A new skew-normal model for the application-oriented skew-t model

Among many papers of Professor Clive W. J. Granger, the one that strongly draws my attention is his work [7] using the skew-t model to analyze common factors in conditional distributions for bivariate time series. Different from many existing versions of theory-oriented skew-t models, the skew-t model that Professor Granger and his collaborators used was directly motivated by applications in analyzing economics data. This application-oriented skew-t model has discernible features on enabling model flexibility and keeping the practical standardizing conditions [10]. On the other hand, the skew-t model is in need of a proper statistical justification to solidify its theoretical foundation. In this paper, we initiate a new skew normal family that enhances the skew-t model in [10] and [7]. 2000 Mathematics Subject Classifications: 62E15, 62P20