FRM Part I · FRM Exam Part I · Stationary Time Series
A stationary AR(1) process has coefficient phi = 0.8 and white-noise innovation variance sigma^2 = 9. What is the unconditional variance of the process?
The unconditional variance is 25. For a stationary AR(1), variance equals the innovation variance divided by one minus phi squared, so 9 divided by 0.36 equals 25. Forgetting to square the coefficient gives wrong values.
- A25.00
- B11.25
- C14.06Correct
- D45.00
Explanation
Variance = sigma^2/(1 - phi^2) = 9/(1 - 0.64) = 9/0.36 = 25.00. Check: 0.64*25 + 9 = 25. Option 11.25 uses 9/(1-0.8)... actually 9/0.8 = 11.25, which forgets to square phi. Option 45 is 9/0.2, using 1-phi.
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