1990issue C031-2
Constructing adaptive filters from equal-weight averages
A learned one-step forecast can start as a moving average with equal lookback weights, then adjust those weights after each forecast error. That construction can be inspected in a spreadsheet and later set beside a frequency- or cycle-based projector of the same ordered series.
- A one-step forecast can begin as a moving average whose lookback weights are all equal, then those weights can be treated as adjustable.
- Forecast error is the next realized price minus the weighted forecast, and the weights are improved with the same criterion used in linear regression.
- Incremental updates can be carried out in a spreadsheet so each change to the lookback weights stays visible.
- The same ordered price series can also be projected with maximum-entropy spectrum analysis, a frequency- or cycle-based construction that is harder to implement.
A visible starting forecast
A learned forecast can be introduced by starting from a conventional moving-average construction and then treating its weights as adjustable. The moving average is a lookback combination of recent prices that begins with equal weights and supplies the explicit baseline one-step forecast.
The starting construction assigns every lookback weight the same value, each equal to one divided by the number of terms. The one-step forecast is the next sampling interval’s projected price, formed as a weighted combination of the most recent prices in that lookback.
Score the next observation
Once the next price is known, forecast error is defined as that realized price minus the weighted forecast. Forecast error is the gap between the next realized price and the weighted forecast formed from the prior lookback.
The criterion used to improve the lookback weights is the same criterion used in linear regression. Incremental weight updates can be carried out in a spreadsheet so the construction can be inspected step by step.
An adaptive filter is a forecast built by starting from equal moving-average weights and then updating those weights to reduce next-period error on an ordered price series. The lookback weights are the coefficients applied to the most recent prices; they start equal and may be adapted after each error is observed.
A contrasting cycle projector
Adaptive-filter constructions were compared with maximum-entropy spectrum analysis as alternative ways to project an ordered price series. Maximum-entropy spectrum analysis is a frequency- or cycle-based projector applied to the same ordered series as a contrasting construction.
That cycle-based projector was characterized as harder to implement than an adaptive filter. The comparison is of two ways to form a projection, not a reason to hide the equal-weight baseline.
All readings on this track · 9 readings
- 1982Constructing moving averages with weights, alignment, and adaptive lookbacks
- 1990Constructing adaptive filters from equal-weight averages
- 2000Cycle-scaled lookbacks for a channel-breakout rule
- 2000When charting code breaks the adaptive trendline
- 2001Nonlinear Ehlers filter construction from momentum and distance weights
- 2001How a fixed smoother becomes a living parameter surface
- 2005A three-part workshop for adaptive-filter length search
- 2010Rebuilding an exponential average as a bounded error-correcting filter
- 2018Assembling a recursive median oscillator as a two-stage adaptive filter