Analysis of forecast errors from Facebook Prophet I created a forecasting model Facebook Prophet and now trying to analyse the forecast errors (yhat - forecasted). Following are 3 graphs I plotted


First one is raw forecast errors, second one is their ACF and the last one is residual plot (actual vs forecasted).
Based on ACF plot (2nd plot)
The X axis is the lag 40, and the Y axis is the Pearson’s correlation coefficient at each lag. The blue shaded region is a confidence interval. If the height of the bars is outside this region, it means the correlation is statistically significant and samples are correlated, hence your error/residual is not white noise
Our residual is inside this region hence it is white noise. We can say residuals are independent and identically distributed
In time series forecasting, if the differences between predictions and actual values represent a white noise distribution, one can pat himself on the back for a job well done.
My confusion is with first and third plot, specifically third plot. Do you see any patterns in residuals, as I read if there is any pattern then there is more room to improve your model. Please help me do you see any pattern, further ACF 2nd plot tell me there is white noise in errors, it means the errors does not follow any pattern.
If third plot seems to you has some pattern then why ACF telling me the same there is no pattern (white noise). What to believe for residual analysis? How can I decide about my model stability?

Here I am editing with your suggestion




The ACF plot does not say that the data is "white noise in errors, it means the errors do not follow any pattern". It shows that there is autocorrelation of about 0.6 at lag 1, which is clearly non-zero. This is also what you see on the third plot, there is some autocorrelation in residuals.
