Academic Papers

Momentum Strategies with L1 Filter

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 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.