|  JAN 1994

Smoothing Data With Faster Moving Averages by Patrick G. Mulloy

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 BASICS 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.

by Patrick G. Mulloy