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I am writing a dissertation and for one part I want to validate an estimator I derived given different systems. In particular, the most basic system is a VAR(1) model: $$ X_t = AX_{t-1} + \epsilon_t $$

Where $\epsilon$ denotes white noise.

My question is, I want to test if my estimator works under non-linear transformations of this model. In particular I want to test a stable and an unstable coupling. I came up with the following: $$ X_t = Af(X_{t-1}) + \epsilon_t $$

Where in the stable case, $$ f(x) = \frac{1}{1+|x|} $$

and in the non-stable case, $$ f(x) = \frac{1}{x} $$

My question is thus, is this the normal way to transform a VAR model. Also, how can I verify whether the configuration of $A$ changes the stability / stationarity of the system?

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    $\begingroup$ The only stupid questions on this website are ones that don't demonstrate a sincere effort to understand or attempt their own problem. I don't see that here, so try give yourself a little credit. I say this as someone that often struggles to determine whether or not my own questions are "stupid" as well. $\endgroup$ Commented Jun 4 at 17:33

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