How to calculate max/min scales on a scatter plot?

How to calculate max/min scales on a scatter plot

• I have 3 log scatter plots that I want to establish smooth maximum and minimum lines. What is the usual mathematical method to do that? (Image and Excel file links below.) The black lines on the scatter plot images are hand drawn. The third scatter plot is especially tricky and not amenable to a moving average plus stddev because of the data clumping. Note: This is time series data so new data constantly comes in. In other words, I cannot just use the whole data population in one shot. Any ideas would be greatly appreciated. Excel File: https://dl.dropboxusercontent.com/u/44057708/Three%20Scatters.xls Image at: https://dl.dropboxusercontent.com/u/44057708/ThreeScatters.jpg

• Answer:

  I don't know that there is a usual method to do this. If the data came all at once, I'd recommend quantile regression using a spline representation of time. But in your case, they do not. So, one relatively simple thing is a moving quantile. The $k$th smallest or largest of the last $K$ gives a first stab at this. The closer $k/K$ is to 0.5, the closer you are to the middle. The larger $k$ and $K$ are, the less this will fluctuate (including jumps, as aberrant points join or leave windows). The result won't look as smooth as your lines without more work, e.g. updating the moving quantile more smoothly with some weights.