Skip to main content
Track Trend filter
4 / 33
Search the archiveLibrary
Library

1992issue C091

Building a random walk index trend filter

This archive note reconstructs a trend filter from ordered daily highs, lows, and closes. The random walk index divides the distance from a prior opposite extreme to today's extreme by the lookback-window average of true range times the square root of that lookback length.

  • The filter is assembled from ordered daily highs, lows, and closes, with the newest bar last and the current high and low treated as if the session is still open.
  • The random walk index denominator is the lookback-window average of true range multiplied by the square root of that lookback length.
  • The reported low-side index is the largest of the one-through-nine lookback ratios, and a reading greater than 1 is treated as a trending low rather than a random range.
  • The high-side index keeps the same denominator and replaces the numerator with today's high minus the low from n days earlier.
Entries in this reading1 entry
Current trackTrend filter137 readings

How the series is assembled

The trend filter is assembled from ordered daily highs, lows, and closes, with the newest bar last and the current high and low treated as if the session is still open.

The random walk index is the ratio of the distance from a prior opposite extreme to today's extreme, divided by average true range times the square root of the lookback length.

True range and the denominator

True range is the greater of the current high minus the current low and the prior close minus today's low. It is the larger of the current high-to-low span and the gap from the prior close to today's low, so an overnight gap is not recorded as a narrow day.

The index denominator is the lookback-window average of true range multiplied by the square root of that lookback length. Lookback is the number of sampling intervals used both to average true range and to set the square-root time scaling.

Building the low-side index

The low-side index places a prior high minus today's low in the numerator to test whether the current low has left a random range.

On the low side, a two-interval reading uses yesterday's high minus today's low, divided by the two-day average true range times the square root of 2. On the low side, a three-interval reading uses the high from two days earlier minus today's low, divided by the three-day average true range times the square root of 3.

The low-side ratio is repeated for lookbacks of 1 through 9 intervals, and the reported index is the largest of those ratios. A reading greater than 1 on any lookback is treated as a trending low rather than a random range. In the worked example the largest reading is 1.25.

The high-side index and longer lookbacks

The high-side index keeps the same denominator and replaces the numerator with today's high minus the low from n days earlier.

Lookback lengths longer than 8 days are the setting given for longer-horizon trend readings. The trend filter labels a price extreme as trending when its displacement exceeds a true-range baseline scaled by the square root of the lookback.

Low-side random walk index by lookback

Four of the eight windows print above 1, so today's low is read as a trend extreme rather than a random-range dip. The largest reading is 1.25 at four days. The points are the exact spreadsheet outputs for lookbacks of two through nine days on the simulated bar.
Four of the eight windows print above 1, so today's low is read as a trend extreme rather than a random-range dip. The largest reading is 1.25 at four days. The points are the exact spreadsheet outputs for lookbacks of two through nine days on the simulated bar.Simulated daily bars · Daily

Only the low-side index is shown, and the last bar has no close because the session is still open. The sidebar stops at nine days; Poulos treats windows longer than eight days as the longer-horizon test.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
4 of 33 in the Trend filter track
19921-9 pp.Next on Trend filterPhase diagrams for moving-average trend filtersPhase is the signed distance of the close from a moving average: positive when price is above that average and negative when price is below it.
All readings on this track · 33 readings
  1. 1988Opening-range brackets, a two-bar trend filter, and bounded stops
  2. 1990Bezier-curve price trend filter
  3. 1992Constructing a damping-index trend filter
  4. 1992Building a random walk index trend filter
  5. 1992Phase diagrams for moving-average trend filters
  6. 1993Volume-weighted change smoothing and trend ranking
  7. 1993Concurrent highest-low filter with a largest-low-fall trigger
  8. 1994Unit-invariant trend filters and the c-test
  9. 1995Constructing cup and cap entries with a three-bar net line
  10. 1997Why a daily timing evaluation depends on interval, lookbacks, and the fitting objective
  11. 2001A volume budget clock for trend-segment construction
  12. 2001Keep three jobs separate when you test a composite score
  13. 2002Evaluating the weekly four-percent close filter as a market-state procedure
  14. 2003Constructing a confirmed zigzag trend filter
  15. 2004Decompose high, low, and close into separate forecast streams
  16. 2005Three-state moving-average breakout bar coloring
  17. 2005Constructing a volume and move-adjusted trend filter
  18. 2005A fifty-day average breakout as a trend permission filter
  19. 2005Current-bar inclusion can mute a stochastic channel break
  20. 2006A stochastic oscillator gated by a long-term exponential average
  21. 2010A construction test for a modified volume-price trend filter
  22. 2011Constructing a Spearman rank trend filter
  23. 2013Constructing a repeated-median slope as a resistant trend filter
  24. 2014Combining a relative-strength index and trend filters for oversold setups
  25. 2014Price-rooted lookbacks for a relative strength index, a moving average, and a trend filter
  26. 2015Evaluating next-session intermarket range forecasts
  27. 2018Read the intermarket weight matrix first, then the predicted moving-average filter
  28. 2018Constructing the stiffness trend filter from moving-average holds
  29. 2018The averaging kernel and the lagged trend gate are separate specifications
  30. 2019A trend filter is not ready to compare until portfolio constraints are written down
  31. 2019Lookback, threshold, and position-capacity for a stiffness trend-filter
  32. 2020Combining a trend filter with a moving average and a stochastic oscillator
  33. 2020Constructing a relative-strength oscillator with a rank-agreement trend filter
By fieldIndicators and filters682 readingsBy year1992115 readings
All 137 readings tagged Trend filter
Also on Trend filter5 readings
1982An odd-length smoother from a cycle cutoff1987Testing price-volume agreement after percent reversal filters1988Auditing the forty-month stock-price cycle1988Opening-range brackets, a two-bar trend filter, and bounded stops1988Remaining life on a percent-filtered swing chart