On High-Dimensional, Non-Linear, Non-Gaussian Continuous-Time Likelihood Evaluation

Tired of trying to beat the particle filter into submission?  Life has gotten a lot easier, at least for evaluating DSGE model likelihoods in continuous time.  See the concluding section of the new and insightful survey, "Estimating DSGE Models: Recent Advances and Future Challenges" by Fernández-Villaverde and Guerrón-Quintana, which echoes section 5.1 of  "Financial Frictions and the Wealth Distribution", by Fernández-Villaverde, Hurtado and Nuño (FVHN).  FVHN show how to take advantage of the mathematical structure of a continuous-time DSGE model to evaluate its associated likelihood with almost no computational effort.  In particular, solution of the Kolmogorov forward equation (the key to likelihood evaluation; see Lo (1987)) simply amounts to transposing and inverting a sparse matrix already computed when solving the model, which makes likelihood evaluation trivial and lightening-fast.