Prediction of Extremal Expectile Based on Regression Models With Heteroscedastic Extremes

Xu, Wen; Hou, Yanxi; Li, Deyuan

doi:10.1080/07350015.2020.1833890

Cited by 9 publications

(5 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Section: Resultsmentioning

confidence: 99%

“…Under heteroscedastic extremes, [5] develops a variant for the classical Hill estimator and shows that its asymptotic properties are similar to the traditional Hill estimator. In addition, [11] further develops the regression framework for heteroscedastic extremes and applies it to the prediction of conditional expectiles with extreme levels.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

EVIboost for the Estimation of Extreme Value Index under Heterogeneous Extremes

Hou¹,

Li²,

Wang³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

Modeling heterogeneity on heavy-tailed distributions under a regression framework is challenging, and classical statistical methodologies usually place conditions on the distribution models to facilitate the learning procedure. However, these conditions are likely to overlook the complex dependence structure between the heaviness of tails and the covariates. Moreover, data sparsity on tail regions also makes the inference method less stable, leading to largely biased estimates for extreme-related quantities. This paper proposes a gradient boosting algorithm to estimate a functional extreme value index with heterogeneous extremes. Our proposed algorithm is a data-driven procedure that captures complex and dynamic structures in tail distributions. We also conduct extensive simulation studies to show the prediction accuracy of the proposed algorithm. In addition, we apply our method to a real-world data set to illustrate the state-dependent and time-varying properties of heavy-tail phenomena in the financial industry.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

EVIboost for the Estimation of Extreme Value Index under Heterogeneous Extremes

Hou¹,

Li²,

Wang³

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Our dataset contains weekly market returns for four large commercial banks: Bank of America (BAC), Citigroup (C), JPMorgan Chase (JPM), and Wells Fargo (WFC). The entire period is from the first week of 1971 to the end of June 2013, which has been partly studied in Xu et al (2020) and Adrian and Brunnermeier (2016). The sample sizes for the four banks are 1771, 1386, 2210, and 2210, respectively, and we consider seven macro-economic variables as predictors/covariates: 1. x 1 : The weekly market return of S&P500; 2. x 2 : The change in the three-month yield from the Federal Reserve Board's H.15 release; 3. x 3 : Equity volatility, which is computed as the 22-day rolling standard deviation of the daily CRSP equity market return; 4. x 4 : The change in the credit spread between Baa bonds (rated by Moody's) and the ten-year Treasury rate from the Federal Reserve Board's H.15 release; 5. x 5 : The change in the slope of the yield curve, measured by the spread between the composite long-term bond yield and the three-month bill rate; 6. x 6 : A short-term TED spread, defined as the difference between the three-month LIBOR rate and the three-month secondary market treasury bill rate.…”

Section: Datamentioning

confidence: 99%

“…Under heteroscedastic extremes, Einmahl et al (2016) develops a variant for the classical Hill estimator and shows that its asymptotic properties are similar to the traditional Hill estimator. In addition, Xu et al (2020) further develops the regression framework for heteroscedastic extremes and applies it to the prediction of conditional expectiles with extreme levels.…”

Section: Introductionmentioning

confidence: 99%

EVIboost for the Estimation of Extreme Value Index Under Heterogeneous Extremes

Hou¹,

Li²,

Wang³

2022

Journal of Data Science

Self Cite

View full text Add to dashboard Cite

Modeling heterogeneity on heavy-tailed distributions under a regression framework is challenging, yet classical statistical methodologies usually place conditions on the distribution models to facilitate the learning procedure. However, these conditions will likely overlook the complex dependence structure between the heaviness of tails and the covariates. Moreover, data sparsity on tail regions makes the inference method less stable, leading to biased estimates for extreme-related quantities. This paper proposes a gradient boosting algorithm to estimate a functional extreme value index with heterogeneous extremes. Our proposed algorithm is a data-driven procedure capturing complex and dynamic structures in tail distributions. We also conduct extensive simulation studies to show the prediction accuracy of the proposed algorithm. In addition, we apply our method to a real-world data set to illustrate the state-dependent and time-varying properties of heavy-tail phenomena in the financial industry.

show abstract

“…Ref. [ 34 ] studied the estimation of extremal conditional expectile based on quantile regression and expectile regression models. Considering the advantages of EVaR, we will propose the estimation of the DTARCH model based on expectile regression theory.…”

Section: Introductionmentioning

confidence: 99%

The Financial Risk Measurement EVaR Based on DTARCH Models

Liu

Tan

et al. 2023

Entropy

View full text Add to dashboard Cite

The value at risk based on expectile (EVaR) is a very useful method to measure financial risk, especially in measuring extreme financial risk. The double-threshold autoregressive conditional heteroscedastic (DTARCH) model is a valuable tool in assessing the volatility of a financial asset’s return. A significant characteristic of DTARCH models is that their conditional mean and conditional variance functions are both piecewise linear, involving double thresholds. This paper proposes the weighted composite expectile regression (WCER) estimation of the DTARCH model based on expectile regression theory. Therefore, we can use EVaR to predict extreme financial risk, especially when the conditional mean and the conditional variance of asset returns are nonlinear. Unlike the existing papers on DTARCH models, we do not assume that the threshold and delay parameters are known. Using simulation studies, it has been demonstrated that the proposed WCER estimation exhibits adequate and promising performance in finite samples. Finally, the proposed approach is used to analyze the daily Hang Seng Index (HSI) and the Standard & Poor’s 500 Index (SPI).

show abstract

Prediction of Extremal Expectile Based on Regression Models With Heteroscedastic Extremes

Cited by 9 publications

References 29 publications

EVIboost for the Estimation of Extreme Value Index under Heterogeneous Extremes

EVIboost for the Estimation of Extreme Value Index under Heterogeneous Extremes

EVIboost for the Estimation of Extreme Value Index Under Heterogeneous Extremes

The Financial Risk Measurement EVaR Based on DTARCH Models

Contact Info

Product

Resources

About