Sensitivity to Serial Dependency of Input Processes: A Robust Approach

We propose a distribution-free approach to assess the sensitivity of stochastic simulation withrespect to serial dependency in the input model, using a notion of “nonparametric derivatives”.Unlike classical derivative estimators that rely on parametric models and correlation parameters,our methodology uses Pearson’s φ-coefficient as a nonparametric measurement of dependency,and computes the sensitivity of the output with respect to an adversarial perturbation of thecoefficient. The construction of our estimators hinges on an optimization formulation over the in-put model distribution, with constraints on its dependency structure. When appropriatey scaledin terms of φ-coefficient, the optimal values of these optimization programs admit asymptoticexpansions that represent the worst-case infinitesimal change to the output among all admissibledirections of model movements. Our model-free sensitivity estimators are intuitive and readilycomputable: they take the form of an analysis-of-variance (ANOVA) type decomposition ona “symmetrization”, or “time-averaging”, of the underlying system of interest. They can beused to conveniently assess the impact of input serial dependency, without the need to build adependent model a priori, and work even if the input model is nonparametric. We report someencouraging numerical results in the contexts of queueing and financial risk management.