Critiquing exponential variants of Bollinger Bands

Two related envelopes

A published letter distinguished two related envelopes. The earlier construction used ordinary standard deviation. The later construction used an exponential deviation measure, a recursively weighted dispersion statistic used in place of ordinary standard deviation when setting envelope width.

The letter writer argued that ordinary standard deviation was a long-standing statistical measure and therefore not created by the later popularization of price bands. The same writer asserted that the exponential deviation used in the later envelope was independently developed after a search that did not turn up prior use of that specific measure.

Both constructions mapped onto one family

A commentator mapped both constructions onto an exponential form of the established band method rather than treating them as a separate indicator family. Bollinger Bands are a volatility envelope that adds and subtracts a multiple of a deviation statistic from a moving average of ordered price observations over a defined lookback.

That commentator dated the exponential standard-deviation construction as more than 20 years old. Exponential standard-deviation bands pair an exponential average with ordinary standard deviation of the same series. Exponential deviation bands were described as already known under the same family name for about three decades. Exponential variants of the established band method were described as already included in packaged implementations of that method.

What the critique keeps fixed

Editorial reading: keep the ordered price series and the sampling interval unchanged. Both envelopes still add and subtract a deviation statistic from a moving average. One construction uses ordinary standard deviation. The other replaces that width measure with exponential deviation. The commentator's mapping treats both as exponential forms of Bollinger Bands.

Editorial reading: a construction that changes a kernel or a volatility estimator inside an existing envelope family, without changing the forecast task or the input class, is a variant, not a new model. On that check, the overlay remains inside the established band family.