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on Econometric Time Series |
| By: | Magid Maatallah (The Financial Mathematics Research Group at King's College - King's College London, Birkbeck College - University of London) |
| Abstract: | We construct proxy regions based on local time arguments and consider numerical approximations. These are then available for a more incisive assessment of the Monte Carlo procedure and thence of the estimate itself. |
| Date: | 2009–11–23 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00492440_v1&r=ets |
| By: | Abdelkoddousse Ahdida (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - Ecole Nationale des Ponts et Chaussées); Aurélien Alfonsi (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - Ecole Nationale des Ponts et Chaussées) |
| Abstract: | This work deals with the simulation of Wishart processes and affine diffusions on positive semidefinite matrices. To do so, we focus on the splitting of the infinitesimal generator, in order to use composition techniques as Ninomiya and Victoir or Alfonsi. Doing so, we have found a remarkable splitting for Wishart processes that enables us to sample exactly Wishart distributions, without any restriction on the parameters. It is related but extends existing exact simulation methods based on Bartlett's decomposition. Moreover, we can construct high-order discretization schemes for Wishart processes and second-order schemes for general affine diffusions. These schemes are in practice faster than the exact simulation to sample entire paths. Numerical results on their convergence are given. |
| Keywords: | Wishart processes, affine processes, exact simulation, discretization schemes, weak error, Bartlett's decomposition. |
| Date: | 2010–06–11 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-00491371_v1&r=ets |
| By: | Jonathan H. Wright |
| Abstract: | This paper proposes Bayesian forecasting in a vector autoregression using a democratic prior. This prior is chosen to match the predictions of survey respondents. In particular, the unconditional mean for each series in the vector autoregression is centered around long-horizon survey forecasts. Heavy shrinkage toward the democratic prior is found to give good real-time predictions of a range of macroeconomic variables, as these survey projections are good at quickly capturing endpoint-shifts. |
| Keywords: | Forecasting ; Real-time data |
| Date: | 2010 |
| URL: | http://d.repec.org/n?u=RePEc:fip:fedpwp:10-19&r=ets |
| By: | Karim M. Abadir (Imperial College, London, UK); Michel Lubrano (Greqam-Cnrs, Centre de la Vieille Charité, Marseille, France) |
| Abstract: | Least squares cross-validation (CV) methods are often used for automated bandwidth selection. We show that they share a common structure which has an explicit asymptotic solution that we derive. Using the framework of density estimation, we consider unbiased, biased, and smoothed CV methods. We show that, with a Student t(v) kernel which includes the Gaussian as a special case, the CV criterion becomes asymptotically equivalent to a simple polynomial. This leads to optimal-bandwidth solutions that dominate the usual CV methods, definitely in terms of simplicity and speed of calculation, but also often in terms of integrated squared error because of the robustness of our asymptotic solution, hence also alleviating the notorious sample variability of CV. We present simulations to illustrate these features and to give practical guidance on the choice of v. |
| Keywords: | bandwidth choice; cross validation; nonparametric density estimation; analytical solution |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:16_10&r=ets |
| By: | Karim M. Abadir (Imperial College Business School, Imperial College London, London, UK); Walter Distaso (Imperial College Business School, Imperial College London, London, UK); Liudas Giraitis (Department of Economics, Queen Mary, University of London, London, UK) |
| Abstract: | This paper deals with models allowing for trending processes and cyclical component with error processes that are possibly nonstationary, nonlinear, and non-Gaussian. Asymptotic confidence intervals for the trend, cyclical component, and memory parameters are obtained. The confidence intervals are applicable for a wide class of processes, exhibit good coverage accuracy, and are easy to implement. |
| Keywords: | fractional integration, trend, cycle, nonlinear process, Whittle objective function |
| JEL: | C22 |
| Date: | 2010–01 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:18_10&r=ets |