My test results with R on ARIMA model became ambiguous when the ACF residual graph show no statistical significant i.e good model for forecast ( no white noise,constant mean and variance). In another way round the Ljung Box statistic test plot show p-value ranges between 0.4 and 0.8 which is too high theoretically.
O.O. Ade-Ikuesan could you please kindly share both your model estimates and the correlogram of residuals so we can have a better understanding of your results and maybe suggest some course of action?
CONFIDENCE INTERVAL is the probability that your finding will be found in the population parameters; what is not found is called ERROR. This error level is called pValue. If the confidence interval is 95%, the pValue level is 5% or 0.05.
In this case, if your pValue (error) level is 0.40 and 0.80, the frequency proportion that your finding will be found in the population parameter is only 0.60 and 0.20, respectively. With such low confidence interval from empirical finding, the model should be rejected.
The objective is to reject the null hypothesis. The null hypothesis may be rejected if the test statistic exceeds the null hypothesis threshold or the p-value (error level) is less than the preset p-value. H(0): pValue > 0.05.
Hypothesis testing is the verification of a set of observations by a set of statistical rule (Stuart and Ord, 1999). A confidence interval is specified and the observed data is tested against that confidence interval. If the result exceeds the pre-specified interval, it is considered statistically significant (Rice, 2007).
Both confidence interval and error comparison lead to the same conclusion (Triola, 2001). This approach to hypothesis testing is called test of significance (Fisher, 1925).
REFERENCES:
[1] Fisher, R.A. (1925). Statistical Methods for Research Workers, Edinburgh: Oliver and Boyd, 1925, p.43.
[2] Rice, John A. (2007). Mathematical Statistics and Data Analysis (3rd ed.). Thomson Brooks/Cole. §9.3.
[3] Stuart A., Ord K., Arnold S. (1999), Kendall's Advanced Theory of Statistics: Volume 2A—Classical Inference & the Linear Model (Arnold) §20.2.
[4] Triola, Mario (2001). Elementary statistics (8 ed.). Boston: Addison-Wesley. p. 388. ISBN 978-0-201-61477-0.
You may find this link of use. I recommend that you try at least one of these if that is possible. Best, David Booth
https://www.google.com/search?q=adaptive+lasso+for+time+series+model&spell=1&sa=X&ved=2ahUKEwjy67-1x8TpAhXGAp0JHZzkD7gQBSgAegQIDBAm&biw=1584&bih=779
First of all, be sure that you have tested for the residuals, not the original series.
If your p-values 0.4 and 0.8, tests agree that you can not reject the null of no auto-correlation. I suggest you read this discussion
https://stats.stackexchange.com/questions/64711/ljung-box-statistics-for-arima-residuals-in-r-confusing-test-results
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