I am modeling a time series data using ARIMA with regressors for monthly and weekly seasonality (Fourier term approach is very slow). I am using Hyndman's forecast package for modeling the data. My question has to do with the test for white noise. I have tried two different tests to check if residuals have been reduced to white noise. The tests are Bartlett's test and Ljung Box test. These seem to be giving different results. Bartlett's test results in a p-value of 0.9, whereas the Ljung Box test gives a very small p-value of 1e-8. I don't understand why these two tests are giving diverging results. Moreover, I am not sure if my data has indeed been reduced to white noise.

In addition, these two tests return the same result if I remove the seasonal part of the series using regression (lm) before feeding the data to auto.arima. I am essentially creating a matrix with numerical dummies for weekdays and months to use as regressors with ARIMA (in the other approach). I am not sure why I am getting this weird behavior. Any insights?


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