What is the null hypothesis for Ljung-Box test?
The null hypothesis of the Box Ljung Test, H0, is that our model does not show lack of fit (or in simple terms—the model is just fine). The alternate hypothesis, Ha, is just that the model does show a lack of fit. A significant p-value in this test rejects the null hypothesis that the time series isn’t autocorrelated.
How does Ljung-Box test work?
Ljung and George E. P. Box) is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness at each distinct lag, it tests the “overall” randomness based on a number of lags, and is therefore a portmanteau test.
How many lags to use in the Ljung Box test of a time?
It has a parameter, h, which is the number of lags to be tested. Some texts recommend using h =20; others recommend using h =ln (n); most do not say what h to use. Rather than using a single value for h, suppose that I do the Ljung-Box test for all h <50, and then pick the h which gives the minimum p value.
When to use Breusch Godfrey instead of Ljung Box?
The thread “Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey” shows that the Ljung-Box test is essentially inapplicable in the case of an autoregressive model. It also shows that Breusch-Godfrey test should be used instead.
When to use BIC for lag order selection?
If you want to recover the true model (from a pool of candidate models that includes the true model), a sensible lag order selection criterion is BIC. Asymptotically it should select the true model with probability 1.
Which is the best criterion for lag order selection?
Model selection should depend on the intended use of the model. If you intend to do forecasting, a sensible lag order selection criterion is AIC. AIC tends to select the model (from the pool of candidate models) that yields the smallest squared forecast error 1 step ahead.