Observation-driven filtering of time-varying parameters using moment conditions

We develop a new and flexible semi-parametric approach for time-varying parameter models when the true dynamics are unknown. The time-varying parameters are estimated using a recursive updating scheme that is driven by the influence function of a conditional moments-based criterion. We show that the updates ensure local improvements of the conditional criterion function in expectation. The dynamics are observation driven, which yields a computationally efficient methodology that does not require advanced simulation techniques for estimation. We illustrate the new approach using both simulated and real empirical data and derive new, robust filters for time-varying scales based on characteristic functions.