Abstract
In this paper we develop a statistic test in order to compare two discrete stochastic dynamical systems with autoregressive structures under heteroskedasticity, more specifically the variance of the errors follows a general function depending on time. The random disturbances or errors can also be contemporaneously correlated through some structure varying in time. The approach is based on a Wald test and we present three consistent estimates for the asymptotic covariance matrix. The study of the asymptotic properties is based on the Lp-mixingale processes theory since we consider errors generated from martingale difference processes. In order to evaluate the performance of the test in finite samples, we ran some simulations with satisfactory results. A real application is also provided.
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