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:

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

upon receipt of the 497 daily values I obtained a plot 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 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 suggest sufficiency ( supported by the acf of the residuals)

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

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