They are executed against the residuals left over after a modeling fit operation and are aimed at determining whether the residuals can be classified as being “white noise” – meaning: zero mean, no evidence of serial correlation amongst the residual/error terms, and the residuals exhibit homoscedastic variance.. All these portmanteau tests treat the residuals as an input series and then use that series as an input to calculate the auto-correlation coefficients or partial auto-correlation coefficients associated with that series. Finally, these coefficients are then used in a subsequent formula to calculate the test statistic value.. The Null Hypothesis associated with all these tests is that the ARIMA model is adequate and that there is no evidence of serial correlation amongst the residuals.
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