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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Bibliographic Details
Published in:Statistical papers (Berlin, Germany) Vol. 65; no. 5; pp. 2973 - 3006
Main Authors: Nasir, Muhammad Jaffri Mohd, Khan, Ramzan Nazim, Nair, Gopalan, Nur, Darfiana
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2024
Springer Nature B.V
Subjects:
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
SETAR
Group LASSO
Sparsity conditions
Karush–Kuhn–Tucker
algorithm
ISSN:0932-5026, 1613-9798
Online Access:Get full text
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Summary: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.
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ISSN:0932-5026
1613-9798
DOI:10.1007/s00362-023-01472-7