In Hamilton's text I ran across the following statement: if $X$ includes a constant then the linear projection of $aY+b$ is $aP(Y\mid X)+b$ where $P(Y\mid X)$ is the linear projection of $y$ on $x$. I’m having trouble proving this. Specifically this implies that if $X$ has a constant then $E(X’)E(XX’)X=I$ which I don’t see.

  • $\begingroup$ In Hamilton text? $\endgroup$ – StatsStudent Jan 10 at 16:23
  • 1
    $\begingroup$ James Hamilton Times series analysis $\endgroup$ – Alex Jan 10 at 16:24
  • $\begingroup$ Do you have a page number? $\endgroup$ – StatsStudent Jan 10 at 17:17
  • $\begingroup$ It’s the first section of chapter 4 discussing linear projection right before he talks about OLS estimate $\endgroup$ – Alex Jan 10 at 17:37
  • $\begingroup$ It’s page 75 of Hamilton $\endgroup$ – Alex Jan 10 at 18:11

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