Dynare forums

Hello. Could you please advise any good books or papers regarding the following problems:
1) Is linearisation of initial system of equaions legitimate and to what end? I mean how close solution of the linearised system to the solution of initial system? What are necessary and sufficient conditions?
2) For example, I want to include stochastic trends which are represented as mix of random walk and deterministic trends. Is this legitimate and to what end? As far as I understand, standard procedures of computing solutions(e.g. Sims) imply that we are looking for stationary solution. But what if I include mentioned above trends? Now solution is no more stationary (am I right?). How to deal with this issue?
3) What conditions should data series satisfy?
Excuse me for my English.
Thank you in advance!
Best regards.

1) Please see Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December, https://ideas.repec.org/a/eee/dyncon/v30y2006i12p2477-2508.html
2) In this case, you need to detrend the equilibrium conditions. See e.g. Pfeifer(2013): "A Guide to Specifying Observation Equations for the Estimation of DSGE Models" https://sites.google.com/site/pfeiferecon/Pfeifer_2013_Observation_Equations.pdf for an example
3) The question is too unspecific, but part of the answer may be in 2)