Autocorrelation at lag 1 but scatterplot shows no linear relationship

by UDE_Student   Last Updated October 08, 2018 19:19 PM

I have a time series consisting of 490 days and for each day I have the residual of a forecasting model. I wanted to check if the residuals somehow correlate and calculated the ACF at lag 1 which is acf(1)=0.42 Here is the ACF plot: ACF

Now I wanted to check the linear relationship between lag=0 (denoted as x1 in the scatterplot) and lag=1 (x2 in the scatterplot) so I plotted a scatterplot, but I don't see any linear relationship. Why do I have a correlation of 0.42 at lag 1 but I don't see the linearity between lag 0 and 1?

Am I missing a point here?

Update: I uploaded a CSV file with the time series here


Answers 1

upon receipt of the 497 daily values I obtained a plot enter image description here which supported my "guess" that there were other/latent factors present ( i.e. one clear level shift and one masked by anomalies ) . I used AUTOBOX my tool of choice and it identified a model enter image description here enter image description here excerpting some pulse indicators. The final equation does indeed include an AR(1) and some possible seasonal/monthly dummies along with a bunch of anomalies.

The residual plot enter image description heresuggest sufficiency ( supported by the acf of the residuals) enter image description here

Hope this helps you and others regarding interpreting unconditional statistics either visual or written.

The forecast for the next 21 days is shown here enter image description here

March 16, 2018 20:58 PM

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