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This article examines and compares, from a digital signal processing (DSP) time domain perspective, several filters that are modeled on the assumption that the input follows a second order process, i.e., the input contains a linear trend. These filters are, by design, better able to track linear trends than some other more commonly-used filters, such as moving average, exponential smoothing, etc., which exhibit lag, or a time delay, in response to trends. Filters modeled on a second order process are commonly referred to in the technical analysis literature as “zero lag” filters.

This article describes digital filters derived from time series regression models that can be used as technical analysis tools. The filters are analyzed from a digital signal processing (DSP) frequency domain perspective to illustrate their properties. Example charts of the filters applied to the S&P 500 index are also included.

This article examines four digital filters commonly used for trend-following: moving average linear weighted moving average exponential smoothing time series momentum

1. Introduction Many traders use strategies based on trends that occur in stock, bond, currency, commodity, and other financial asset price time series in order [...]