Constructing incremental moving average filters

Filling the output series in one pass

Editorial interpretation: TradersWeek treats a moving average as retained state rather than a one-line formula. The construction problem is naming what must be carried from the previous bar so the next simple, linear, or exponential value is exact without rebuilding the window. The archive facts describe only the historical workflow that follows.

When many dates are required, invoking a single-date average once per date repeats call overhead. A routine that fills an entire output series in one pass avoids that repetition.

Simple, linear, and exponential averages all smooth ordered observations over a stated lookback, but they assign different weights to old versus recent data.

Equal weights and the running sum

A simple moving average gives every observation in the window the same weight, so an old change offsets a new change of the same size.

After the first simple-average window sum is known, the next sum is obtained by subtracting the observation that leaves the window and adding the observation that enters it. That retained window total is the running sum.

For a 10-period simple average on 10 successive output dates, that running-sum update replaces 100 additions and 10 divisions with 28 additions and 10 divisions.

Linear weights and a once-computed total

A linear moving average multiplies the oldest point by 1 and the newest by the lookback length, then divides by the sum of those integer weights rather than by the period count.

The linear weight total from 1 through L equals L times (L plus 1) divided by 2 and can be computed once, outside the inner loop.

A recursive exponential blend

An exponential average is recursive: the current value blends the newest observation with the prior average, so that prior value must be retained or the history is rebuilt.

The exponential blending weight for a chosen period length can be written as 2 divided by (period length plus 1).

Integer totals and overflow

Integer construction requires postponing division until the last step and guarding overflow, because a long-period linear weighted sum can exceed a 32-bit integer range.

A scaled integer stores a price in whole units of the smallest tick so integer arithmetic can replace floating-point arithmetic. Division is still postponed until the last step.