Feature Selection in Jump Models

32 Pages Posted: 18 Mar 2021

See all articles by Peter Nystrup

Peter Nystrup

Lund University; Technical University of Denmark - Department of Applied Mathematics and Computer Science

Petter N. Kolm

New York University (NYU) - Courant Institute of Mathematical Sciences

Erik Lindstrom

Lund University

Date Written: March 16, 2021

Abstract

Jump models switch infrequently between states to fit a sequence of data while taking the ordering of the data into account. We propose a new framework for joint feature selection, parameter and state-sequence estimation in jump models. Feature selection is necessary in high-dimensional settings where the number of features is large compared to the number of observations and the underlying states differ only with respect to a subset of the features. We develop and implement a coordinate descent algorithm that alternates between selecting the features and estimating the model parameters and state sequence, which scales to large data sets with large numbers of (noisy) features. We demonstrate the usefulness of the proposed framework by comparing it with a number of other methods on both simulated and real data in the form of financial returns, protein sequences, and text. The resulting sparse jump model outperforms all other methods considered and is remarkably robust to noise.

Keywords: High-dimensional; sequential data; time series; clustering; unsupervised learning; regime switching

JEL Classification: C22, C38, C51, C58, C61, G11

Suggested Citation

Nystrup, Peter and Kolm, Petter N. and Lindstrom, Erik, Feature Selection in Jump Models (March 16, 2021). Available at SSRN: https://ssrn.com/abstract=3805831 or http://dx.doi.org/10.2139/ssrn.3805831

Peter Nystrup

Lund University ( email )

Box 117
Lund, SC Skane S221 00
Sweden

Technical University of Denmark - Department of Applied Mathematics and Computer Science ( email )

Denmark

Petter N. Kolm (Contact Author)

New York University (NYU) - Courant Institute of Mathematical Sciences ( email )

251 Mercer Street
New York, NY 10012
United States

Erik Lindstrom

Lund University ( email )

Box 117
Lund, SC Skane S221 00
Sweden

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