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I am having trouble having to explain what the asterisks signify after equation 8? The pdf of the paper is downloaded below, please anyone's help is appreciated

It says equation 8 is transition equation, more specifically equation 8 is in VAR(1) form. In contrast, equation 5 and 6 are AR(p) and VAR(k) respectively. In order to estimate unobservable variable C(t) and u(t), we need transform equation 5 and 6 into VAR(1) form. Otherwise we can't use Kalman fi...

I am currently reading the Stock and Watson Methodology for Businesses Cycle indexes, specifically the coincident index. After reading most of their previous work on this study, I can't figure out what the asterisks signify once they introduced the transition equation (pg.7). I know they show what s...