Urban travel demand: The impact of Box-Cox transformations with nonspherical residual errors

We develop an algorithm for solving regression models with Box-Cox transformations on both the dependent and independent variables, while simultaneously taking into account corrections for serial correlation of several orders and for heteroscedasticity. The latter correction is of a general form which contains as special cases most specifications of heteroscedasticity found in practice. We apply the procedure to three urban travel demand functions, two of which are currently used in their linear form by the Montreal Transit Authority, and analyze more than 100 specifications. Our results show that taking into account nonsphericalness of the residuals has a major impact on model parameter estimates, notably on those which determine the functional form of the model, and that, conversely, modifications of the functional form have strong implications for both the structure of autocorrelation and the importance of heteroscedasticity; moreover, we find interactions between autocorrelation and heteroscedasticity structures. We introduce a special measure of elasticity for variables which contain zero observations, particularly dummy variables. Moreover, we find that elasticities of demand and implicit values of time depend to a large extent on the stochastic specification of the model.