ON STATE-INDEPENDENT IMPORTANCE SAMPLING FOR THE GI|GI|1 TANDEM QUEUE1

In this paper, we consider a d-node GI|GI|1 tandem queue with i.i.d. inter-arrival process and service processes that are independent of each other. Our main interest is to estimate the probability to reach a high level N in a busy cycle of the system using simulation. As crude simulation does not give a sufficient precision in reasonable time, we use importance sampling. We introduce a method to find a state-independent change of measure and we show that this is equivalent to a change of measure that was earlier, but implicitly, described by Parekh and Walrand [8]. We also show that this change of measure is the only exponential state-independent change of measure that may result in an asymptotically efficient estimator. Lastly, we provide necessary conditions for this state-independent change of measure to give an asymptotically efficient estimator.

A Model-Free Measure of Aggregate Idiosyncratic Volatility and the Prediction of Market Returns

In this paper, we formally show that the cross-sectional variance of stock returns is a consistent and asymptotically efficient estimator for aggregate idiosyncratic volatility. This measure has two key advantages: It is model free and observable at any frequency. Previous approaches have used monthly model-based measures constructed from time series of daily returns. The newly proposed cross-sectional volatility measure is a strong predictor for future returns on the aggregate stock market at the daily frequency. Using the cross section of size and book-to-market portfolios, we show that the portfolios’ exposures to the aggregate idiosyncratic volatility risk predict the cross section of expected returns.

On asymptotically efficient simulation of large deviation probabilities

Let {νε, ε>0} be a family of probabilities for which the decay is governed by a large deviation principle, and consider the simulation of νε0(A) for some fixed measurable set A and some ε0>0. We investigate the circumstances under which an exponentially twisted importance sampling distribution yields an asymptotically efficient estimator. Varadhan's lemma yields necessary and sufficient conditions, and these are shown to improve on certain conditions of Sadowsky. This is illustrated by an example to which Sadowsky's conditions do not apply, yet for which an efficient twist exists.

On asymptotically efficient simulation of large deviation probabilities

Let {νε, ε>0} be a family of probabilities for which the decay is governed by a large deviation principle, and consider the simulation of νε0(A) for some fixed measurable setAand some ε0>0. We investigate the circumstances under which an exponentially twisted importance sampling distribution yields an asymptotically efficient estimator. Varadhan's lemma yields necessary and sufficient conditions, and these are shown to improve on certain conditions of Sadowsky. This is illustrated by an example to which Sadowsky's conditions do not apply, yet for which an efficient twist exists.

Principal Components Analysis of Cointegrated Time Series

This paper considers the analysis of cointegrated time series using principal components methods. These methods have the advantage of requiring neither the normalization imposed by the triangular error correction model nor the specification of a finite-order vector autoregression. An asymptotically efficient estimator of the cointegrating vectors is given, along with tests forcointegration and tests of certain linear restrictions on the cointegrating vectors. An illustrative application is provided.