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FRM Part I · FRM Exam Part I · Stationary Time Series

For the MA(1) process y_t = e_t + 0.8 e_{t-1}, what is the first-order autocorrelation of y_t, and what is the autocorrelation at lag 2?

The lag-1 autocorrelation is 0.488 and the lag-2 autocorrelation is zero. The first is theta divided by one plus theta squared, 0.8 over 1.64. An MA(1) process has autocorrelations that cut off to zero after lag 1.

  1. A0.488 at lag 1 and 0.488 at lag 2
  2. B0.800 at lag 1 and 0.640 at lag 2
  3. C0.488 at lag 1 and 0 at lag 2Correct
  4. D0.800 at lag 1 and 0 at lag 2

Explanation

Lag-1 autocorrelation is theta/(1+theta^2) = 0.8/1.64 = 0.488. An MA(1) has zero autocorrelation beyond lag 1, so lag 2 is 0. Using 0.8 directly ignores the denominator.

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