Order-statistic Filters

What are Order-statistic Filters?

Order-statistic filters smooth a series by ranking rather than averaging. Slide a window of the last N values along the chart, sort the contents, and output the value at a chosen rank: the middle value gives the moving median, a chosen percentile gives a percentile filter, the two extremes give running maximum and minimum, and the most frequent value gives a moving mode. Because the output is chosen by rank, always an actual data point or an interpolation between two adjacent ones rather than a weighted blend of the whole window, these are nonlinear filters and behave differently from any moving average.

The family comes from signal processing and robust statistics. John Tukey proposed running-median smoothing in the early 1970s as part of exploratory data analysis, and median filters went on to become a staple of digital image processing because they remove salt-and-pepper noise while preserving edges. Traders inherited the tools directly: a bad tick is the chart's version of a corrupted pixel, and a genuine gap or regime break is an edge worth preserving. On modern platforms the general case is built in; Pine Script® provides median and percentile functions, and array support makes arbitrary ranks straightforward to compute.

The practical appeal is robustness. A single bad tick or one violent bar drags a mean in proportion to its size but barely moves a median, and where linear smoothers round off sharp level shifts, a median tends to preserve them, at the cost of a steppy, plateau-prone output. The family also generalizes familiar tools: Donchian channels are simply the 100th and 0th percentile filters plotted as a channel, and a median crossover system is a moving average crossover setup with means swapped for ranks.

How to calculate a moving median

The moving median is the flagship order-statistic filter, and every other member of the family is the same procedure with a different rank.

1. 1Choose a window length N and, at each bar, collect the most recent N values of the source series (close, volume, an indicator, anything).
2. 2Sort the window's values in ascending order.
3. 3Output the middle value. With an odd N that is the single center element; with an even N, average the two center elements.
4. 4For the general case, output a different rank instead: the p-th percentile (interpolating between neighboring ranks where needed), the maximum, the minimum, or the most frequent value for a moving mode.

How it's calculated

Filters that output a chosen rank of the last n prices rather than an average; the moving median is the best-known case.

Ranks r = 1 and r = n give the moving minimum and maximum; applied to the lows and highs these are the lower and upper Donchian channel lines.

A moving median follows clean step changes and ignores isolated spikes better than a mean of the same length, at the cost of a staircase-like output.

Exact price repeats are rare, so the moving mode is only meaningful on binned or rounded prices.

How traders use it

• To despike raw data: a short moving median strips isolated bad ticks and single-bar anomalies before other indicators are computed, standard outlier handling.
• As a robust baseline: swapping a moving median in place of an SMA or EMA gives a centerline that one wide bar barely moves, useful in gappy or thinly traded markets.
• As percentile channels: an upper and lower percentile of price over a lookback frame a range that ignores the most extreme excursions, a softer alternative to pure high-low channels and a rank-based cousin of the MA envelope.
• Inside classic constructs: median-based variants of tools like Supertrend or MACD replace the mean component so the signal reacts less to single-bar shocks.
• As a regime condition: price holding above a rising moving median, or the median's own slope, provides a robust trend regime label, the same role an MA slope filter plays but harder for one news bar to flip.

Order-statistic Filters vs linear smoothers