FRM Part I · FRM Exam Part I · Stationary Time Series
For the MA(1) process y_t = e_t + 0.5 e_{t-1}, with e_t white noise of variance 9, what is the variance of y_t?
The variance is 11.25. For an MA(1) process the variance equals the shock variance times one plus the squared coefficient, so 9 times 1.25 gives 11.25. Forgetting to square the coefficient would give 13.5, which is incorrect.
- A9.00
- B11.25Correct
- C13.50
- D14.50
Explanation
Var(y_t) = sigma^2(1 + theta^2) = 9(1 + 0.25) = 11.25. Using 9(1+0.5)=13.5 forgets to square theta.
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