# Second moments vary between simulations

Dear all,
a happy and sucessful New Year to everyone. I am facing the following problem: I am conducting a stochastic simulation using the second order approximation (Schmitdt-Groehe Uribe). The second moments (sd., autocorrelations) and also the variables means differ a lot from simulation to simulation. Sometimes they are very close to the results from a first order approximation, but often they are really far away. How can I render my results more robust? Is increasing the number of periods the answer?
Best,
Ansgar

Hi Ansgar,

Yes the moments (second and first order) obtained with stochastic simulations may vary quite a lot from simulation to simulation.

To get a more robust evaluation of the moments, you may :

[1] Compute theoretical moments (but this would be meaning less for second order moments).

[2] Increase periods (the size of the simulated time series).

In some case the simulated time series and so the moments may diverge, and this can explain large deviations with respect to the moments associated to a first order approximation of the model. This is a well known issue (see the papers by Schmidt-Grohé and Uribe or Sims et al.). To overcome this difficulty you may reduce the size of the exogenous shocks or implement the prunning algorithm advocated by Sims.

Best,
Stéphane.

[quote=“Ansgar”]Dear all,
a happy and sucessful New Year to everyone. I am facing the following problem: I am conducting a stochastic simulation using the second order approximation (Schmitdt-Groehe Uribe). The second moments (sd., autocorrelations) and also the variables means differ a lot from simulation to simulation. Sometimes they are very close to the results from a first order approximation, but often they are really far away. How can I render my results more robust? Is increasing the number of periods the answer?
Best,
Ansgar[/quote]

Dear Stephane,
many thanks, I have now tested for a unit root in the observations I have generated and the unit root can not be rejected. So it seems that it was that. Many thanks!
Best,
Ansgar