3,716 research outputs found
Semiparametric Cross Entropy for rare-event simulation
The Cross Entropy method is a well-known adaptive importance sampling method
for rare-event probability estimation, which requires estimating an optimal
importance sampling density within a parametric class. In this article we
estimate an optimal importance sampling density within a wider semiparametric
class of distributions. We show that this semiparametric version of the Cross
Entropy method frequently yields efficient estimators. We illustrate the
excellent practical performance of the method with numerical experiments and
show that for the problems we consider it typically outperforms alternative
schemes by orders of magnitude
Asymptotic optimality of the cross-entropy method for Markov chain problems
The correspondence between the cross-entropy method and the zero-variance
approximation to simulate a rare event problem in Markov chains is shown. This
leads to a sufficient condition that the cross-entropy estimator is
asymptotically optimal.Comment: 13 pager; 3 figure
Yet another breakdown point notion: EFSBP - illustrated at scale-shape models
The breakdown point in its different variants is one of the central notions
to quantify the global robustness of a procedure. We propose a simple
supplementary variant which is useful in situations where we have no obvious or
only partial equivariance: Extending the Donoho and Huber(1983) Finite Sample
Breakdown Point, we propose the Expected Finite Sample Breakdown Point to
produce less configuration-dependent values while still preserving the finite
sample aspect of the former definition. We apply this notion for joint
estimation of scale and shape (with only scale-equivariance available),
exemplified for generalized Pareto, generalized extreme value, Weibull, and
Gamma distributions. In these settings, we are interested in highly-robust,
easy-to-compute initial estimators; to this end we study Pickands-type and
Location-Dispersion-type estimators and compute their respective breakdown
points.Comment: 21 pages, 4 figure
Combining long memory and level shifts in modeling and forecasting the volatility of asset returns
We propose a parametric state space model of asset return volatility with an accompanying estimation and forecasting framework that allows for ARFIMA dynamics, random level shifts and measurement errors. The Kalman filter is used to construct the state-augmented likelihood function and subsequently to generate forecasts, which are mean- and path-corrected. We apply our model to eight daily volatility series constructed from both high-frequency and daily returns. Full sample parameter estimates reveal that random level shifts are present in all series. Genuine long memory is present in high-frequency measures of volatility whereas there is little remaining dynamics in the volatility measures constructed using daily returns. From extensive forecast evaluations, we find that our ARFIMA model with random level shifts consistently belongs to the 10% Model Confidence Set across a variety of forecast horizons, asset classes, and volatility measures. The gains in forecast accuracy can be very pronounced, especially at longer horizons
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