Appendix BMoments of Ratios of Quadratic Forms
Appendix A presented methods for the calculation of the density and cumulative distribution function of (ratios of) quadratic forms. This appendix considers their moments and some applications.
Relatively straightforward expressions are available for the mean and variance of a quadratic form in normal variables, and also for higher moments via recursion (A.12) in the special case with 
. Matters are not as nice when working with ratios of such forms, but results are available. Unsurprisingly, these increase in complexity as we move from 
to 
. We consider these in turn. Throughout, let 
.
Note: In an effort to use interesting, illustrative examples throughout this appendix, some basic notions of the linear regression, AR(1), and ARX(1) models, as developed in Chapters 1 4, and 5, respectively, are required.
B.1 For 
and 
First note that can be ...
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