Smoothing Data With Less Lag by Patrick G. Mulloy Last time, Mulloy discussed basic moving averages, introduced a new filter called DEMA1 and demonstrated a method with which to utilize exponential moving averages. Mulloy also explained how this new filter could be used in the moving average convergence/divergence (MACD) indicator. Now, Mulloy summarizes with more filtering techniques for the MACD and trading the Nasdaq. Two opposing properties are always at work in the standard moving average smoothing used in technical analysis, increasing the moving average (MA) length to cull more random fluctuations but in so doing thereby increasing the lag between the MA and the data. In my first article, I discussed the industry standards, the simple moving average (SMA, which is a straightforward moving mean of the data) and the faster-responding exponential moving average (EMA). Both the SMA and the EMA smoothing indicators have the same lag in the steady state long term, which is: (1 - a)/a where a = 2/(w+1) and w is the moving average period. In terms of the MA period w, the lag is: (w-1)/2 A new exponential moving average called DEMA1 was introduced in the previous article, which eliminated this lag for the steady state (see sidebar “Calculating TEMA1 and DEMA1”). Now, here are two other moving averages. One is known as TEMA1, which is an extension of the multiple smoothing technique using single, double and triple EMAs, while the other is a subset of a modification of the double-smoothing technique to include a second smoothing constant to smooth the trend of the data model, which I call DEMA2. |
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