2017issue C0228-31
Rebuild a Hull moving average with linear-regression intercepts
The Hull moving average is assembled from two weighted averages, an interpolation, and a final weighted average. Linear regression replaces that weighted-average role with leading-edge intercepts, producing a Leavitt projection, a Leavitt convolution, and a four-state Rule-based entry map.
- A Hull moving average is assembled in three steps: weighted averages of lengths N and N/2, an interpolation of twice the shorter average minus the longer average, and a weighted average of that interpolation at a length equal to the square root of N.
- Linear regression can replace the weighted-average role by fitting a line to N consecutive prices and treating the leading-edge intercept as a zero-lag representation of current price.
- The Leavitt projection is the sequence of one-bar intercepts from successive linear regressions of price, and the Leavitt convolution is a further linear regression of that projection series.
- A Rule-based entry map can be formed from convolution trend, linear-regression trend, and whether convolution is below the linear-regression series, while projection-convolution crossovers are timing inputs rather than standalone forecasts of returns.
The Hull moving average is assembled in three steps. First, two weighted averages of lengths N and N/2 are formed. Next, those series are interpolated as twice the shorter average minus the longer average. Last, a weighted average of that interpolation is taken with length equal to the square root of N.
Lengths in the weekly table
In the weekly construction table, the Hull interpolation uses price weighted averages of lengths 25 and 13. The Hull moving average is the weighted average of that interpolation at length 5.
Linear regression in place of a weighted average
Linear regression replaces the weighted-average role in the new indicators. A line is fit to N consecutive prices, and the leading-edge intercept is treated as a zero-lag representation of current price.
The Leavitt projection is the sequence of one-bar intercepts from successive linear regressions of price. The Leavitt convolution is a further linear regression of that projection series.
Read slope, not location versus price
Unlike a conventional Moving average, a linear-regression series is not read as bullish or bearish from its position above or below price. Only the sign of the slope of successive plotted points is used.
A four-state Rule-based entry map
A Rule-based entry map can be formed from three binary states: convolution trend, linear-regression trend, and whether convolution is below the linear-regression series. Those joint states yield labeled regimes such as aggressive bull, conservative bull, threat, and caution.
Crossovers between the projection and the convolution can be used as a timing input inside this Rule-based entry map, rather than as a standalone forecast of returns.
All readings on this track · 6 readings
- 2010Constructing a Hull smoother and a Hull-based oscillator gate
- 2015Evaluating moving-average lag in cycle filters
- 2017Rebuild a Hull moving average with linear-regression intercepts
- 2017A Hull moving-average forecast in a credit-spread trend procedure
- 2019Constructing nested regression projections as smoothers
- 2020Evaluating countertrend ETF rules against a buy-and-hold control