1994issue C011-2
Polarized fractal efficiency with a shared exponential smoother
Two daily series share the same 10-period first-to-last spacing, path length, and polarity. After those signed values are formed, both series use one five-period exponential smoother with a 0.333 weight on each new observation.
- First-to-last spacing and path length are measured on the same 10-period close window before a sign or a smoother is applied.
- Polarity is the sign of the newest close minus the oldest close in that window, and it is attached after the unsigned lengths are formed.
- One series divides first-to-last spacing by path length and scales the ratio by 100. A parallel series uses a fractal-dimension transform of the same two lengths.
- Both signed series start from the first raw daily value and then share a five-period exponential smoother that applies a 0.333 weight to each new observation.
Polarized fractal efficiency is a signed lookback measure that compares net close travel with the summed one-step close path and then applies a short exponential smoother. The construction below uses a 10-period window of closes. One finished series is expressed on a percentage scale. A second daily series is built from the same window with a fractal-dimension transform.
Shared close-path geometry
First-to-last spacing is the straight-line distance from the oldest close in a fixed window to the newest close, using the window length as the horizontal component. For the 10-period series, that spacing is the square root of the squared net close change plus 10 squared.
Path length is the sum of successive one-step close spacings across the same window, each using a unit horizontal increment. Each one-step spacing is the square root of the squared adjacent-close change plus 1.
Polarity and the two daily series
Polarity is a plus or minus sign taken from whether the newest close is above or below the oldest close in the window. Daily polarity is taken from the sign of the newest close minus the oldest close.
The percentage series divides first-to-last spacing by path length, scales that ratio by 100, and then attaches polarity. The result is a signed daily percentage value.
The parallel series uses a fractal-dimension transform: 1 plus the common-log difference between path length and first-to-last spacing, divided by the common-log difference between 10 and 1. That series is signed by the same first-to-last close comparison.
A shared exponential smoother
Exponential smoothing is a five-period recurrence that starts from the first raw daily value and then mixes each new observation at weight 0.333 with the prior smoothed value.
The signed percentage values are initialized with the first raw observation and then updated with that recurrence. The signed fractal-dimension transform is passed through the same five-period recurrence with the same 0.333 new-observation weight.
All readings on this track · 41 readings
- 1984Matching average age across price filters
- 1984Residual-impact construction of exponential smoothers
- 1988Constructing simple and exponential moving averages as specified filters
- 1989Evaluating smoothed free reserves and funds-discount spreads
- 1990Integer construction of moving averages and exponential smoothing
- 1990Constructing incremental moving average filters
- 1991Constructing a double-smoothed stochastic oscillator
- 1991Constructing an exponential average from a smoothing weight
- 1991Constructing a double-smoothed momentum oscillator family
- 1991Competing certainty rules from exponential-average conditions
- 1991Hybrid construction of a mechanical timing system from smoothed signals
- 1991Constructing an exponential smoother from a moving-average length
- 1991Equivalent relative-strength-index constructions from a ratio and from smoothed momentum
- 1991Constructing the true strength index from double-smoothed momentum
- 1991True strength index from signed, double-smoothed momentum
- 1992Constructing exponential averages from simple lookbacks
- 1992Constructing exponential averages by the smoothing constant, startup length and lag
- 1992Nested range smoothing and windowed high-low damping
- 1992A weekly equity stance from the discount-bill spread
- 1993Double-smoothed stochastics momentum index construction
- 1993Constructing the true strength index with double exponential smoothing
- 1994Polarized fractal efficiency with a shared exponential smoother
- 1994Five-interval exponential smoothing of ten-interval signed path-efficiency
- 1994Hand-ranked price-volume series with stacked smoothing and stochastic
- 1995Range expansion filter on multi-horizon averages
- 1995The exponential smoothing constant from averaging lag
- 1997Construct a nested-average rainbow band and oscillator
- 1998Filter stacks that combine a moving average with exponential smoothing
- 2002Smoothed relative-strength construction from wilder-averaging and a price prefilter
- 2003Reverse-engineered RSI price targets
- 2004Piecewise trend quality from moving-average reversals
- 2004Nested smoothing recipes versus unaudited oscillator experiments
- 2008Weight construction beyond the N-day label
- 2010A consensus filter for objective RSI and smoothing construction
- 2012Sentiment-zone oscillator from signed closes
- 2012Classic RSI one-over-N smoothing versus the standard exponential average
- 2013Why exponential smoothing uses two over n plus one
- 2015Constructing ratio indicators with moving-average and exponential-smoothing weights
- 2015Slow relative-strength index from an exponentially smoothed price
- 2017Rebuilding the relative strength index as open-scale buy-sell pressure
- 2017Comparing Wilder and exponential smoothing inside a relative-strength index