# DW and serial correlation

Dear Hubber, Refering to the question below I got " inconclusive" decision for DW . Hence, Holems and Briars are not correct. However, the answers is that " They need to analyze the residuals and compute autocorrelation coefficients of the residuals to better determine if serial correlation is a problem" Can someone shed some lights on why we perform the DW test; as here it gives the same conclusion Question ID#: 86428 -------------------------------------------------------------------------------- Clara Holmes, CFA, is attempting to model the importation of an herbal tea into the United States. She gathers 24 years of annual data, which is in millions of inflation-adjusted dollars. The real dollar value of the tea imports has grown steadily from \$30 million in the first year of the sample to \$54 million in the most recent year. She computes the following equation: (Tea Imports)t = 3.8836 + 0.9288 × (Tea Imports)t − 1 + et t-statistics (0.9328) (9.0025) R2 = 0.7942 Adj. R2 = 0.7844 SE = 3.0892 N = 23 Holmes and her colleague, John Briars, CFA, discuss the implication of the model and how they might improve it. Holmes is fairly satisfied with the results because, as she says “the model explains 78.44 percent of the variation in the dependent variable.” Briars says the model actually explains more than that. Briars asks about the Durbin-Watson statistic. Holmes said that she did not compute it, so Briars reruns the model and computes its value to be 2.1073. Briars says “now we know serial correlation is not a problem.” Holmes counters by saying “rerunning the model and computing the Durbin-Watson statistic was unnecessary because serial correlation is never a problem in this type of time-series model.” With respect to the statements made by Holmes and Briars concerning serial correlation and the importance of the Durbin-Watson statistic: A) Holmes was correct and Briars was incorrect. B) Briars was correct and Holmes was incorrect. C) they were both incorrect. -------------------------------------------------------------------------------- Click for Answer and Explanation Briars was incorrect because the DW statistic is not appropriate for testing serial correlation in an autoregressive model of this sort. Holmes was incorrect because serial correlation can certainly be a problem in such a model. They need to analyze the residuals and compute autocorrelation coefficients of the residuals to better determine if serial correlation is a problem. (Study Session 3, LOS 12.g)

It is a time series model. That is why it will have serial correlation and that is why DW test cannot be used over here. The question over here what we need to find out the serial correlation will effect our model or not. DW test is automatically performed in most statistical packages. That does not mean that it will give a good answer to whether serial correlation is present or not. For eg: You get a high correlation (R2) for a model in which two independent variables are correlated. This does not mean that the model is correct. You will not be able to base your answer just on the high correlation.