Estimating And Testing the Parameters of a Generalization of the First Order Nonstationary Autoregressive Process.

Cover Estimating And Testing the Parameters of a Generalization of the First Order Nonstationary Autoregressive Process.
Estimating And Testing the Parameters of a Generalization of the First Order Nonstationary Autoregressive Process.
Downing, Darryl Jon, 1947-
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Now suppose t and t_ have a bivariate t-distribution with v degrees of freedom. Their joint density is given by fl . «. v _ T(h(v + 2)) III 2 77 r {hv) [1+ h Wj z U -u ; ] i-i 2 • 2 M 2 2 M 2 x ' ' v>0 , (4.3.30) where u, and y_ are the expected values of t and t~ respectively. Also I is the (2x2) variance-covariance matrix of (t , t ) . Relating this to a. and a we would replace (Vi-,y_) ^Y ( a i' a 2^ anc -* ^ wou ld be a diagonal matrix since we have shown the covariance of ex.. and a., to b
...e zero. With- out any loss of generality we may take \x =\i =0 and Z = I. The marginal density of t, is Hence the conditional density of t- given t, is f(t,,t 9 ) r( 1 -§(v+2)) u+t*] 3s(v+1) 1 : -co

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