In this paper we compute the asymptotic variance-covariance matrix of the method of moments estimators for the canonical Stochastic Volatility model. Our procedure is based on a linearization of the initial process via the log-squared transformation of Breidt and Carriquiry (Modelling and prediction, honoring Seymour Geisel. Springer, Berlin, 1996). Knowledge of the asymptotic variance-covariance matrix of the method of moments estimators offers a concrete possibility for the use of the classical testing procedures. The resulting asymptotic standard errors are then compared with those proposed in the literature applying different parameter estimates. Applications on simulated data support our results. Finally, we present empirical applications on the daily returns of Euro-US dollar and Yen-US dollar exchange rates.