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1996issue C111-4

Normalize price and volume onto a common scale

A traditional construction maps each observation onto a standard normal curve around its own series mean. When volume is not treated as normal, a symbol-level alternative sets mean volume to 100, and price changes are divided by a first-open base so names at different levels can share one scale.

  • Z-score-normalization maps a raw observation onto a standard normal curve so it can be described as average or as a stated number of standard-deviation units from its own series mean.
  • The worked sample has a skewed-volume-distribution: on a scale that sets mean volume to 100, about 63 percent of daily volumes sit below the mean because a long right tail lifts the average.
  • Relative-volume divides each day's volume by that symbol's mean and restates it on a mean-100 scale, so nearly identical raw prints of 433 and 434 became 46.146 and 61.733 against different symbol-level baselines.
  • Relative-price-change divides an absolute move by the symbol's first opening price, and that base is reset after a split or consolidation so each segment uses its own first-open reference.
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Current trackZ-score normalization11 readings

Map each observation onto its own series

A traditional construction maps raw values onto a standard normal curve so an observation can be described as average or as a stated number of standard-deviation units away from its own series mean.

That mapping is z-score-normalization: an observation is rescaled by its distance from a series mean, counted in standard-deviation units, so unlike series can be compared on one axis.

Use relative volume when the histogram is skewed

Volume in the worked sample is not bell-shaped. On a scale that sets mean volume to 100, about 63 percent of daily volumes sit below the mean because a long right tail lifts the average. That pattern is a skewed-volume-distribution: the mean sits above the typical day because a long right tail of unusually large sessions pulls the average higher.

When a series is not treated as normal, an alternative construction sets each symbol's mean volume to 100 and reports each day as relative-volume: that day's volume divided by the symbol mean, times 100, over the sampled interval.

Two sessions with nearly identical raw volume, 433 and 434, produced different relative volumes of 46.146 and 61.733 after each was divided by its own symbol mean.

Most sampled days print below average volume

On a scale that sets each name's mean volume to 100, the two bins below that mean already hold about 63 percent of sampled days, and only a thin right tail reaches 800 or more. The percentages are the labels printed on each bar of the source histogram.
On a scale that sets each name's mean volume to 100, the two bins below that mean already hold about 63 percent of sampled days, and only a thin right tail reaches 800 or more. The percentages are the labels printed on each bar of the source histogram.Daily

Average volume is indexed to 100. The source draws the same percentages on a log scale and notes one day above 1,600.

Join a symbol-level baseline to every row

Symbol-level mean volumes can be built by averaging volume grouped by symbol, stored as a lookup table, and written back onto each row by matching the current symbol.

A symbol-level-baseline is a single average or first-print reference computed per ticker and joined back to every row of that ticker.

Scale price change to a first-open base

A fixed dollar price change is treated as incomparable across price levels, so the absolute change is converted to relative-price-change by dividing it by that symbol's first opening price in the sample. The chosen base is typically the first opening price of the symbol or of a split-defined segment.

After a split or consolidation, the price-change base is reset so the pre-event and post-event segments each use their own first-open reference.

The first-open base can be carried down a symbol-sorted table by taking the current open when the symbol changes and otherwise reusing the previous row's base.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
4 of 11 in the Z-score normalization track
20011-5 pp.Next on Z-score normalizationConstructing pair spreads with z-score triggersCandidate books can be assembled from a regularly recomputed correlation screen. A shared recurrent price pattern is enough to start construction even when a corporate income link is left unused.
All readings on this track · 11 readings
  1. 1991Constructing standardized sentiment trend filters
  2. 1995Market z-score residuals for style pair construction
  3. 1995Constructing scaled z-score normalization for model inputs
  4. 1996Normalize price and volume onto a common scale
  5. 2001Constructing pair spreads with z-score triggers
  6. 2003Rebuilding band distance as a z-score crossover
  7. 2003Constructing price z-scores with dual averages and bands
  8. 2003Zigzag target zones from a normalized deviation oscillator
  9. 2005Constructing a z-score scored range-breakout filter
  10. 2006Constructing a trend system from Bollinger Bands and z-scores
  11. 2011How an adjustable-bands z-test resizes the no-trade zone
By fieldIndicators and filters56 readingsBy year19969 readings
All 11 readings tagged Z-score normalization
Also on Z-score normalization5 readings
1991Constructing standardized sentiment trend filters1995Constructing scaled z-score normalization for model inputs1995Market z-score residuals for style pair construction2001Constructing pair spreads with z-score triggers2003Constructing price z-scores with dual averages and bands