Same-scale trend filter from a rolling least-squares endpoint

How the moving-trend is formed

A moving-trend is built by fitting a least-squares line to the most recent n observations, storing that line's value on the current bar, and repeating the fit as the window advances. The result is a trend-filter: a rolling construction that estimates the current level from the recent slope of ordered prices instead of from a lagged central average of those prices.

The current-bar endpoint has a closed form that uses only the window length n, the unweighted sum of the n prices, and the time-weighted sum that multiplies those prices by 1 through n.

A same-window average locates an earlier midpoint

A simple five-bar moving-average is described as locating the market two and a half bars earlier, while the same-length moving-trend is treated as a forecast of today's level rather than as lagged data. A moving-average, in this terminology, is an equal-weight smoother of the same window whose positive coefficients locate a past midpoint of the sample rather than today's fitted endpoint.

Exponential weighting of a moving average is described as reducing that lag without removing it, so the moving-trend endpoint is a different construction rather than a faster average of the same type.

The endpoint as a weighted-moving-average

The regression endpoint equals a weighted sum whose chronological weights are each index k minus (n+1)/3, then multiplied by 6/(n(n+1)), so some weights are negative. That rewrite is a weighted-moving-average: a linear combination of the same ordered observations in which the coefficients may be unequal and may change sign.

For n = 5 those weights are -1/5, 0, 1/5, 2/5, and 3/5, which match the five-bar moving-trend and can be coded as a weighted moving sum without a regression routine.

A hybrid that stays on the price scale

The construction is not a conventional moving average, whose coefficients are positive and sum to one, and not an oscillator, whose coefficients sum to zero. It is a coefficient-hybrid: a weight vector that sums to one, like an average, while including negative terms, like an oscillator, so the output stays on the original scale.

A surrogate-series and a related smoother

The series can be computed on close-only, midrange, or open-high-low-close inputs and then used as a same-scale surrogate on which ordinary technical tools, including candlestick rendering, are applied. That output is a surrogate-series: filter output kept near the original price scale and then treated as a stand-in close, midrange, or full bar for other tools.

A related seven-bar weighted smoother uses mixed-sign chronological weights and, if those weights are divided by the sum of their absolute values, produces a differently scaled series that can be renormalized for comparison with a five-bar moving-trend.