We propose a new method for estimating time-varying parameters in linear and non-linear econometric models called the Generalized Autoregressive Method of Moments (GAMM). GAMM extends the Generalized Method of Moments (GMM) for estimating models where a subset of the parameters are expected to vary over time with autoregressive-moving average type dynamics. The driving mechanism of the time-varying parameter is the scaled conditional moment condition. This approach provides a unified framework for estimating time-varying parameters with autoregressive dynamics by the method of moments. When the conditional moments are the scores of a fully parametric model, the GAMM methodology reduces to the generalized autoregressive score (GAS) methodology recently proposed in the literature. GAMM therefore generalizes GAS models to a semi-parametric setting. We study the properties of GAMM and provide several applications in finance and macroeconomics. Joint with Drew Creal, Siem Jan Koopman, and Andre Lucas.

Keywords: dynamic models, time-varying parameters, generalized method of moments, non-linearity.