A stochastic variance model may be estimated by quasi-maximum likelihood procedure by transforming to a linear state space form. The properties of observations corrected for heteroscedasticity can be derived. A model with explanatory variables can be handled by correcting the observations for heteroscedasticity after estimating a stochastic variance model from the OLS residuals and then constructing a feasible GLS estimator. A model with stochastic variance, or standard deviation, as an explanatory variable can also be formulated. The paper explores the properties of these procedures and shows how they may be used as part of a model specification strategy/ It is argued that the approach is relatively robust since distributions need not be specified for the disturbances.