Match the following econometric tests with the issues they are designed to detect: Choose the correct option:

Solution

A. Durbin-Watson (DW) Statistics III. Autocorrelation Detection: The DW statistic is used specifically to detect the presence of first-order autocorrelation (serially correlated errors) in the residuals of a regression analysis. Mechanism: The value of the DW statistic ranges from 0 to 4. A value near 2 indicates no autocorrelation. Values approaching 0 indicate positive autocorrelation, while values approaching 4 indicate negative autocorrelation. B. Breusch-Pagan-Godfrey Test  IV. Heteroscedasticity Detection: This test checks for heteroscedasticity, which occurs when the variance of the error terms is not constant across observations. Mechanism: It regresses the squared residuals from the original model on the independent variables. If the resulting Chi-square test is significant, we reject the null hypothesis of homoscedasticity (constant variance). C. Variance Inflation Factor (VIF)  I. Multicollinearity Detection: VIF measures how much the variance of an estimated regression coefficient is "inflated" due to multicollinearity (correlation between independent variables). Mechanism: A VIF of 1 suggests no correlation. Generally, a VIF exceeding 5 or 10 indicates high multicollinearity, suggesting that the independent variables are too closely related to provide unique information to the model. D. Unit Root Test  II. Stationarity Detection: Tests like the Augmented Dickey-Fuller (ADF) or Phillips-Perron test check for a unit root to determine if a time series is stationary. Mechanism: If a series has a unit root, it is non-stationary (its mean and variance change over time). Stationarity is a critical requirement for most time-series modeling to avoid "spurious" or misleading regression results.