I am stuck on an AR (1) process spectral density question for a time series ( please see the image for the question and my answer). Would you please explain the next steps for solving this question?...

I am stuck on an AR (1) process spectral density question for a time series ( please see the image for the question and my answer). Would you please explain the next steps for solving this question?

Show that for an AR(1) process, X, = pX;-1 + et, with |p| < 1 the<br>spectral density is<br>g2<br>f(ω)<br>1+ ф2 — 2 сos(2по)<br>Xt = pxt-1 + e,<br>with ø| < 1<br>.2<br>|k|<br>Vk =<br>k = 0,±1,±2<br>X.<br>(1-ф2)<br>-ikw<br>f(ω)<br>1+<br>2п<br>Deika<br>k=1<br>i=1<br>

Extracted text: Show that for an AR(1) process, X, = pX;-1 + et, with |p| < 1="" the="" spectral="" density="" is="" g2="" f(ω)="" 1+="" ф2="" —="" 2="" сos(2по)="" xt="pxt-1" +="" e,="" with="" ø|="">< 1="" .2="" |k|="" vk="k" =="" 0,±1,±2="" x.="" (1-ф2)="" -ikw="" f(ω)="" 1+="" 2п="" deika="" k="1" i="">

Jun 11, 2022

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I am stuck on an AR (1) process spectral density question for a time series ( please see the image for the question and my answer). Would you please explain the next steps for solving this question?...

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