FRM Part I · FRM Exam Part I · Stationary Time Series
A time series follows an MA(1) process y_t = 2 + e_t + 0.6 e_{t-1}, where e_t is white noise with variance 4. What is the unconditional mean of y_t?
The unconditional mean is 2.0. Because white noise shocks have zero expectation, the MA terms contribute nothing to the mean, so it equals the constant in the model. The MA coefficient affects the variance and autocorrelation, not the mean.
- A0.6
- B2.0Correct
- C2.6
- D1.2
Explanation
The expected value of each white noise term is zero, so E[y_t] = 2 + 0 + 0.6(0) = 2. The value 2.6 wrongly adds the MA coefficient to the constant, treating it as if it shifted the mean.
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