TD_WHITES_GENERAL checks is a statistical test that checks for the presence of homoscedastic or heteroscedastic variance among the residual terms after running a regression. Homoscedastic and heteroscedasticity are the variability of the error term. For example, heteroscedasticity is when the difference between observed values and predicted values is not constant across all levels of the independent variables. The variance of the error term is different for different levels of the variables.
If heteroscedasticity is present in the data, then an ordinary least squares (OLS) estimator can provide unbiased estimates of the regression coefficients but it can lead to inefficient estimates. The estimated standard errors of the coefficients are biased and can underestimate the true standard errors. As a result, the hypothesis tests may be unreliable and can lead to incorrect conclusions about the significance of the coefficients.
While heteroscedasticity can lead to biased and inefficient estimates, it is not a major concern for OLS. For example, when the variations in the error variance are small, the OLS estimator can still be unbiased and efficient. If the sample sizes are large, the OLS estimator is more robust to heteroscedasticity or the estimates are used for prediction, not inference.
TD_WHITES_GENERAL estimates the residuals of a regression model, and then regresses the squared residuals on the independent variables and their squares. The null hypothesis of the test indicates the variance of the errors is constant across all observations. If the test statistic is large enough, indicating that the null hypothesis can be rejected, then it suggests that there is heteroscedasticity present in the model. The function can also test for the presence of other forms of model misspecification, such as omitted variables or functional form misspecification.
The function does not require reordering of the series like the Goldfeld-Quandt test, and is not sensitive to the normal distribution assumption like the Breusch-Pagan-Godfrey test.
- Use TD_MULTIVAR_REGR with RESIDUALS(1) to perform a fit operation and generate an ART with a ARTFITRESIDUALS layer.
- Extract the residuals into an ART using TD_EXTRACT_RESULTS.
- Use TD_WHITES_GENERAL on the ART containing the TD_MULTIVAR_REGR residuals.
- Retrieve the TD_WHITES_GENERAL results from the primary layer to determine if the variance is homoscedastic or heteroscedastic.ACCEPT means apparent homoscedastic variance. REJECT means heteroscedastic variance.