Moving Box is an generalization of John Tukey's "wandering schematic plot" where "schematic plot" was a name he used for the box plot.
As I recall (I don't have his book handy), his version used 10 or so overlapping intervals and made a box plot for each interval and then connected the key values with lines.
Our generalization uses the local kernel smoother to compute moving versions of the 5 key values (lower whisker, lower quartile, median, upper quartile, and upper whisker). Except a whisker is hard to translate to a local kernel fitter, so we use 0.005 and 0.995 quantiles instead, which are about what a 1.5 IQR whisker would translate to for a Gaussian distribution.
