Can I use the Ljung-Box test on out-of-sample prediction errors?

Question

I know that tests like Ljung-Box and Breusch-Godfrey are often used to test the residuals of a fitted ARMA model for whiteness. But say I want to evaluate how well my model describes a new data set that is independent of the one used to fit the model. Is there any problem with just using the prediction errors from this data set as the "residuals" in the LB test?

My experiments suggest that this works well for the purposes of detecting anomalous data sets. The test statistic fits well with the chi-square distribution with L degrees of freedom, where L is the number of lags. But I haven't seen this method described anywhere, so I would like to know if it is OK to use.

If anyone can suggest relevant articles on the topic, that would be very helpful.

Answer 1

For the Ljung-Box test, the null hypothesis is:

$$H_0\colon \phi_1 = \phi_2 = ... = \phi_k = 0$$

where $\phi_k$ is the autocorrelation for the $k$-lag.

The alternative hypothesis is:

$$H_1\colon \text{at least one }\phi \neq 0.$$

So yes, you can use it to evaluate how well the model describes a new data set that is independent of the one used for fitting.