2003issue C021-16
Constructing price z-scores with dual averages and bands
Archive notes build a price z-score from a chosen open, high, low, or close and one shared lookback. Documented panes then add a dual-smoother and same-length Bollinger Bands on price.
- The z-score subtracts a lookback mean from a chosen price and divides by the standard deviation of that same price over the same lookback.
- The dual-smoother is a short moving average of the raw z-score, then a second moving average of that first average.
- A coded pane places a 20-bar close z-score beside 20-bar, two-standard-deviation Bollinger Bands on price and uses a band-touch-exit when the high meets the upper envelope.
- A related normalized-deviation rescales deviation from a mean over an 80-bar window, with a 40-bar average length in the listed inputs.
A locked lookback, then optional overlays
The raw series is a z-score of a chosen price. It is built by subtracting a lookback average of that price from the price and dividing by the standard deviation of the same price over the same lookback. The price input may be the open, high, low, or close. A separate length input sets the sample used in the mean and standard-deviation terms.
Editorial: treat the z-score as a classroom build rather than a finished oscillator. Lock one lookback for both the mean and the deviation, then add a second moving-average layer and a same-length Bollinger envelope as optional overlays. That split lets students see which piece is the standardized residual and which piece is a rule or display choice.
The dual-smoother display
One documented display uses a 20-bar z-score of the close, a 3-bar average of that series, and a further 5-bar average of the 3-bar series. The dual-smoother is that short moving average of the raw z-score, then a second moving average of the first average. A demonstration chart plots those two successive averages of the z-score together with a Bollinger Band study on price.
Bands on price and a band-touch-exit
A later coded pane plots a 20-bar close z-score beside 20-bar, two-standard-deviation upper and lower Bollinger Bands on price. Those bands are a price envelope set a stated number of standard deviations above and below a moving average of price. In that coded variant, a band-touch-exit closes a long when the high meets the upper band, and the short-side rules are described as the reverse.
An extreme, then a smoother cross
One coded entry filter allows a 3-bar versus 5-bar smoother cross only after a 10-bar extreme of the raw z-score has risen above 2 or fallen below -2, depending on direction.
Editorial: the extreme-then-cross test is a rule layered on the residual. It does not change the lookback that defines the z-score.
A related normalized-deviation
A related construction measures deviation from a mean and rescales it over an 80-bar window, using a 40-bar average length in the listed inputs. That normalized-deviation rescales the current deviation from a mean over a longer window so values can be compared across bars.
All readings on this track · 11 readings
- 1991Constructing standardized sentiment trend filters
- 1995Market z-score residuals for style pair construction
- 1995Constructing scaled z-score normalization for model inputs
- 1996Normalize price and volume onto a common scale
- 2001Constructing pair spreads with z-score triggers
- 2003Rebuilding band distance as a z-score crossover
- 2003Constructing price z-scores with dual averages and bands
- 2003Zigzag target zones from a normalized deviation oscillator
- 2005Constructing a z-score scored range-breakout filter
- 2006Constructing a trend system from Bollinger Bands and z-scores
- 2011How an adjustable-bands z-test resizes the no-trade zone