The DOI matches its Crossref record; 77 of the 77 references it cites were found in a registry or an index.
$\ell_1$ Trend Filtering
Abstract
The problem of estimating underlying trends in time series data arises in a variety of disciplines. In this paper we propose a variation on Hodrick–Prescott (H-P) filtering, a widely used method for trend estimation. The proposed $\ell_1$ trend filtering method substitutes a sum of absolute values (i.e., $\ell_1$ norm) for the sum of squares used in H-P filtering to penalize variations in the estimated trend. The $\ell_1$ trend filtering method produces trend estimates that are piecewise linear, and therefore it is well suited to analyzing time series with an underlying piecewise linear trend. The kinks, knots, or changes in slope of the estimated trend can be interpreted as abrupt changes or events in the underlying dynamics of the time series. Using specialized interior-point methods, $\ell_1$ trend filtering can be carried out with not much more effort than H-P filtering; in particular, the number of arithmetic operations required grows linearly with the number of data points. We describe the method and some of its basic properties and give some illustrative examples. We show how the method is related to $\ell_1$ regularization-based methods in sparse signal recovery and feature selection, and we list some extensions of the basic method.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Boyd, S., & Vandenberghe, L. (2004) · doi:10.1017/cbo9780511804441 · Cited by 56,601
Self-citationRegression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
The Elements of Statistical Learning
Hastie, T., Friedman, J., & Tibshirani, R. (2001) · Springer Series in Statistics · doi:10.1007/978-0-387-21606-5 · Cited by 24,162
Donoho, D. L. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2006.871582 · Cited by 23,994
Regularization and Variable Selection Via the Elastic Net
Zou, H., & Hastie, T. (2005) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2005.00503.x · Cited by 20,957
Donoho, D. L. (2004) · Cited by 16,703
Nonlinear total variation based noise removal algorithms
Rudin, L. I., Osher, S., & Fatemi, E. (1992) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(92)90242-f · Cited by 15,704
Candes, E. J., Romberg, J., & Tao, T. (2006) · IEEE Transactions on Information Theory · doi:10.1109/tit.2005.862083 · Cited by 15,639
(2021) · A First Course in Statistical Programming with R · doi:10.1017/9781108993456.011 · Cited by 13,724
Koenker, R., & Bassett, G. (1978) · Econometrica · doi:10.2307/1913643 · Cited by 13,316
Cited by
Boyd, S., Parikh, N., Chu, E., Peleato, B., & Eckstein, J. (2011) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000016 · Cited by 17,075
Self-citationEnhancing Sparsity by Reweighted ℓ 1 Minimization
Candès, E. J., Wakin, M. B., & Boyd, S. P. (2008) · Journal of Fourier Analysis and Applications · doi:10.1007/s00041-008-9045-x · Cited by 4,863
Self-citationDeep learning for short-term traffic flow prediction
Polson, N. G., & Sokolov, V. O. (2017) · Transportation Research Part C: Emerging Technologies · doi:10.1016/j.trc.2017.02.024 · Cited by 1,015
Compressed Sensing With Quantized Measurements
Zymnis, A., Boyd, S., & Candes, E. (2010) · IEEE Signal Processing Letters · doi:10.1109/lsp.2009.2035667 · Cited by 316
Self-citationReal-Time Convex Optimization in Signal Processing
Mattingley, J., & Boyd, S. (2010) · IEEE Signal Processing Magazine · doi:10.1109/msp.2010.936020 · Cited by 300
Self-citation
Metadata
- Authors
- Kim, S.-J., Koh, K., Boyd, S., & Gorinevsky, D.
- Venue
- SIAM Review
- Published
- 2009-05
- Volume
- 51
- Issue
- 2
- Pages
- 339-360
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2089700840
- Cited by
- 615
- References
- 77
- FWCI
- 12.30
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: $\ell_1$ Trend Filtering. https://app.cochat.ai/papers/10.1137/070690274
- The paper
- Kim, S.-J., Koh, K., Boyd, S., & Gorinevsky, D. (2009). $\ell_1$ Trend Filtering. SIAM Review. https://doi.org/10.1137/070690274
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
