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 Jackknifed Whittle Estimators

The Whittle estimator has been widely used in time series analysis. Although it is Gaussian asymptotically efficient, it suffers from large bias, especially, when the process concerned has near unit roots. In this paper we introduce the jackknife technique to the Whittle likelihood in the frequency domain, and elucidate the asymptotics of the Jackknifed Whittle estimator. For non-Gaussian stationary processes, it is shown that the second-order bias of it vanishes when the unknown parameter is innovation-free. Some numerical studies confirm the theoretical results. Because the Whittle estimator is applicable to many fields, e.g., natural sciences, signal processing and econometrics, use of the bias-reduced Jackknifed Whittle estimator is profitable.

Resampling Procedure to Construct Value at Risk Efficient Portfolios for ARMA-GARCH Returns of Assets

We discuss resampling procedures to construct Value at Risk (VaR) Efficient Plortfolios when returns are vector-valued ARMA-GRCH processes. We investigate a model based bootstrap procedure with minimal model misspecification under ARMA-GARCH model. By use of Bayesian InformationCriterion (BIC), we fit the observations to AR(p)-ARCH(q) process. Then, wepropose the resampled return process based on the Yule Walker estimator.Finally, we propose estimators of VaR efficient portfolio based on the resampled return process.

The Method of Simulated Quantiles

In this paper we present inference methods based on quantiles, in the sense that functions of theoretical quantiles, which depend on the parameters of the assumed probability law, are matched with empirical quantiles, which depend on data. The optimization is based on simulations and the method provides consistent and asymptotically normal estimators of the parameters of interest. This method is useful for situations where the density function does not have a closed form but it is simple to simulate. A Monte Carlo study based on alpha stable distributions show the usefulness of the approach. Joint with Yves Dominicy

Long-run commonness and short-run idiosyncrasy for a large panel of volatilities (Matteo Barigozzi, Christian Bronwlees, Giampiero Gallo and David Veredas)

We propose a multivariate multiplicative error model for a large number of assets that disentangles between the common smooth long-run movements and the idiosyncratic short-run dynamics. Estimation rests in a t-copula where the marginal densities, which include the long-run and short-run components, are first estimated with profile likelihood. The parameters of the copula are estimated in a second step through an iterative procedure -avoiding hence the maximization of the copula density.
The model is applied 3 years of daily realized volatilities of stocks that are constituents of the Spanish stock exchange index.

QML estimation and prediction of GARCH models

We start by recalling the asymptotic properties of the Gaussian quasi-maximum likelihood estimator (QMLE) in GARCH models. The consistency and asymptotic normality hold under mild conditions, including the strict stationarity of the observed process, the existence of fourth-order moments for the strong white noise driving the dynamics and the non nullity of the volatility coefficients. When the moment condition on the noise is not satisfied, the QMLE remains consistent but may have a non standard asymptotic distribution. When the parameter stands at the boundary of the parameter space, the asymptotic normality is also in failure: the asymptotic distribution is obtained as the projection of a Gaussian vector on the local parameter space. Based on these results, we consider the problem of optimal prediction of powers, or logarithms, of the absolute process. A standard procedure for estimating this prediction is to estimate the volatility by Gaussian QML in a first step, and then use empirical means based on rescaled innovations in a second step. We suggest an alternative one-step procedure, based on an appropriate non-Gaussian QML estimation of the model. The performances of the two approaches are compared.

Testing linear causality in mean in presence of other forms of causality

This paper consider the test for linear causality in mean in the large set of processes given by Vector AutoregRessive (VAR) models with dependent but uncorrelated errors. We see that this framework allows to take into account the possible presence of causality in mean and/or causality in variance. Using the asymptotic normality of the Quasi Maximum Likelihood Estimator (QMLE), we propose various modified tests for testing the causality in mean in presence of dependent errors. We study the finite sample performances of the modified tests by mean of Monte Carlo experiments. An application to the daily returns of the exchange rates of U.S. Dollars (USD hereafter) to one British Pound (BP hereafter) and of USD to one New Zealand Dollar (NZD hereafter) is proposed to illustrate the theoretical results.