FRM Part I · FRM Exam Part I · Regression Diagnostics
Residuals from a time-series regression have 50 observations. The sample first-order autocorrelation of the residuals is 0.30. Using the large-sample result that the standard error of a sample autocorrelation under the null of no autocorrelation is approximately 1/√T, what is the test statistic for H0: ρ1 = 0, and what is the conclusion at the 5% level (critical value 1.96)?
The test statistic is 2.12, found by dividing 0.30 by the standard error 1/√50 ≈ 0.1414. Since 2.12 exceeds the 5% critical value of 1.96, the null of zero first-order autocorrelation is rejected.
- Az = 2.12; reject H0Correct
- Bz = 1.50; fail to reject H0
- Cz = 2.12; fail to reject H0
- Dz = 0.30; fail to reject H0
Explanation
SE = 1/√50 = 0.1414. z = 0.30/0.1414 = 2.12, which exceeds 1.96, so reject H0. Using 1.50 would come from dividing by 0.20 incorrectly, and z = 0.30 ignores the standard error.
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