I am trying to do time series forecasting on different data sets.

I created a lag plot on each set and received an unusual, 'symmetric' but grouped pattern:symmetric lag plot

I would say that this implies a lack of autocorrelation but the separated groups confuse me.

What does this tell about the data?

EDIT: Here is a plot of the same data set itself: time series data
(source: ibin.co)

  • $\begingroup$ It is strange, yes. A plot of the time series, and some description of what the time series is, might help us. $\endgroup$ Oct 8, 2018 at 18:15
  • $\begingroup$ Be careful when inferring no-trend from scatter-plot point-clouds and non-transparent points. It's impossible to discern the actual frequency of observations that fall in a specific cloud. Use a hexbin or transparent point-fills instead. Or estimate the actual trendline. $\endgroup$
    – AdamO
    Oct 9, 2018 at 15:22

1 Answer 1


It tells you that the $y(t)$ are grouped around -5, 0 and 5.

You can read this information on the horizontal projection only. The facts that there 9 groups of dots is an unintended but inevitable secondary result.

As the central point seams to be less represented, the variable $y(t)$ and $y(t+1)$ are correlated, but maybe not in a linear way.

To go further (if the data is not simulated), you should first ask if the values $\pm10$, $\pm15$ and $\pm20$ have a meaning or if they are outliers. You can then introduce the variable $y^*(t) = 5* round(\frac {y(t)}{5})$ which is equal to -5, 0 and 5 which ever is the nearest. Then study the randomness $\epsilon(t) = y(t)-y^*(t)$. You can also study the lag correlation between $y^*(t)$ and $y^*(t+1)$ with a probability transition matrix (instead of a graph).

  • $\begingroup$ This is great, thank you! I also would like to read upon this, however, most of the material I found (e.g. about lag plots) discusses more common cases. Would you suggest keywords (or even sources) to find more information? $\endgroup$
    – nocibambi
    Oct 9, 2018 at 8:41

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