Testing for Heteroskedastic Mixture of Ordinary Least Squares Errors

There is no procedure available in the existing literature to test for heteroskedastic mixture of distributions of residuals drawn from ordinary least squares regressions. This is the first paper that designs a simple test procedure for detecting heteroskedastic mixture of ordinary least squares residuals. The assumption that residuals must be drawn from a homoscedastic mixture of distributions is tested in addition to detecting heteroskedasticity. The test procedure has been designed to account for mixture of distributions properties of the regression residuals when the regressor is drawn with reference to an active market. To retain efficiency of the test, an unbiased maximum likelihood estimator for the true (population) variance was drawn from a log-normal normal family. The results show that there are significant disagreements between the heteroskedasticity detection results of the two auxiliary regression models due to the effect of heteroskedastic mixture of residual distributions. Forecasting exercise shows that there is a significant difference between the two auxiliary regression models in market level regressions than non-market level regressions that supports the new model proposed. Monte Carlo simulation results show significant improvements in the model performance for finite samples with less size distortion. The findings of this study encourage future scholars explore possibility of testing heteroskedastic mixture effect of residuals drawn from multiple regressions and test heteroskedastic mixture in other developed and emerging markets under different market conditions (e.g. crisis) to see the generalisatbility of the model. It also encourages developing other types of tests such as F-test that also suits data generating process. Practitioners could minimize the risk of misrepresentation in advisory work by qualifying and disclaiming for possible pricing errors in cost of capital computations and valuations based on detection test results. Findings of this paper encourage stock exchanges and governments to effectively promote firm-specific trading by, for example, timely discloser of corporate announcements and investor education programs, to improve functional efficiency of stock markets.