Parameter Estimation Using Surrogates with Applications to Stable Distributions

In this article, we present an empirical-based parameter estimation method called Search via Simulation. Using a hierarchical simulation procedure, surrogate data is propagated and selected based on its ability to mimic the inherent behavior of the observed data via the Kolmogorov-Smirnov distance. This method can be easily applied to probability distributions that do not have a density, distribution or characteristic function in closed form. We define strong Kolmogorov-Smirnov continuity for the assumed parameter estimator. The performance of this method is compared to established estimation methods using a simulation study which includes an execution on stable distributions. We also demonstrate the comparative performance of the Search via Simulation method in fitting stable distributions to CRSP excess returns data typically characterized by heavy tails. This research opens a new global and effective simulation-based inference approach to parameter estimation in accordance with current advances in data science and computational technology.