic programming principle in order to write down an approximation of this partial differential equation. A quantization method based on the underlying diffusion process (which is a not the signal itself) is used.

math.PR↗

arXiv2012

Deviation probability bounds for fractional martingales and related remarks

In this paper we prove exponential inequalities (also called Bernstein's inequality) for fractional martingales. As an immediate corollary, we will discuss weak law of large numbers for fractional martingales under divergence assumption on the $β-$variation of the fractional martingale. A non trivial example of application of this convergence result is proposed.

math.PR↗

arXiv2012

Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion

We establish Talagrand's $T_1$ and $T_2$ inequalities for the law of the solution of a stochastic differential equation driven by a fractional Brownian motion with Hurst parameter $H>1/2$. We use the $L^2$ metric and the uniform metric on the path space of continuous functions on $[0,T]$. These results are applied to study small-time and large-time asymptotics for the solutions of such equations by means of a Hoeffding-type inequality.

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