Stocks & Commodities V. 12:12 (537-541): Letters To S&C

LETTERS TO S&C

DOUBLE EXPONENTIAL MOVING AVERAGES

Editor,

In "Smoothing data with faster moving averages"(January 1994 STOCKS & COMMODITIES), author Patrick Mulloy refers to the steps used to calculate the 26-week one-parameter double exponential moving averages (DEMA1). Figure 6 is titled "Weekly NASDAQ, 26-week EMA and 26-week DEMA1" and its caption states the DEMA1 shows higher response to the changing prices than the single EMA.

Actually, the principal reason for this greater responsiveness is that the plot for the EMA1 "equivalent" moving average of 26 weeks is being compared to that of one about half that long. This is because the formula a = 2/(w+1) used for computing equivalent simple moving average periods for exponential smoothing, while valid for EMA1, isn't valid for DEMA1. Over the range of useful values of a, for any given a, much more weight is given to the most recent price (C) for DEMA1 than for EMA1. Specifically, the weight of the most recent price is a(2-a) for DEMA1. On the other hand, it is obvious that the weight given the most recent price for EMA1 is a. This means that, for a given a, the "average age" of data in a DEMA1 lot is significantly less than one for EMA1. This, in turn, means that DEMA1's equivalent moving average period is much shorter.