ARTICLE | doi:10.20944/preprints201905.0311.v1
Subject: Business, Economics And Management, Econometrics And Statistics Keywords: Mallows criterion; Model averaging; Model selection; Shrinkage; Tuning parameter choice.
Online: 27 May 2019 (10:28:22 CEST)
Model selection and model averaging have been the popular approaches in handling modelling uncertainties. Fan and Li(2006) laid out a uniﬁed frame work for variable selection via penalized likelihood. The tuning parameter selection is vital in the optimization problem for the penalized estimators in achieving consistent selection and optimal estimation. Since the OLSpost-LASSO estimator by Belloni and Chernozhukov (2013), few studies have focused on the ﬁnite sample performances of the class of OLS post-penalty estimators with the tuning parameter choice determined by diﬀerent tuning parameter selection approaches. We aim to supplement the existing model selection literature by studying such a class of OLS post-selection estimators. Inspired by the Shrinkage Averaging Estimator (SAE) by Schomaker(2012) and the Mallows Model Averaging (MMA) criterion by Hansen (2007), we further propose a Shrinkage Mallows Model Averaging (SMMA) estimator for averaging high dimensional sparse models. Based on the Monte Carlo design by Wang et al. (2009) which features an expanding sparse parameter space as the sample size increases, our Monte Carlo design further considers the eﬀect of the eﬀective sample size and the degree of model sparsity on the ﬁnite sample performances of model selection and model averaging estimators. From our data examples, we ﬁnd that the OLS post-SCAD(BIC) estimator in ﬁnite sample outperforms most of the current penalized least squares estimators as long as the number of parameters does not exceed the sample size. In addition, the SMMA performs better given sparser models. This supports the use of the SMMA estimator when averaging high dimensional sparse models.
ARTICLE | doi:10.20944/preprints201807.0318.v1
Subject: Business, Economics And Management, Econometrics And Statistics Keywords: difference kernel estimator; integrated difference kernel estimator; M-estimation; Monte Carlo; nonparametric threshold regression
Online: 18 July 2018 (08:24:47 CEST)
This paper compares the finite sample performance of three non-parametric threshold estimators via Monte Carlo method. Our results show that the finite sample performance of the three estimators is not robust to the relative position of the threshold level along the distribution of threshold variable, especially when a structural change occurs at the tail part of the distribution.
ARTICLE | doi:10.20944/preprints201804.0076.v1
Subject: Business, Economics And Management, Finance Keywords: conditional dependence index; Kendall's Tau; leverage effect; nonparametric copula; tail dependence index; volatility feedback effect
Online: 6 April 2018 (11:17:36 CEST)
This paper studies the contemporaneous relationship between S&P 500 index returns and log-increments of the market volatility index (VIX) via a nonparametric copula method. Specifically, we propose a conditional dependence index to investigate how the dependence between the two series varies across different segments of the market return distribution. We find that: (a) the two series exhibit strong, negative, extreme tail dependence; (b) the negative dependence is stronger in extreme bearish markets than in extreme bullish markets; (c) the dependence gradually weakens as the market return moves toward the center of its distribution, or in quiet markets. The unique dependence structure supports the VIX as a barometer of markets' mood in general. Moreover, applying the proposed method to the S&P 500 returns and the implied variance (VIX²), we find that the nonparametric leverage effect is much stronger than the nonparametric volatility feedback effect, although, in general, both effects are weaker than the dependence relation between the market returns and the log-increments of the VIX.