1992issue C081-2
Constructing exponential averages from simple lookbacks
An exponentially smoothed series is another moving average, usually updated from a closing-price series. Lookback length and the smoothing constant can be treated as one construction choice so a simple average and an exponential update are built from the same ordered prices.
- An exponentially smoothed series is presented as another form of moving average, typically built from successive closing prices.
- Each new value adds a scaled gap between the latest price and the previous average, which is the same two-term mix of the latest price and that prior average.
- The mixing weight is a smoothing constant between 0 and 1, and it may be estimated from a simple-average length as 2 divided by n plus one.
- Editorial view: treat lookback length and smoothing weight as one construction choice so a simple moving-average baseline and an exponential update can be compared on equal terms.
One construction from the same prices
An exponentially smoothed series is presented as another form of moving average, typically built from successive closing prices. The usual input is a closing-price series, and each new average is updated from the latest close and the value already in hand.
Editorial view: lookback length and smoothing weight can be treated as one construction choice. A simple moving-average baseline and an exponential update can then be built from the same ordered prices and compared on equal terms.
The recursive update
Each new value is formed by adding a scaled gap between the latest price and the previous average to that previous average.
The same update can be written as a two-term mix: alpha times the latest price plus one minus alpha times the previous average.
The mixing weight alpha is a smoothing constant constrained to the range from 0 to 1. It sets how much of the latest price enters the updated average.
A companion diagram is used to illustrate the recursive update from yesterday’s average and today’s price.
From simple-average length to alpha
Alpha may be estimated from a simple moving-average length n by the conversion 2 divided by n plus one. Under that conversion, a 10-day simple length corresponds to an alpha of 0.18.
That integer lookback n is the simple-average length used to approximate the smoothing constant.
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