# Lagged scatterplot

This online calculator builds scatterplot of the time series against itself offset in time

This online calculator builds **lagged scatterplot** (or **lag plot**) of the time series.

What is lag plot? It is the plot of lag function which can be defined for arbitrary *k* as follows:

,

where is the *i*-th value of time series.

Thus we are plotting the time series against itself offset in time, for example, .

This is the simplest graphical way to detect autocorrelation (the correlation of a time series with its own past and future values). A random scattering of points in the lagged scatterplot suggests little or no autocorrelation. On the opposite side, alignment or any other organized curvature in dots' pattern might suggest dependence between time-separated values. And one of the advantages of the lagged scatterplot is that it can show dependence regardless of the form (i.e., non-linear).

For example, the default time series in the calculator below was obtained by noising the sine function using Noisy function generator. And, as you can see, the lag plot definitely suggests that there is a dependence.

For your convenience, you can plot up to six lag functions on a single chart. They will differ by color and used marker symbol. Just enter the lag value into the corresponding marker box.

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