Smoothing Data With Faster Moving Averages By Patrick G. Mulloy
Has the lag time of moving averages ever irritated you? Well, there is a way around it: a modified statistical version of exponential smoothing with less lag time than the standard exponential moving average that is used in securities technical analysis, a double exponential moving average.
All moving averages smooth or reduce the noise level of a time series such as closing stock market prices
by increasing the moving average (MA) length. But moving averages have an inherent detrimental lag
time that increases as the MA length increases. The solution is a modified statistical version of
exponential smoothing with less lag time than the standard exponential moving average (EMA) that is
commonly used in securities technical analysis. Implementing this faster version of the EMA in indicators
such as the moving average convergence/divergence (MACD), Bollinger bands or TRIX can provide
different buy/sell signals that are ahead (that is, lead) and respond faster than those provided by the single
EMA. In Figure 1, the MACD indicator is applied to the weekly closing price of the NASDAQ composite
index. Using the standard MACD EMA lengths of 12, 26 and nine, the indicator generates 11 buy signals
with six losses. Figure 2 uses the same filter lengths of 12, 26 and nine, but the filters are not EMAs but
are derivations of one-parameter double exponential moving averages (DEMA1). This time, the indicator
generated nine trades, with only three losses due to the increased response of the DEMA1 filter. Here are the attributes of the DEMA1 filters and the methods by which to calculate the filters.
The term statistical is used qualitatively here because exponential smoothing is not based on any formal
statistical theory, and for that reason, these smoothing techniques are best regarded as descriptive rather
than inferential in statistical terminology. With that in mind, data smoothing by using moving averages is
a common methodology in the statistical world of time series forecasting. The moving average smoothing
technique removes the rapid fluctuations in the time series so that the secular (that is, long-term) trend is
more apparent. Exponential smoothing was originally developed to primarily forecast time series that can
be represented by a polynomial function of time.