We present a procedure for testing the goodness-of-fit of the conditional variance function of a Markov model of order 1, under stationarity and ergodicity. The autoregressive parameter, the distribution of the noise and the stationary distribution of the observations are assumed to be unknown. Under the null hypothesis H 0 that the conditional variance function belongs to a class of parametric functions, we define an estimator \tilde\theta_n of θ0 , the assumed true parameter, and we establish its consistency and asymptotic normality. We define a marked empirical process A n (·), for which we state and prove a functional limit theorem under H 0 . The asymptotic behavior of this process is studied under fixed alternatives H 1 . Based on the process A n (·), a chi-squared test is derived. Simulation experiments show that the test is powerful against some heteroscedastic time series models.