Simulating an AR1 process

[eloualiche]

I am trying to understand how to simulate an AR1 process. I was having some issues with negative values even after taking exponentials.

I will try to reproduce this in a simple example below.

@model AR1 begin
    exp_z[0] = exp(z[0])
    z[0] = rho * z[-1] + std_z * eps_z[x]
end;

@parameters AR1 begin
    std_z = 0.01
    rho = 0.2
end;

simulation = simulate(AR1, periods=1000, algorithm=:third_order);
df_res = unstack(simulation |> DataFrame, :Periods, :Variables, :value)
@combine(df_res, :exp_z=mean(:exp_z), :z=mean(:z))

Both of the variables are set at zero (when we would expect exp_z to be at 1).

The counterpart in dynare would look like

var 
z exp_z junk;

varexo 
eps_z ;

parameters 
rho std_z ;
std_z   =   0.01;
rho =   0.2;

model;
    z(0) = rho * z(-1) + std_z * eps_z;
    exp_z(0) = exp(z(0));
    junk=0.9*junk(+1);
end;

shocks;
var eps_z   =   1;
end;

initval;
   z    =   0.0;
    exp_z = 1.0;
    junk = 0.0;
end;

stoch_simul(
    irf_shocks = (
        eps_z
    ),
    order = 3,
    irf = 0,
    noprint,
    periods = 1000,
    replic  = 1
)
  z exp_z;

and in matlab, looking at the simulation results gives:

mean(oo_.endo_simul,2)

ans =

    0.0001
    1.0001
         0

I am wondering if I am missing something about the log-linearization of the variables here?

[thorek1]

the standard behaviour of simulate is to return absolute deviations from steady state. if you want levels just do: simulate(AR1, levels = true, periods=1000, algorithm=:third_order). you can also plot the simulations: plot_simulations(AR1, algorithm = :third_order, periods=1000) in which case he automatically shows the level and percent deviations for strictly positive variables.

I guess you expected levels as output from simulate. I forgot why I made absolute deviations the default output of simulate. let me think about it again

[thorek1]

going through the code it seems there is no good reason to return absolute deviations by default. In the next release simulate will return levels by default

[eloualiche]

Thank you!