I know how to compute eigenvalues to test stability.
The question If i have for example a 10 node model with 5 lags, how do i choose stable parameters without just guessing.
You should first guess a candidate set of parameters. Then you should check for the dynamic stability condition to hold. If it holds with this candidate set, you can "choose" it. Otherwise, you should guess another candidate set and check for stability. You continue until you get an "stable candidate set".
The approach outlined by Carlos R. Barrera-Chaupis is of course what we all do some variant of.
Specifically, we choose a set of parameters, and then apply a scale factor to reduce them recursively till the model stabilizes.
I am actually asking is there a more principled way to think about this.
Well, as in many montecarlo simulations, we can just generate the coeficients randomly, for instance from a uniform distribution. Clearly, this is just a guess, but wee need an stable guess. So we repeat until we get one. Frankly, we can do other things to any guess, like detect and substitute the value of some outliers. Since this procedure requires robust scale factors and can be done individually or as a group, it will "reduce" the vectorial size of the parameter vector (ie., the guess). Of course, we can go further deep and discuss the statistical principles for doing any robust procedure, add some check for the invertibility degree behind the VAR vector of means to the stability check (which should link the guess to the "data generating process", DGP), add some other checks for the desiderability of stationary /non-stationarity of the DGP, etc. But we cannot avoid the guessing. I hope I have clarify the Ramesh's question a little bit for the benefit of the discussion he begun.
This is not a full answer as I don't know the system you are working on. However, most instabilities in covariance matrices (that are used for VaR) are due to data. The simplest and often best approach is to simply use a moving average on the data used for the covariance matrix, e.g., just 3 points in the moving average, could suffice. See:
R. Litterman and K. Winkelmann, ‘‘Estimating covariance matrices,’’ Report, Goldman Sachs, New York, 1998.
For an alternative approach, see
L. Laloux, P. Cizeau, J.-P. Bouchaud, and M. Potters, ‘‘Noise dressing of financial correlation matrices,’’ Phys. Rev. Lett. 83, 1467-1470 (1999).
Lester Ingber makes a good suggestion for stabilizing VAR models. (Derivatives can also work.). But I am really asking about a pure simulation where I postulate a VAR model from scratch.
I'm not sure about what you are asking, but "scaling" should not be an issue. Take a look at https://www.ingber.com/private/markets11_trd_report.pdf , where copula methods are addressed. You need not go through all these steps, but the point is that Eqs. (13)-(14) give a methodology to properly include "noise" from all sources. Only noise is considered in those Eqs., but the methodology has been carried through including time-dependent and nonlinear drifts and noise.
- Badges
- Science topic
- Similar topics
- Engineering
- Computer Engineering
- Computer