Unbiased Adaptive LASSO Parameter Estimation for Diffusion Processes

Abstract

The adaptive Least Absolute Shrinkage and Selection Operator (aLASSO) method is an algorithm for simultaneous model selection and parameter estimation with oracle properties. In this work we derive an adaptive LASSO type estimator for diffusion driven stochastic differential equation under weak conditions, specifically that the algorithm does not rely on high frequency properties.All conditional moments needed in our quasi likelihood function are computed from the Kolmogorov Backward equation. This means that a single equation is solved numerically, regardless of the number of observations. The LASSO problem is solved using the Alternating Direction Method of Multipliers (ADMM) method.Our simulations show that the resulting algorithm is able to find the correct model with high probability while obtaining unbiased parameter estimates when evaluated on two qualitatively different data sets.