FRM Part I · FRM Exam Part I · Stationary Time Series
Consider the MA(1) process Y_t = e_t + 0.6 e_{t-1} with white noise e_t. What is the first-order autocorrelation of Y_t?
The first-order autocorrelation is 0.441. For an MA(1) it equals theta divided by one plus theta squared, so 0.6 divided by 1.36 gives about 0.441. It is not equal to theta itself.
- A0.600
- B0.441Correct
- C0.375
- D0.882
Explanation
rho_1 = theta/(1+theta^2) = 0.6/1.36 = 0.441. The value 0.600 mistakes theta itself for the autocorrelation. The value 0.375 uses 0.6/(1+0.6)^2... actually it divides by 1.6, forgetting to square theta. 0.882 doubles the correct value.
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