Trend-Following Filters – Part 10
1. Introduction Two previous articles, “Trend-Following Filters – Part 7” [1] and “Trend-Following Filters – Part 9” [2], examined, from a digital signal processing (DSP) [...]
About Henry Stern
Henry Stern is retired following a career in financial software. He worked as a product manager for a small company that developed technical analysis and portfolio accounting software and later was the fixed income and derivatives product manager for a portfolio management/compliance/electronic trading system. He also worked at several institutional money management firms in different capacities and as a developer implementing interest rate and fixed income derivatives pricing models. His educational background is a B.S. in electrical engineering and computer science from MIT and an M.S. from the Graduate School of Industrial Administration (now the Tepper School of Business) at Carnegie Mellon University.Trend-Following Filters – Part 9
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.
Trend-Following Filters – Part 8
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.
Trend-Following Filters – Part 7
This article examines four digital filters commonly used for trend-following: moving average linear weighted moving average exponential smoothing time series momentum
Trend-Following Filters – Part 6
This article analyzes six trend-following indicators from a digital signal processing (DSP) frequency domain perspective in which the indicators are considered as digital filters and their frequency response characteristics are determined.
Trend-Following Filters – Part 5
There are two general types of Kalman filter models: steady-state and adaptive. A steady-state filter assumes that the statistics of the process under consideration are constant over time, resulting in fixed, time-invariant filter gains. The gains of an adaptive filter, on the other hand, are able to adjust to processes that have time-varying dynamics, such as financial time series which typically display volatility and non-stationarity.
Trend-Following Filters – Part 4
This article considers a different type of filter called the Kalman filter. The Kalman filter is a statistics-based algorithm used to perform the estimation of random processes. Our research will explain what Kalman Filters are and utilize them with financial time series data for trend following purposes.
Trend-Following Filters – Part 3
Introduction This is the third article in a series of three, the first two are available here and here. Those articles focus on examining from [...]
Trend-Following Filters – Part 2/2
1. Introduction Part 1 of this analysis, which is available here, examines filters modeled on second-order processes from a digital signal processing (DSP) perspective to [...]
Trend-Following Filters: Part 1/2
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 [...]
An Introduction to Digital Signal Processing for Trend Following
Original: August, 2020 Updated: March, 2025 Overview Digital signal processing (DSP), specifically the use of digital filters, is embedded in many indicators used by technical [...]