Solving VAR Model - Innovation Generation Option

[gopvan]

Hi, I trying to understand the simulation options. I am using Eviews Version 7.2.

Example: Let's say I have data for 4 variables- X1, X2, X3, X4 for the period 2000m01 to 2014m08. VAR model looks like;

LOG(X1) = C(1,1)*LOG(X1(-1)) + C(1,2)*LOG(X2(-1)) + C(1,3)*LOG(X3(-1)) + C(1,4)*LOG(X4(-1)) + C(1,5)

LOG(X2) = C(2,1)*LOG(X1(-1)) + C(2,2)*LOG(X2(-1)) + C(2,3)*LOG(X3(-1)) + C(2,4)*LOG(X4(-1)) + C(2,5)

LOG(X3) = C(3,1)*LOG(X1(-1)) + C(3,2)*LOG(X2(-1)) + C(3,3)*LOG(X3(-1)) + C(3,4)*LOG(X4(-1)) + C(3,5)

LOG(X4) = C(4,1)*LOG(X1(-1)) + C(4,2)*LOG(X2(-1)) + C(4,3)*LOG(X3(-1)) + C(4,4)*LOG(X4(-1)) + C(4,5)

Estimation sample: 2000m01 to 2014m02
Solution sample: 2014m03 to 2014m08

For each equation, say
LOG(X1) = C(1,1)*LOG(X1(-1)) + C(1,2)*LOG(X2(-1)) + C(1,3)*LOG(X3(-1)) + C(1,4)*LOG(X4(-1)) + C(1,5) + Epsilon

Normal Random Numbers
In Stochastic option under Innovation generation if Normal Random Numbers are chosen, random numbers are generated for each time period in the solution sample(every month for 6 months). Using these as values for Epsilon and Coefficients obtained upon estimation of the VAR model, the model is solved. Is this correct ?

Bootstrap
On the other hand if Bootstrap option is chosen, residuals obtained upon estimation of the VAR model (4 residual series, one for each equation) are re-sampled. Using these re-sample residuals for Epsilon and Coefficients obtained upon estimation of the VAR model, the model is solved. Is this correct ?

Baseline mean
If the Repetition is set to 1000, then for each variable, 1000 sets of 6 values (one for each time period in the solution sample) i.e. 6000 values are forecast. The mean of 1000 forecasts for each time period gives the baseline mean, therefore arriving at 6 mean values. Is this correct ?

Stochastic Components
Are the residuals and coefficients the only 2 components that are varied under stochastic simulation ? With residual variation being default and coefficient variation being optional ?

Bootstrapping Sample
Assuming this is how stochastic simulation works, if I would like to repeat this for different samples, should I simply a) re-sample b)estimate c)solve the VAR model within a FOR loop ? Are there any other elegant methods to bootstrap samples ?

Any help is much appreciated. Thank You.

[EViews Chris]

Lots of statements in your post, which I think basically all sound correct. Here are some comments:

Normal Random Numbers: Yes. We draw normally distributed random numbers for the epsilons with a distribution that matches the covariance of the observed pre-forecast residuals (or the covariance observed within a specific sample if one is specified). The coefficients will be set to the coefficient point estimates from the VAR unless you check 'include coefficient uncertainty' in which case the coefficients will be randomly drawn from a normal distribution matching the covariance of the coefficient estimates.

Boostrap: Yes. We randomly draw from the set of observed pre-forecast residuals (or some other specified sample if a 'bootstrap residual draw sample' is specified).

Baseline mean: Yes. For each repeitition we generate the paths of each variable of the model conditional on the random draws of the residuals and (optionally) the coefficients within that repetition. We then calculate the mean for these paths over all repetitions.

Stochastic Components: Yes. Only the residuals and coefficients are randomly varied during the stochastic simulation.

Bootstrapping Sample: Not quite sure what you're getting at here. it is true that there is no built in procedure to vary the solution sample or bootstrap sample or to re-estimate the VAR itself within a single 'solve' command.

[gopvan]

Hi Chris - Thank you very very much.

What I mean by bootstrapping samples is, I would like to estimate and solve the model for different estimation samples.

In the example the estimation sample is 2000m01 to 20014m02 which is the sample used to run the coefficient estimates. After which I solve the model using stochastic and dynamic options, varying the error term.

Now, could I repeat this for different sets of samples by re-sampling the original data set - 2000m01 to 20014m02 (i.e picking samples from within my sample) to arrive at several sets of samples of size N and run VAR model on each one of these samples.

Also, would this exercise amount to be the same as choosing "coefficient uncertainty" along with "bootstrap innovation generation" as each sample probably generates different set of estimates and residuals and this is what essentially the above stochastic options do.

Any thoughts on this would be helpful. Thank you in Advance.