Rose powdery mildew
This page is not about time series at all. It applies lowess smoothing to a scatterplot. (This is the application for which it was originally developed.)
Again click on any value to see the adjacent values that is used. The least squares line from these points provides a smoothed fitted value. Windows of about 10 points give a reasonably smooth curve.
You could mention that the version of lowess that is implemented by most computer programs is more complex, using weighted polynomial least squares for the observations within each window. However the simpler version here illustrates the basis of the method.
The data set gives the results of an experiment that was conducted to determine how the latent period (time in days from initial infection to sporation) of rose powdery mildew is affected by temperature.