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# Documents  Bardet, Jean-Marc | enregistrements trouvés : 3

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## Asymptotic behavior of the Laplacian quasi-maximum likelihood estimator of affine causal processes Bardet, Jean-Marc | CIRM H

Post-edited

Research talks;Probability and Statistics

We prove the consistency and asymptotic normality of the Laplacian Quasi-Maximum Likelihood Estimator (QMLE) for a general class of causal time series including ARMA, AR($\infty$), GARCH, ARCH($\infty$), ARMA-GARCH, APARCH, ARMA-APARCH,..., processes. We notably exhibit the advantages (moment order and robustness) of this estimator compared to the classical Gaussian QMLE. Numerical simulations confirms the accuracy of this estimator.

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## Testing the existence of moments for GARCH-type processes Zakoïan, Jean-Michel | CIRM H

Multi angle

Research talks;Probability and Statistics

It is generally admitted that financial time series have heavy tailed marginal distributions. When time series models are fitted on such data, the non-existence of appropriate moments may invalidate standard statistical tools used for inference. Moreover, the existence of moments can be crucial for risk management. This talk considers testing the existence of moments in the framework of standard and augmented GARCH models. In the case of standard GARCH, even-moment conditions involve moments of the independent innovation process. We propose tests for the existence of moments of the returns process that are based on the joint asymptotic distribution of the estimator of the volatility parameters and empirical moments of the residuals. To achieve efficiency gains we consider non Gaussian QML estimators founded on reparametrizations of the GARCH model, and we discuss optimality issues. We also consider augmented GARCH processes, for which moment conditions are less explicit. We establish the asymptotic distribution of the empirical moment Generating function (MGF) of the model, defined as the MGF of the random autoregressive coefficient in the volatility dynamics, from which a test is deduced. An alternative test is based on the estimation of the maximal exponent characterizing the existence of moments. Our results will be illustrated with Monte Carlo experiments and real financial data. It is generally admitted that financial time series have heavy tailed marginal distributions. When time series models are fitted on such data, the non-existence of appropriate moments may invalidate standard statistical tools used for inference. Moreover, the existence of moments can be crucial for risk management. This talk considers testing the existence of moments in the framework of standard and augmented GARCH models. In the case of ...

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## Detecting seasonality changes in multivariate extremes from climatological time series Naveau, Philippe | CIRM H

Multi angle

Research talks;Probability and Statistics

Many effects of climate change seem to be reflected not in the mean temperatures, precipitation or other environmental variables, but rather in the frequency and severity of the extreme events in the distributional tails. The most serious climate-related disasters are caused by compound events that result from an unfortunate combination of several variables. Detecting changes in size or frequency of such compound events requires a statistical methodology that efficiently uses the largest observations in the sample.
We propose a simple, non-parametric test that decides whether two multivariate distributions exhibit the same tail behavior. The test is based on the entropy, namely Kullback-Leibler divergence, between exceedances over a high threshold of the two multivariate random vectors. We study the properties of the test and further explore its effectiveness for finite sample sizes.
Our main application is the analysis of daily heavy rainfall times series in France (1976 -2015). Our goal in this application is to detect if multivariate extremal dependence structure in heavy rainfall change according to seasons and regions.
Many effects of climate change seem to be reflected not in the mean temperatures, precipitation or other environmental variables, but rather in the frequency and severity of the extreme events in the distributional tails. The most serious climate-related disasters are caused by compound events that result from an unfortunate combination of several variables. Detecting changes in size or frequency of such compound events requires a statistical ...

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