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The residuals are uncorrelated. If there are correlations between residuals, then there is information left in the residuals which should be used in computing forecasts. The residuals have zero mean. If the residuals have a mean other than zero, then the forecasts are biased.
Is p-value of 0.001 significant?
Most authors refer to statistically significant as P < 0.05 and statistically highly significant as P < 0.001 (less than one in a thousand chance of being wrong).
How does the Box Ljung test work for residuals?
Because the test is applied to residuals, the degrees of freedom must account for the estimated model parameters so that \\(h = m-p-q\\), where \\(p\\) and \\(q\\) indicate the number of parameters from the ARMA(\\(p,q\\)) model fit to the data.
How is the Ljung test applied to a time series?
The test is applied to the residuals of a time series after fitting an ARMA(\\(p,q\\)) model to the data. The test examines \\(m\\) autocorrelations of the residuals. If the autocorrelations are very small, we conclude that the model does not exhibit significant lack of fit.
Which is better FIT1 or Ljung Box test?
The autocorrelation function looks like this: Despite such obvious autocorrelation at several first lags, the Ljung-Box test gave me much better results at 20 lags, than fit1: whereas just checking autocorrelation at lag1, also gives me the confirmation of the null-hypothesis!
What is pvalue for residual autocorrelation in MATLAB?
When you count the estimated parameters, skip the constant and variance parameters. pValue = 0.0130 suggests that there is significant autocorrelation in the residuals at the 5% level. Residual series for which the software computes the test statistic, specified as a numeric vector. The last element corresponds to the latest observation.