1995issue C061
The exponential smoothing constant from averaging lag
An exponential smoother weights the current observation with a smoothing constant and the previous smoothed value with one minus that constant. If a series rises by one unit each interval and the smoother sits a constant averaging lag behind, the current smoothed value equals the current series value minus that lag. Substituting that identity into the update sets the smoothing constant to one divided by one plus the assumed lag. Setting the constant from expected delay is treated as more usable than mapping it onto a simple moving-average period.
- An exponential smoother weights the current observation with a smoothing constant and the previous smoothed value with one minus that constant.
- If a series rises by one unit each interval and the smoother lags by a constant averaging lag, the current smoothed value equals the current series value minus that lag.
- That ramp-and-lag identity sets the smoothing constant to one divided by one plus the assumed lag, the reciprocal of one plus the expected delay.
- Setting the exponential constant from expected delay is treated as a more usable construction than mapping that constant onto a simple moving-average period.
How the exponential smoother is built
An exponential smoother is built by weighting the current observation with a smoothing constant and the previous smoothed value with one minus that constant. The smoothing constant is the weight placed on the current observation. One minus that weight is applied to the previous smoothed value.
Averaging lag on a steadily rising series
If a series rises by one unit each interval and the smoother lags by a constant averaging lag, the current smoothed value equals the current series value minus that lag. Averaging lag is the constant delay, in sampling intervals, between a steadily changing series and the smoother that tracks it.
The smoothing constant from expected delay
Substituting that ramp-and-lag identity into the exponential update produces a smoothing constant of one divided by one plus the assumed lag. Under this construction the exponential constant is the reciprocal of one plus the expected delay of the average.
Expected delay is the lag assumed in advance when backing out a smoothing constant. Under the ramp construction it is equal to one less than the reciprocal of that constant.
Expected lag rather than a moving-average period
Setting the exponential constant from expected lag is treated as a more usable construction than mapping that constant onto a simple moving-average period. A moving average applies equal weight across a stated lookback of ordered observations and is often used as a period reference when building other filters.
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