Is there a difference between recursive parameter estimates and time-varying parameters? As the title indicates, is there a difference between recursive parameter estimates and time-varying parameters. I ask this in the context of time-series.
For example, recursive parameter estimates can be obtained by, say, taking a linear regression model, estimating the model on an extending sample period, and recording how the parameter estimates evolve as the sample period extends. This can be used, for example, to identify parameter instability.
Time-varying parameters, on the other hand, tend to be unobserved states in the context of dynamic linear regression models (or state-space models). These are not necessarily the same as recursive coefficients because the transition equations associated with the unobserved components that represent parameters (as opposed to unobserved variables like trend or cycle) may contain non-zero transition equation errors. 
Is it true that in the context of state-space models, a state variable that represents a parameter (not an unobserved variable like trend or cycle) is a equivalent to a recursive parameter when the corresponding transition equation error is zero?
Confirmation on this issue would be most welcome! If it's unclear, I can perhaps return and write out the necessary equations. 
 A: 
Is it true that in the context of state-space models, a state variable
  that represents a parameter (not an unobserved variable like trend or
  cycle) is a equivalent to a recursive parameter when the corresponding
  transition equation error is zero?

Yes, the Kalman filter simplifies to regular recursive least squares in the case where state transitions are trivial and noiseless.

These are not necessarily the same as recursive coefficients because
  the transition equations associated with the unobserved components
  that represent parameters (as opposed to unobserved variables like
  trend or cycle) may contain non-zero transition equation errors.These are not necessarily the same as recursive coefficients because the transition equations associated with the unobserved components that represent parameters (as opposed to unobserved variables like trend or cycle) may contain non-zero transition equation errors. 

Yes, I like to classify models according to this criterion as well. 
A: Time-varying parameters are generally parameters that evolve through time. From a system identification point of view there are various ways to track such parameters but essentially there are 2 main approaches. The piecewise stationary and the recursive approach. The piecewise stationary is based on the idea that the parameters remain constant for a limited period and thus we can use classical LS estimation on windows of a predefined length.The recursive approaches, like RLS and Kalman Filter, update the parameter estimates at each time step. Thus i am not really sure why you make the differentiation between time-varying parameters and recursive estimates. TV parameters is just a description and recursive estimates is just the approach you use to estimate the parameter variations. I am not an expert on state space models but in your last question are you referring to the Kalman Filter? Because if you assume that your state vector is your model parameters and the transition matrix is the identity matrix then you can get the Kalman Filter adaptation algorithm for recursive parameter estimation: https://www.mathworks.com/help/ident/ug/recursive-algorithms-for-online-estimation.html#buagqe2-1
