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author:

Zhong, Chen (Zhong, Chen.) [1] | Zhang, Yuanyuan (Zhang, Yuanyuan.) [2] | Yang, Lijian (Yang, Lijian.) [3]

Indexed by:

Scopus SCIE

Abstract:

A kernel distribution estimator (KDE) is obtained based on residuals of innovation distribution in ARCH time series. The deviation between KDE and the innovation distribution function is shown to converge to a Gaussian process. Based on this convergence, a smooth simultaneous confidence band is constructed for the innovation distribution and an invariant procedure proposed for testing the symmetry of innovation distribution function. Quantiles are further estimated from the KDE, and multi-step-ahead prediction intervals (PIs) of future observations are constructed using the estimated quantiles, which achieve asymptotically the nominal prediction level. The multi-step-ahead PI is constructed for the S&P 500 daily returns series with satisfactory performance, which corroborates the asymptotic theory.

Keyword:

Brownian motion Conditional symmetry Kernel distribution estimator Prediction interval Simultaneous confidence band

Community:

  • [ 1 ] [Zhong, Chen]Fuzhou Univ, Sch Math & Stat, Fuzhou 350108, Fujian, Peoples R China
  • [ 2 ] [Zhang, Yuanyuan]Soochow Univ, Sch Math Sci, Suzhou 215006, Jiangsu, Peoples R China
  • [ 3 ] [Yang, Lijian]Tsinghua Univ, Dept Stat & Data Sci, Beijing 100084, Peoples R China

Reprint 's Address:

  • [Yang, Lijian]Tsinghua Univ, Dept Stat & Data Sci, Beijing 100084, Peoples R China;;

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Source :

TEST

ISSN: 1133-0686

Year: 2024

Issue: 1

Volume: 34

Page: 48-68

1 . 2 0 0

JCR@2023

CAS Journal Grade:3

Cited Count:

WoS CC Cited Count:

SCOPUS Cited Count:

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 3

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