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

An analyst fits a model to 400 daily residuals that are supposed to be white noise. The sample autocorrelation at lag 1 is 0.12. Using the large-sample approximation that, under white noise, the sample autocorrelation has standard error 1/√T, which conclusion is correct at roughly the 95% level (critical value 1.96)?

Reject white noise. With 400 observations the standard error of a sample autocorrelation is 1/√400 = 0.05, so the 95% band is ±0.098. The observed lag-1 autocorrelation of 0.12 lies outside this band, indicating significant serial correlation.

  1. AReject white noise, because 0.12 exceeds 1.96 × 0.05 = 0.098Correct
  2. BDo not reject white noise, because 0.12 is below 1.96 × 0.05 = 0.098
  3. CReject white noise, because 0.12 exceeds 1.96 × 0.0025
  4. DDo not reject white noise, because the standard error is 0.12

Explanation

SE = 1/√400 = 0.05. The 95% band is ±1.96 × 0.05 = ±0.098. Since 0.12 > 0.098, the lag-1 autocorrelation is significant and white noise is rejected. Option B misstates the comparison.

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