TD_GOLDFELD_QUANDT is a statistical test to determine if the variance associated with a residual series is homoscedastic or heteroscedastic. It accepts a single input that consists of a SERIES_SPEC referencing a multivariate series containing original dependent and explanatory variables.
Heteroscedasticity means the variance of the residuals (errors) in a regression model is not constant across different values of the independent variable. This can lead to biased or inefficient parameter estimates.
The test involves dividing the data set into two subsets based on the values of the independent variable. Separate regression analyses are then conducted on each subset, and the residuals are calculated. The residuals are then squared to obtain the variances of the errors. The variances of the residuals from the two subsets are then compared using an F-test.
Assumptions about the distribution of residuals in the test are:
- Normality: The residuals are normally distributed. This assumption is because the F-test assumes normality of the residuals.
- Homoscedasticity: The variance of the residuals is constant across all levels of the independent variable. The distribution of the residuals around the regression line is the same for all values of the independent variable.
- Independence: The residuals are independent of each other, and there is no correlation between them. The residuals for one observation are not related to the residuals for another observation.
If these assumptions are not met, then the results of TD_GOLDFELD_QUANDT test may be unreliable in detecting heteroscedasticity. For example, if the residuals are not normally distributed, the F-test used may not be reliable. Similarly, if the assumption of homoscedasticity is wrong, then the test may not be effective in detecting heteroscedasticity. Evaluate these assumptions before using TD_GOLDFELD_QUANDT, and consider alternative tests or modeling approaches if the assumptions are not met.
If the F-test statistic is greater than the critical value at a given significance level, the null hypothesis of equal variance is rejected in favor of the alternative hypothesis of unequal variance. This indicates that the variance of the errors is not constant across different values of the independent variable, and that the regression model may not be appropriate for the data. If the null hypothesis is not rejected, then there is no evidence of heteroscedasticity in the regression model.