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APPROXIMATE AND GENERALIZED CONFIDENCE BANDS FOR SOME PARAMETRIC FUNCTIONS OF THE LOGNORMAL DIFFUSION PROCESS WITH EXOGENOUS FACTORS

Approximate and generalized confidence bands for some parametric functions of the univariate lognormal diffusion process with exogenous factors are obtained. The procedures to obtain these bands are developed from the suitable adaptation of the available methods for building confidence intervals for the mean of the lognormal distribution. The obtained bands are similar to those calculated for the homogeneous lognormal diffusion process but, in this case it is not possible a general comparative study in terms of coverage errors, by means of simulation studies, because of the dependence on the exogenous factors of each particular model. Therefore, in each case a particular study is necessary. In this sense, in this paper two models are considered modelling the gross national product of Spain and the global manmade methane emissions, respectively.