This could tell you whether the model is correct or not. If the residuals are white noise, then the autocorrelation should be zero for all lags other than the zero lag, i.e., r(0) = 1. Now, if you are trying to validate a model, you should consider doing the following tests:
1) Autocorrelation test of residuals: Autocorrelation plot with confidence limits. (see Box and Jenkins' book). There are also statistical tests.
2) Cumulative periodogram test of residuals (see Box and Jenkins' book). If 95% of the points of the periodogram fall within the 95% confidence limits, the residuals are white.
3) Normal probability test on the residuals. Normally a histogram with a normal curve superimposed. There are also statistical tests based on skewness and kurtosis (see Bibby's book).
Finally, if the result of these tests indicate that the residuals are not white noise, then you have to go back and update your model, possibly a higher order model is needed.
Alireza:
I found one of my publications that talks about this. I have some chapters from my thesis where I do a lot of data analysis. Please let me know if you need further help.
Hi Alireza,
I am quite sure your plot is NOT autocorrelation of residuals. A very common mistake is to perform correlation analysis (testing for whitness) on one step ahead prediction errors over validation data. By definition, residuals are the one step ahead predicitio errors obtained on estimation data. This subtlety usually helps clarify many doubts concerning residual analysis.
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