A Digital Signal Processing Approach to Moving Averages

Many exotic moving averages are inspired by Digital Signal Processing (DSP) techniques. This chapter explores the connection between moving averages and digital filters, emphasizing that DSP filters are typically analyzed in the frequency domain rather than the time domain. The chapter applies DSP principles to examine the properties of conventional moving averages and the trend-following rules derived from them. It then introduces several DSP-inspired moving average variants and evaluates whether they exhibit unique characteristics absent in conventional or other exotic moving averages. The analysis reveals that DSP-inspired moving averages closely resemble so-called “zero-lag” moving averages, which aim to reduce lag while maintaining high smoothness. However, as with zero-lag variants, these filters achieve their reduced lag by incorporating negative weights, which ultimately come at the cost of lower accuracy. The findings suggest that while DSP principles offer valuable insights into moving average behavior, they do not necessarily lead to universally superior trend-following rules.