Active-set based block coordinate descent algorithm in group LASSO for self-exciting threshold autoregressive model
Group LASSO (gLASSO) estimator has been recently proposed to estimate thresholds for the self-exciting threshold autoregressive model, and a group least angle regression ( gLAR ) algorithm has been applied to obtain an approximate solution to the optimization problem. Although gLAR algorithm is comp...
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| Published in: | Statistical papers (Berlin, Germany) Vol. 65; no. 5; pp. 2973 - 3006 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.07.2024
Springer Nature B.V |
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| ISSN: | 0932-5026, 1613-9798 |
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| Abstract | Group LASSO (gLASSO) estimator has been recently proposed to estimate thresholds for the
self-exciting
threshold autoregressive model, and a group least angle regression (
gLAR
) algorithm has been applied to obtain an approximate solution to the optimization problem. Although
gLAR
algorithm is computationally fast, it has been reported that the algorithm tends to estimate too many irrelevant thresholds along with the relevant ones. This paper develops an
active-set
based block coordinate descent (
aBCD
) algorithm as an exact optimization method for gLASSO to improve the performance of estimating relevant thresholds. Methods and strategy for choosing the appropriate values of shrinkage parameter for gLASSO are also discussed. To consistently estimate relevant thresholds from the threshold set obtained by the gLASSO, the backward elimination algorithm (
BEA
) is utilized. We evaluate numerical efficiency of the proposed algorithms, along with the Single-Line-Search (
SLS
) and the
gLAR
algorithms through simulated data and real data sets. Simulation studies show that the
SLS
and
aBCD
algorithms have similar performance in estimating thresholds although the latter method is much faster. In addition, the
aBCD-BEA
can sometimes outperform
gLAR-BEA
in terms of estimating the correct number of thresholds under certain conditions. The results from case studies have also shown that
aBCD-BEA
performs better in identifying important thresholds. |
|---|---|
| AbstractList | Group LASSO (gLASSO) estimator has been recently proposed to estimate thresholds for the
self-exciting
threshold autoregressive model, and a group least angle regression (
gLAR
) algorithm has been applied to obtain an approximate solution to the optimization problem. Although
gLAR
algorithm is computationally fast, it has been reported that the algorithm tends to estimate too many irrelevant thresholds along with the relevant ones. This paper develops an
active-set
based block coordinate descent (
aBCD
) algorithm as an exact optimization method for gLASSO to improve the performance of estimating relevant thresholds. Methods and strategy for choosing the appropriate values of shrinkage parameter for gLASSO are also discussed. To consistently estimate relevant thresholds from the threshold set obtained by the gLASSO, the backward elimination algorithm (
BEA
) is utilized. We evaluate numerical efficiency of the proposed algorithms, along with the Single-Line-Search (
SLS
) and the
gLAR
algorithms through simulated data and real data sets. Simulation studies show that the
SLS
and
aBCD
algorithms have similar performance in estimating thresholds although the latter method is much faster. In addition, the
aBCD-BEA
can sometimes outperform
gLAR-BEA
in terms of estimating the correct number of thresholds under certain conditions. The results from case studies have also shown that
aBCD-BEA
performs better in identifying important thresholds. Group LASSO (gLASSO) estimator has been recently proposed to estimate thresholds for the self-exciting threshold autoregressive model, and a group least angle regression (gLAR) algorithm has been applied to obtain an approximate solution to the optimization problem. Although gLAR algorithm is computationally fast, it has been reported that the algorithm tends to estimate too many irrelevant thresholds along with the relevant ones. This paper develops an active-set based block coordinate descent (aBCD) algorithm as an exact optimization method for gLASSO to improve the performance of estimating relevant thresholds. Methods and strategy for choosing the appropriate values of shrinkage parameter for gLASSO are also discussed. To consistently estimate relevant thresholds from the threshold set obtained by the gLASSO, the backward elimination algorithm (BEA) is utilized. We evaluate numerical efficiency of the proposed algorithms, along with the Single-Line-Search (SLS) and the gLAR algorithms through simulated data and real data sets. Simulation studies show that the SLS and aBCD algorithms have similar performance in estimating thresholds although the latter method is much faster. In addition, the aBCD-BEA can sometimes outperform gLAR-BEA in terms of estimating the correct number of thresholds under certain conditions. The results from case studies have also shown that aBCD-BEA performs better in identifying important thresholds. |
| Author | Khan, Ramzan Nazim Nair, Gopalan Nasir, Muhammad Jaffri Mohd Nur, Darfiana |
| Author_xml | – sequence: 1 givenname: Muhammad Jaffri Mohd orcidid: 0000-0001-9423-0218 surname: Nasir fullname: Nasir, Muhammad Jaffri Mohd email: jaffri.mn@umk.edu.my organization: Faculty of Entrepreneurship and Business, Universiti Malaysia Kelantan – sequence: 2 givenname: Ramzan Nazim orcidid: 0000-0003-3349-5006 surname: Khan fullname: Khan, Ramzan Nazim organization: Department of Mathematics and Statistics, The University of Western Australia – sequence: 3 givenname: Gopalan orcidid: 0000-0003-3883-4986 surname: Nair fullname: Nair, Gopalan organization: Department of Mathematics and Statistics, The University of Western Australia – sequence: 4 givenname: Darfiana orcidid: 0000-0002-7690-1097 surname: Nur fullname: Nur, Darfiana organization: Department of Mathematics and Statistics, The University of Western Australia |
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| Snippet | Group LASSO (gLASSO) estimator has been recently proposed to estimate thresholds for the
self-exciting
threshold autoregressive model, and a group least angle... Group LASSO (gLASSO) estimator has been recently proposed to estimate thresholds for the self-exciting threshold autoregressive model, and a group least angle... |
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| SubjectTerms | Algorithms Autoregressive models Economic Theory/Quantitative Economics/Mathematical Methods Economics Finance Group theory Insurance Management Mathematics and Statistics Operations Research/Decision Theory Optimization Performance enhancement Probability Theory and Stochastic Processes Regular Article Statistics Statistics for Business Thresholds |
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| Title | Active-set based block coordinate descent algorithm in group LASSO for self-exciting threshold autoregressive model |
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