I am used to seeing Ljung-Box test used quite frequently for testing autocorrelation in raw data or in model residuals. I had nearly forgotten that there is another test for autocorrelation, namely, Breusch-Godfrey test. Question: what are the main differences and similarities of the Ljung-Box and the Breusch-Godfrey tests, and when should one be preferred over the other? (References are welcome. Somehow I was not able to find any comparisons of the two tests although I looked in a few textbooks and searched for material online. I was able to find the descriptions of each test separately, but what I am interested in is the comparison of the two.). The Breusch–Godfrey serial correlation LM test is a test for autocorrelation in the. In SAS, the GODFREY option of the MODEL statement in PROC AUTOREG. $ begingroup$ @Aksakal, Also, part of the problem might be that the focus is jumping a bit here and there. We should separate the issues of (1) which of the tests is better from (2) which test works under which assumptions, and importantly, (3) which test works for which model (due to different model assumptions). The latter is perhaps the most useful question for practitioners. For example, I would not use L-B for residuals of an ARMA model because of what Alecos has shown. Do you argue that L-B can still be used for residuals of ARMA models (which is now also the central question in the other thread)? $ endgroup$ – Apr 3 '16 at 20:04 •. $ begingroup$ The residuals are not independent but linearly restricted; first, they sum to zero; second, their autocorrelations are zero for the first $k$ lags. What I just wrote may not be exactly true, but the idea is there. Also, I have been aware that Ljung-Box test should not be applied for lag. Greene (Econometric Analysis, 7th Edition, p. 963, section 20.7.2): 'The essential difference between the Godfrey-Breusch [GB] and the Box-Pierce [BP] tests is the use of partial correlations (controlling for $X$ and the other variables) in the former and simple correlations in the latter. Under the null hypothesis, there is no autocorrelation in $e_t$, and no correlation between $x_t$ and $e_s$ in any event, so the two tests are asymptotically equivalent. On the other hand, because it does not condition on $x_t$, the [BP] test is less powerful than the [GB] test when the null hypothesis is false, as intuition might suggest.' (I know that the question asks about Ljung-Box and the above refers to Box-Pierce, but the former is a simple refinement of the latter and hence any comparison between GB and BP would also apply to a comparison between GB and LB.) As other answers have already explained in more rigorous fashion, Greene also suggests that there is nothing to gain (other than some computational efficiency perhaps) from using Ljung-Box versus Godfrey-Breusch but potentially much to lose (the validity of the test). The main difference between the tests is the following: • The Breusch-Godfrey test is as Lagrange Multiplier test derived from the (correctly specified) likelihood function (and thus from first principles). • The Ljung-Box test is based on second moments of the residuals of a stationary process (and thus of a comparatively more ad-hoc nature). The Breusch-Godfrey test is as Lagrange Multiplier test asymptotically equivalent to the uniformly most powerful test. Be that as it may, it is only asymptotically most powerful w.r.t. ![]() ![]() The alternative hypothesis of omitted regressors (irrespective of whether they are lagged variables or not). Gta vice city audio hardware files download. The strong point of the Ljung-Box test may be its power against a wide range of alternative hypotheses.
0 Comments
Leave a Reply. |