Using stochastic simulations

[PMaier]

Hi,

I would like to double-check that I am correctly using models in EViews. Suppose I have the following two equations....

y(t) = c(1) * y(t-1) + c(2)* x(t-1) +e1(1)
x(t) = c(5)*y(t-1) + c(6)* x(t-1) +e2(t)

... and I want to estimate them, and simulate possible outcome under all sorts of shocks hitting my system. The "build-in" approach in EViews would be:

1. Estimate the two equations, either equation-by-equation, or jointly in a system by OLS.
2. Build a model with these two equations (or system.makemodel(model))
3. Then, if I'm correct, a stochastic simulation (model.solve(s=b) would show me a 95% interval within which simulations fall (i.e. outcomes in which e1, e2 are drawn randomly in each period, and the outcome is calculated.

So if I wanted to perform a similar calculation manually, then an alternative way would be the following:
- Take a random draw for e1, e2 (uncorrelated) for each period of my simulation horizon;
- Set the add factors for the first and second equation identical to the random draws for e1, e2
- Simulate the model.

Is this correct?

So, to take this a step further, if it turns out that the two residuals are correlated, my stochastic simulation would not take this into account -- but I could account for that in my "manual" step-by-step procedure.... no?

Many thanks,

Philipp

[EViews Chris]

You are mostly right, but, by default, EViews models *do* take into account error covariance variance between equations in stochastic simulations.

There are several options you can set in the 'Innovation generation' section of the 'Stochastic Options' tab in the model solve dialog that will affect this.

To make the errors uncorrelated, you would need to check the box 'diagonal covarariance matrix - no cross equation corelation'. Otherwise, EViews will calculate the observed covariance between the errors and use this when generating errors during the stochastic simulation (by premultipying an independent set of random draws by a square root of the correlation matrix).