Smoothing function for displaying stacked lines without the smoothing introducing crossings

Question

I'm displaying time-series data as a "stacked line" or "stacked area" chart. (E.g. with percentage data, data points at 10%, 20% and 30% are displayed at 10%, 30% and 60% on the chart.) Unsmoothed lines through the data points obviously never cross (and never go below the minimum data value or above the maximum total; think 0% and 100% again for instance). I'm looking for a smoothing function that will preserve these properties; that is, the smoothed lines should never cross (including between data points), should never exceed the maximum/minimum values given by the data points, and (ideally) should only touch at data points. Does such a beast exist?

As is probably apparent, I'm not a statistician. The smoothing here is only for visual appeal, so solutions that are theoretically less than ideal are still definitely on the cards.

Answer 1

If all series have the same number of data points at the same x positions, then a LOESS smoother with lambda=0 (essentially a weighted moving average) will satisfy your constraints.

At each position, you're computing $z_i = \frac{w_i * y_i}{n}$, where $w$ is the local smoothing function around the position. Given that $w_i$ and $n$ are the same for each series, if all the $y_i$ in one series are greater than or equal to the corresponding $y_i$ in another series, then the $z_i$ will follow the same rule. The external bounds condition is met by applying the above logic with a series of all min values or all max values.

This smoother will not usually go through the data points.