Run sequence plot

A simple run sequence plot of the original time series with time on x-axis and the variable on y-axis is good for indicating the following properties of the time series:

• Movements in mean of the series
• Shifts in variance
• Presence of outliers

The following figure is the run sequence plot of a hypothetical time series that is obtained from the mathematical formulation x_t = (At + B) sin(t) + ?(t) with a time-dependent mean and error ?(t) that varies with a normal distribution N(0, at + b) variance. Additionally, a few exceptionally high and low observations are also included as outliers.

In cases such as this, a run sequence plot is an effective way of identifying shifting mean and variance of the series as well as outliers. The plot of the de-trended time series of the CO2 concentrations is an example of a run sequence plot.