Adaptive quadrature for maximum likelihood estimation of a class of dynamic latent variable models

Maximum likelihood estimation of models based on continuous latent variables generally requires to solve integrals that are not analytically tractable. Numerical approximations represent a possible solution to this problem. We propose to use the adaptive Gaussian–Hermite (AGH) numerical quadrature approximation for a particular class of continuous latent variable models for time-series and longitudinal data. These dynamic models are based on time-varying latent variables that follow an autoregressive process of order 1, AR(1). Two examples are the stochastic volatility models for the analysis of financial time series and the limited dependent variable models for the analysis of panel data. A comparison between the performance of AGH methods and alternative approximation methods proposed in the literature is carried out by simulation. Empirical examples are also used to illustrate the proposed approach.