On the difference between parameter driven models and observation driven models Could I have an explanation on what are parameter driven models and what are observation driven models as categorized by Cox (1981) in Statistical analysis of time series: some recent developments with an example for each? 
 A: Koopman et al. (2015) includes the following:

Cox (1981) classiﬁes time-varying parameter models into two classes: observation-driven and parameter-driven speciﬁcations. In an observation-driven model, current parameters are deterministic functions of lagged dependent variables as well as contemporaneous and lagged exogenous variables. In this setting, parameters evolve randomly over time but are perfectly predictable one-step-ahead given past information. <...> In parameter-driven models, parameters vary over time as dynamic processes with idiosyncratic innovations. Special cases of this class are stochastic volatility models as discussed by Tauchen and Pitts (1983) and Ghysels, Harvey, and Renault (1996), the stochastic conditional duration model of Bauwens and Veredas (2004), and the stochastic copula models of Hafner and Manner (2011).

(Emphasis is mine.)
So my impression is that a key conceptual difference is whether the parameters are deterministic functions of observations (yielding observation-driven models) or not (yielding parameter-driven models).
Examples: 


*

*An example of an observation-driven model could be the standard GARCH model.  

*An example of a parameter-driven model could be the Beta-t-EGARCH model (Harvey & Chakravarty, 2008). 


More examples can be found in Davis & Rodriguez-Yam slides "Parameter- and Observation-Driven State Space Models".
References


*

*Davis, Richard A. and Gabriel Rodriguez-Yam. "Parameter- and Observation-Driven State Space Models" (undated slides).

*Harvey, Andrew C., and Tirthankar Chakravarty. Beta-t-(E)GARCH. University of Cambridge, Faculty of Economics, 2008.

*Koopman, Siem Jan, Andre Lucas, and Marcel Scharth. "Predicting time-varying parameters with parameter-driven and observation-driven models." Review of Economics and Statistics 00 (2015).

