lagplot

A lag plot is a scatter plot of a time series against a lagged version of itself. This type of plot is useful for identifying temporal dependencies in data. Specifically, a lag plot helps visualize autocorrelation, which is the correlation of a time series with itself at different points in time.

To create a lag plot, you select a lag value, say `k`. The plot then displays the data points `(y_t, y_{t-k})` for all `t` where both `y_t` and `y_{t-k}` are defined. The x-axis represents the lagged values (`y_{t-k}`), and the y-axis represents the current values (`y_t`).

If a time series is purely random, the lag plot will show a random scattering of points with no discernible pattern. However, if there is a linear relationship between the current observation and past observations, the points on the lag plot will tend to cluster along a line. The slope of this line indicates the direction of the relationship, and the tightness of the cluster indicates the strength of the correlation.

For example, if a time series exhibits a strong positive autocorrelation at lag 1, the lag plot will show points clustered along a line with a positive slope. This suggests that high values tend to be followed by high values, and low values by low values. Conversely, a negative autocorrelation would result in a line with a negative slope. If the points form a distinct, non-linear pattern, it may indicate more complex dependencies, such as seasonality or non-linear trends. Lag plots are a fundamental tool in exploratory time series analysis.