FRM Part I · FRM Exam Part I · Stationary Time Series
A covariance stationary AR(1) process is Y_t = 2 + 0.6·Y_(t-1) + ε_t, where ε_t is white noise with variance 1.28. What are the unconditional mean and unconditional variance of Y_t?
The mean is the intercept divided by one minus the AR coefficient: 2/0.4 = 5. The variance is the shock variance divided by one minus the squared coefficient: 1.28/0.64 = 2.00. So the mean is 5.0 and the variance is 2.00.
- AMean 5.0; variance 2.00Correct
- BMean 3.2; variance 2.00
- CMean 5.0; variance 3.20
- DMean 2.0; variance 1.28
Explanation
Mean = 2/(1-0.6) = 5.0. Variance = σ²/(1-φ²) = 1.28/(1-0.36) = 1.28/0.64 = 2.00. Option with variance 3.20 divides by (1-φ)=0.4, a wrong denominator, and option with mean 3.2 multiplies 2 by 1.6 instead of dividing by 0.4.
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