Momentum Strategies with L1 Filter

Journal of Investment Strategies 3(4), 1–26

22 Pages Posted: 16 May 2016

See all articles by Tung-Lam Dao

Tung-Lam Dao

Millennium Capital Management, France branch

Date Written: May 27, 2014


In this article, we discuss various implementation of L1 filtering in order to detect some properties of noisy signals. This filter consists of using a L1 penalty condition in order to obtain the filtered signal composed by a set of straight trends or steps. This penalty condition, which determines the number of breaks, is implemented in a constrained least square problem and is represented by a regularization parameter lambda which is estimated by a cross-validation procedure. Financial time series are usually characterized by a long-term trend (called the global trend) and some short-term trends (which are named local trends). A combination of these two time scales can form a simple model describing the process of a global trend process with some mean-reverting properties. Explicit applications to momentum strategies are also discussed in detail with appropriate uses of the trend configurations.

Keywords: Momentum strategy, L1 filtering, L2 filtering, trend following, mean-reverting, cross validation

Suggested Citation

Dao, Tung-Lam, Momentum Strategies with L1 Filter (May 27, 2014). Journal of Investment Strategies 3(4), 1–26, Available at SSRN:

Tung-Lam Dao (Contact Author)

Millennium Capital Management, France branch ( email )

2 Rue Jean Rostand
Orsay, 91400
+33651093563 (Phone)

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