FRM Part I · FRM Exam Part I · Stationary Time Series
A stationary AR(1) process has a long-run mean of 4 and is given by y_t = 1.2 + phi y_{t-1} + e_t. What is the autocorrelation at lag 3?
The long-run mean of 4 equals 1.2 divided by (1 minus phi), so phi is 0.7. In an AR(1), the lag-k autocorrelation is phi to the power k, so lag 3 is 0.7 cubed, which equals 0.343.
- A0.343Correct
- B0.700
- C0.490
- D0.300
Explanation
The mean is c/(1-phi) = 4, so 1.2/(1-phi) = 4, giving 1-phi = 0.3 and phi = 0.7. The autocorrelation at lag k is phi^k, so lag 3 is 0.7^3 = 0.343. Using 0.7 is lag 1 and 0.49 is lag 2.
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