基于傅立叶近似的时变阈值高维阈值模型

IF 0.7 4区 经济学 Q3 ECONOMICS Studies in Nonlinear Dynamics and Econometrics Pub Date : 2022-05-30 DOI:10.1515/snde-2021-0047
Lixiong Yang
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引用次数: 1

摘要

摘要本文研究了用傅立叶函数近似时变阈值的高维阈值模型。我们开发了回归系数和阈值参数的加权LASSO估计器。我们的LASSO估计器不仅可以选择协变量,还可以区分线性模型和阈值模型。我们导出了预测风险的非渐近预言不等式,回归系数的l1和l∞界,并给出了时变阈值估计器的l1估计误差的上界。边界可以很容易地转化为预测和估计的渐近一致性。我们还建立了基于l∞边界的变量选择一致性和阈值检测一致性。通过蒙特卡罗模拟,我们表明,在变量选择方面,阈值化的LASSO在有限样本中工作得相当好,并且即使在阈值中没有时变特征的情况下,在估计过程中允许傅立叶近似也几乎没有危害。相反,当阈值是时变的但被错误地指定为常数时,估计和变量选择是不一致的。该模型通过对著名的债务增长关系的实证应用进行了说明。
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High dimensional threshold model with a time-varying threshold based on Fourier approximation
Abstract This paper studies high-dimensional threshold models with a time-varying threshold approximated using a Fourier function. We develop a weighted LASSO estimator of regression coefficients as well as the threshold parameters. Our LASSO estimator can not only select covariates but also distinguish between linear and threshold models. We derive non-asymptotic oracle inequalities for the prediction risk, the l 1 and l ∞ bounds for regression coefficients, and provide an upper bound on the l 1 estimation error of the time-varying threshold estimator. The bounds can be translated easily into asymptotic consistency for prediction and estimation. We also establish the variable selection consistency and threshold detection consistency based on the l ∞ bounds. Through Monte Carlo simulations, we show that the thresholded LASSO works reasonably well in finite samples in terms of variable selection, and there is little harmness by the allowance for Fourier approximation in the estimation procedure even when there is no time-varying feature in the threshold. On the contrary, the estimation and variable selection are inconsistent when the threshold is time-varying but being misspecified as a constant. The model is illustrated with an empirical application to the famous debt-growth nexus.
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来源期刊
CiteScore
1.40
自引率
12.50%
发文量
34
期刊介绍: Studies in Nonlinear Dynamics & Econometrics (SNDE) recognizes that advances in statistics and dynamical systems theory may increase our understanding of economic and financial markets. The journal seeks both theoretical and applied papers that characterize and motivate nonlinear phenomena. Researchers are required to assist replication of empirical results by providing copies of data and programs online. Algorithms and rapid communications are also published.
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