Autocorrelation tests (Part 2): Breusch-Godfrey LM test (Excel) 

How can one interpret p- value of 48% in Breuch-Godfrey LM (Lagrange multiplier) test.

@@vaibhavbadgi5752 Hi Vaibhav, and thanks for the question! The interpretation could be the following: as p-value is higher than 10%, there is no significant dependence in the model residuals, hence no autocorrelation, and the model is properly specified in this regard. Hope it helps!

Glad you liked the video :)

Hi again and thanks for the feedback! As for the question: yes, Breusch is the same person indeed, he developed an autocorrelation test with Godfrey (Breusch-Godfrey LM test), and a heteroskedasticity test with Pagan (Breusch-Pagan). We have got a video on Breuch-Pagan as well: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-p2TmKdbn5Uk.html Regarding White test, we also have got a video on this: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-c-VGDK8xvz8.html Breuch-Pagan-White can sometimes be mentioned jointly as the logic of the two tests is ultimately similar - to apply auxiliary regressions to determine whether there is heteroskedasticity in the data. White differs from Breuch-Pagan slightly as it includes more regressors. Hope it helps!

Hi Igor, and thanks for the excellent questions! 1. Yes, serial correlation and autocorrelation are most often interchangeable terms. 2. If you found the current model suffers from autocorrelation, you can apply the model to the first differences or rates of change of the dependent variable instead of its levels, include lags of the dependent variable as additional regressors, or use HAC standard errors (the latter is however only implementable if you use the matrix method to do regressions).

@@NEDLeducation thanks so much for your answers, however when I wacthed your videos I was kind of confuse a bit cause I always run the data using regression analysis, and when I saw you run each one of them using just excel, I was kind of confuse a bit, can I use HAC standard errors in just regression analysis terms?

Hi Thien, and thanks for the comment, glad you are enjoying the videos! As for your questions: 1) The tests in this video are all addressing the issue of autocorrelation, for heteroskedasticity, please have a look further into the econometrics playlist, for example here is a tutorial on Breusch-Pagan test for heteroskedasticity: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-p2TmKdbn5Uk.html and on the ARCH test: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Fl7k4pynuN0.html that opens up the realm of ARCH/GARCH volatility modelling. 2) The choice of three degrees of freedom is simply due to us having three lags. Hope this helps!

@@NEDLeducation thank you so much, sir! I'm really grateful!!

Hi Raffaele, and glad you liked the video! To omit independent variables from the estimations, you can simply calculate the residuals as demeaned dependent variable (here - demeaned Tesla returns), and apply the test to lagged residuals. Hope this helps!

Hi Mot, many thanks for your feedback and for the question! Overall, not really, the only circumstance where there might be significant autocorrelation at some lags but none as shown by F-stat or Chi-squared stat is when you include too many lags and only some of these are meaningful. To double-check, you could look at t-stats for individual autoregressive coefficients. If none of them are high, it can be used as additional evidence against the presence of autocorrelation. Hope it helps!

Hi and thanks for the comment! Glad to hear you are implementing your own Python code based on the tutorial! The reason for the discrepancy could be the lagged residuals. Here, I assume lagged residuals for the missing values are zeroes, Python most likely drops them by default. Hope it helps!

@@NEDLeducation Hi Савва, thank you for your reply. Actually, no, I've replaced all nan values with 0. The interesting part is that Durbin-Watson test showed that same results as in your video. But B-G LP test has this problem

Hi Antonio, and glad you liked the video! As for your question, if I recall correctly, your data is cross-sectional (so one measurement at some point in time for a number of sites). Here, autocorrelation is not an issue (it is conventional to test for autocorrelation in time series data, in your example that would be measuring pollution at one source every single day). While it would be not theoretically incorrect to apply autocorrelation tests here, it has little interpretative value. You might check for heteroskedasticity instead if you worry about assumption violation as is is more of a concern for cross-sectional data. I have got a series of videos on that, so check this out if you are interested: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-p2TmKdbn5Uk.html Hope it helps!

@@NEDLeducation understood, thank you very much!

@@NEDLeducation do u have any publications in the scope of linear regression modelling? i would like to cite you! Regards