Hi, I need to simulate the real output from y_t= z_t k_t^alpha h_t^(1-alpha)
I already get alpha, and steady-state values of k, h, and y. I also get the persistence of the z_t (which follows ar(1) process). I have confusions at two points.

To simulate z_t by using ar(1) process, what is the initial value to plug in ar(1) process? is other variables also follow the same path as initializing zt?.

Once I have zt, then i need to simulate y_t, will i simulate y_t using the Cobb-Douglas production function? or just find the st deviation and persistence of detrending actual real GDP and add the generated normal distribution to ss values of calibrated y?. If we use the Cobb-Douglas production function to simulate yt, then how will I get the value of kt and ht?.
Thanks.

This sounds like you imagine the random variable z_{t} has some assumed law of motion like
\begin{align}
z_{t} = \bar{z} + \rho_{z}z_{t-1} + \epsilon_{z,t}
\end{align}
where z_{t} is an endogenous random variable, z_{t} is an exogenous random variable with some distribution, and \bar{z} and \rho_{z} are parameters.

Simulation of such a time series would require values for the parameters \bar{z} and \rho_{z} as well as a specification for the sequence of realizations \left\lbrace z_{t+n}\right\rbrace_{n=0}^{N} for some N.

You say in the subject line that this has something to do with an RBC model. The solution to DSGE models relate the values of endogenous variables to states and exogenous variables at any point in time. The law of motion for your endogenous variables - in non-monetary RBC frameworks this will typically be output, consumption, labor supply, investment, and capital along with driving processes like TFP and the relative price of investment - is characterized by the temporary equilibrium of your model, which is comprised of e.g. market clearing conditions and optimal decision making expressions of agents.

Technically, if you want to simulate the path of y_{t}=z_{t}k_{t}^{\alpha}h_{t}^{1-\alpha} you will need to provide a sequence of values for all variables on the right hand side. It seems you already have in mind some expression for the law of motion of z_{t}. But how have you pinned down \left\lbrace K_{t+n},h_{t+n}\right\rbrace_{n=0}^{N}?

Hi, thanks so much, Actually i could not pinned down K and h yet, that is part of the questions.
Actually mine is a monetary simple DSGE model with Cash in Advance constraint. After manual linearization, I get a seven variables model with 4 shocks, it is probably a VAR model, i saw other people do simulation by running VAR model, but I am not sure how the simulation really works. If you could explain, that would be really helpful.
One more question, by the way, if you do not mind, I am new to Dynare and installed it on computer, but could not find the icon on the desktop, how to install and use it? if you could help, it would be really appreciated.
Thanks.

I think you will benefit from taking some time to read through the well-written guides and tutorials produced by the Dynare team and available at https://www.dynare.org/resources/. In particular, have a look at the Tutorial which will walk you through the implementation of a simple RBC-type model with correlated shocks, as well as the Quick Start guide for getting started with the Dynare processor. It is not a standalone program; rather it is run within MATLAB.

One thing I am noticing from your phrasing and questions is that you seem to be unclear about what exactly you are trying to do. For example you keep using the word “simulation”, but I don’t think you are using it in the same way we typically would. In the context of a DSGE model we would usually think of a simulation as producing predictions for the evolution of endogenous variables based on some solution to the model itself.

Since you seem to be in the beginning stages of working with these types of models, it might be worth reviewing some of Eric Sims’ graduate macro theory notes, which are an excellent resource and easy to find from any online search engine.