FRM Part I · FRM Exam Part I · Stationary Time Series
A stationary AR(1) process has phi = 0.7. Which set gives the theoretical autocorrelations at lags 1, 2 and 3 respectively?
The autocorrelations are 0.70, 0.49 and 0.343. In a stationary AR(1), the autocorrelation at lag k equals phi raised to the power k, so the ACF decays geometrically toward zero rather than cutting off abruptly.
- A0.70, 0.49, 0.343Correct
- B0.70, 0.70, 0.70
- C0.70, 0.14, 0.00
- D0.70, 0.49, 0.49
Explanation
For an AR(1), autocorrelation at lag k is phi^k: 0.7, 0.49, 0.343. The ACF decays geometrically, not cut off (that is MA behaviour; the PACF cuts off after lag 1 for AR(1)). Constant or truncated patterns are incorrect.
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