I want to check whether residuals are white noise or not. When I look at the plot, all lags do not pass(exceed) the significance band except for fourth lag. However, fourth lag's p-value of 0.228 is higher than alpha 0.05. Can I say that residuals are white noise?
Best Answer
You don't really have a basis to assert that they are white noise. Failure to reject the null is not the same thing as H0 actually being true
However, the evidence that they're something else is quite weak -- the values are reasonably consistent with white noise.
I think your interpretation of the p-value for the Q-statistic at the 4th lag is wrong. Take a look at what the Q-statistic is actually doing; it's not looking "at the 4th lag" but at lags up to 4.