- #1

- 21

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## Main Question or Discussion Point

Hi,

I have the following equation

[tex]\gamma_0 = \phi^2 \gamma_0 + (1+\Theta^2)\sigma^2 + 2\Theta\phi\sigma^2[/tex]

The answer is

[tex]\gamma_0 = \frac{(1 + 2\Theta\phi+\Theta^2)}{1-\phi^2}[/tex]

I get how to factorize the numerator. I'm not sure of the denominator. It looks like a geometric series formula, but does this mean [tex]\gamma_0[/tex] = [tex](1+\Theta^2)\sigma^2 + 2\Theta\phi\sigma^2[/tex] ?

I have the following equation

[tex]\gamma_0 = \phi^2 \gamma_0 + (1+\Theta^2)\sigma^2 + 2\Theta\phi\sigma^2[/tex]

The answer is

[tex]\gamma_0 = \frac{(1 + 2\Theta\phi+\Theta^2)}{1-\phi^2}[/tex]

I get how to factorize the numerator. I'm not sure of the denominator. It looks like a geometric series formula, but does this mean [tex]\gamma_0[/tex] = [tex](1+\Theta^2)\sigma^2 + 2\Theta\phi\sigma^2[/tex] ?