Abstract
Moments of scale mixtures of skew normal distribution and their quadratic forms are derived using the simple stochastic relationship between skew normal distribution and scale mixtures of skew normal distribution. An application to time series is discussed. It is shown that the mean, covariance, and correlation structure of the sample autocovariance function for a particular class of time series depend on a measure of multivariate kurtosis, but not on a shape parameter. Unlike the multivariate normal distribution and the elliptical distributions with Muirhead kurtosis parameter 0, the covariance and the correlation of the sample autocovariance function for a particular class of time series with underlying scale mixtures of normal distribution are not always negative. We show this using an example of the generalized t distribution. As a by-product, we derived Muirhead kurtosis for some scale mixtures of normal distribution.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
