This paper studies trend filtering methods. These methods are widely used in momentum

strategies, which correspond to an investment style based only on the history

of past prices. For example, the CTA strategy used by hedge funds is one of the

best-known momentum strategies. In this paper, we review the different econometric

estimators to extract a trend of a time series. We distinguish between linear and nonlinear

models as well as univariate and multivariate filtering. For each approach, we

provide a comprehensive presentation, an overview of its advantages and disadvantages

and an application to the S&P 500 index. We also consider the calibration problem of

these filters. We illustrate the two main solutions, the first based on prediction error,

and the second using a benchmark estimator. We conclude the paper by listing some