Goldfeld's theorem

Goldfeld’s theorem deals with the behavior of certain statistical tests used to analyze financial data, specifically testing if errors from different models have similar variability. It states that if the errors in the data are normally distributed and independent, then a specific test called the Goldfeld-Quandt test will correctly identify differences in variance (spread or volatility) between datasets as the sample size grows large, maintaining its accuracy. Essentially, the theorem provides a mathematical assurance that, under ideal conditions, this test reliably detects changes in volatility in economic or financial data in the long run.