# What does a "symmetrically grouped" lag plot tell about the data?

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:

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:
(source: ibin.co)

• It is strange, yes. A plot of the time series, and some description of what the time series is, might help us. Oct 8, 2018 at 18:15
• 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. Oct 9, 2018 at 15:22

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