The Breusch-Godfrey test statistic follows a:[Fill in the blank]

Question

BlackTom AI · Accepted Answer

The Breusch-Godfrey test is a test for higher-order serial correlation in regression residuals. It converts the test into a statistic that, under the null hypothesis of no serial correlation up to the specified lag order, follows a chi-squared distribution asymptotically.
Option a: t distribution. This is incorrect because the test uses a likelihood-ratio–type statistic that aggregates information from multiple autocovariances; a single t distribution is not appropriate for testing serial correlation across several lags.
Option b: χ2 distribution. This is the correct characterization: the Breusch-Godfrey test statistic is asymptotically chi-squared distributed with degrees of freedom equal to the number of lagged terms tested (the number of restrictions).
Option c: Normal distribution. While the sampling distribution of many estimators under large samples is normal, the Breusch-Godfrey statistic specifically converges to a chi-squared distribution, not a standard normal, under the null.
Option d: F distribution. Some related tests (like the LM test variants) can be expressed with an F distribution in small samples or when certain conditions apply, but the classic Breusch-Godfrey statistic is chi-squared in large samples; treating it as F would be incorrect for the standard formulation.

The Breusch-Godfrey test statistic follows a:[Fill in the blank]

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