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A New Skew-normal Model for the Application-oriented Skew-t Model

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Abstract (2. Language): 
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].



[1] J Chen and A Gupta. Matrix variate skew normal distributions. Statistics, 39(3):247–
253, 2005.
[2] J Chen, A Gupta, and T Nguyen. The density of the skew normal sample mean and its
applications. Journal of Statistical Computation and Simulation, 74(7):487–494, 2004.
[3] J Chen, A Gupta, and C Troskie. Distribution of stock returns when the market is up
(down). Communications in Statistics, 32:1541–1558, 2003.
[4] R Engle. Autoregressive conditional heteroscedasticity with estimates of the variance of
UK inflation. Econometrica, 50:987–1007, 1982.
[5] C Fernandez and M Steel. Multivariate student-t regression models: Pitfalls and inference.
Biometrika, 86:153–167, 1999.
[6] C Granger. Implications of aggregation with common factors. Economic Theory, 3:208–
222, 1987.
[7] C Granger, T Terasvirta, and A Patton. Common factors in conditional distributions for
bivariate time series. Journal of Econometrics, 132:43–57, 2006.
[8] A Gupta and J Chen. Goodness of fit test for the skew-normal distribution. Communica-
tion in Statistics, 30(4):907–930, 2001.
[9] A Gupta and J Chen. A class of multivariate skew-normal models. The Annals of the
Institute of Statistical Mathematics, 56(2):305–315, 2004.
[10] B Hansen. Autoregressive conditional density estimation. International Economic Review,
35:705–730, 1994.
[11] T Nguyen, J Chen, A Gupta, and K Dinh. A proof of the conjecture on positive skewness
of generalized inverse gaussian distributions. Biometrika, 90:245–250, 2003.
[12] J Stock and M Watson. New indexes of coincident and leading economic indicators.
NBER Macroeconomics Annual, 4, 1989.

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