Constructing a lead-lag filter and price channel as one stack

Keep the stack as one construction

Editorial view: treat the lead-lag smoother as a construction project rather than as three separate indicators. First cancel the lag of an exponential average. Then measure residual noise around the corrected path. Then place price channels from that same noise so the trend filter, the smoother, and the channel remain one stack that can be judged as a single hypothesis.

Build the lead-lag filter

The basic lead-lag filter is built from an N-point exponential average of the close plus a second exponential average of a linear combination of that series and a one-bar delay of itself.

Exponential smoothing is a recursive average of ordered closes. It can be nested, delayed, or linearly recombined to change how much lag remains in the estimate. The lead-lag filter is the two-formula form of that idea: take the exponential average and a one-bar delay of that average, then recombine them so the result tracks recent price with less lag than the original average.

The finished path is the trend filter. It is a constructed baseline that estimates the current path of price by combining a smoother with an explicit lag correction, so later signals can be judged against that path.

Estimate residual width in two stages

The residual-width estimate is constructed in two stages. A variance prefilter is a 5-period simple average of squared deviations from the lag-corrected smoother. Residual width is then the square root of a 13-period simple average of that series.

Residual width is the distance unit used later for the channel.

Place the price channel on the same path

Trend channels are formed by subtracting and adding 2.5 residual-width units to the lag-corrected smoother.

A price channel, in this construction, is the pair of upper and lower bands placed a fixed multiple of a residual-volatility measure around the lag-corrected smoother. Editorial view: the channel should not be swapped for a different width measure, or the stack splits into separate indicators.

A modified construction that uses a data shift

A modified lead-lag construction with N equal to 7 first applies a 3-period exponential average that is shifted one bar forward, then a 7-period exponential average, before the lag-correction stage.

That forward placement is a data shift: an intentional look-ahead of a short exponential average before a longer average is applied. It is used only when the construction is allowed to borrow future bars.

A no-shift nested alternative

A no-shift alternative nests a 2-period exponential average inside a 6-period exponential average and then uses 6.5 and 5.5 as the recombination weights so the half-week lag of the first stage is offset.

That nested exponential average places a short exponential average inside a longer one so the first stage reduces noise before the lag-correction stage runs.