scholarly journals Smoothed Conditional Scale Function Estimation in AR(1)-ARCH(1) Processes

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Lema Logamou Seknewna ◽  
Peter Mwita Nyamuhanga ◽  
Benjamin Kyalo Muema
Keyword(s):  
Time Series ◽  
Quantile Regression ◽  
Kernel Smoothing ◽  
Asymptotic Properties ◽  
Scale Function ◽  
Function Estimation

The estimation of the Smoothed Conditional Scale Function for time series was taken out under the conditional heteroscedastic innovations by imitating the kernel smoothing in nonparametric QAR-QARCH scheme. The estimation was taken out based on the quantile regression methodology proposed by Koenker and Bassett. And the proof of the asymptotic properties of the Conditional Scale Function estimator for this type of process was given and its consistency was shown.

scholarly journals Asymptotic Distributions of M-Estimates for Parameters of Multivariate Time Series with Strong Mixing Property

2021 ◽  
Vol 5 (1) ◽  
pp. 19
Author(s):  
Alexander Kushnir ◽  
Alexander Varypaev
Keyword(s):  
Time Series ◽  
Asymptotic Normality ◽  
Multivariate Time Series ◽  
Asymptotic Properties ◽  
Asymptotic Distributions ◽  
Stationary Time Series ◽  
Strong Mixing ◽  
Statistical Estimates ◽  
Distribution Parameters ◽  
M Estimates

The publication is devoted to studying asymptotic properties of statistical estimates of the distribution parameters u∈Rq of a multidimensional random stationary time series zt∈Rm, t∈ℤ satisfying the strong mixing conditions. We consider estimates u^nδ(z¯n), z¯n=(z1T,…,znT)T∈Rmn that provide in asymptotic n→∞ the maximum values for some objective functions Qn(z¯n;u), which have properties similar to the well-known property of local asymptotic normality. These estimates are constructed by solving the equations δn(z¯n;u)=0, where δn(z¯n;u) are arbitrary functions for which δn(z¯n;u)−gradhQn(z¯n;u+n−1/2h)→0(n→∞) in Pn,u(z¯n)-probability uniformly on u∈U, were U is compact in Rq. In many cases, the estimates u^nδ(z¯n) have the same asymptotic properties as well-known M-estimates defined by equations u^nQ(z¯n)=arg maxu∈UQn(z¯n;u) but often can be much simpler computationally. We consider an algorithmic method for constructing estimates u^nδ(z¯n), which is similar to the accumulation method first proposed by R. Fischer and rigorously developed by L. Le Cam. The main theoretical result of the article is the proof of the theorem, in which conditions of the asymptotic normality of estimates u^nδ(z¯n) are formulated, and the expression is proposed for their matrix of asymptotic mean-square deviations limn→∞nEn,u{(u^δ(z¯n)−u)(u^δ(z¯n)−u)T}.

scholarly journals ASYMPTOTIC THEORY FOR NONLINEAR QUANTILE REGRESSION UNDER WEAK DEPENDENCE

2015 ◽  
Vol 32 (3) ◽  
pp. 686-713 ◽  
Author(s):  
Walter Oberhofer ◽  
Harry Haupt
Keyword(s):  
Quantile Regression ◽  
Asymptotic Normality ◽  
Regression Model ◽  
Asymptotic Theory ◽  
Asymptotic Properties ◽  
Covariance Estimation ◽  
First Order ◽  
Regression Quantiles ◽  
Quantile Regression Model ◽  
Consistency And Asymptotic Normality

This paper studies the asymptotic properties of the nonlinear quantile regression model under general assumptions on the error process, which is allowed to be heterogeneous and mixing. We derive the consistency and asymptotic normality of regression quantiles under mild assumptions. First-order asymptotic theory is completed by a discussion of consistent covariance estimation.

Investigating Local Dependence With Conditional Covariance Functions

1998 ◽  
Vol 23 (2) ◽  
pp. 129-151 ◽  
Author(s):  
Jeff Douglas ◽  
Hae Rim Kim ◽  
Brian Habing ◽  
Furong Gao
Keyword(s):  
Kernel Smoothing ◽  
Item Difficulty ◽  
Estimation Procedure ◽  
Local Dependence ◽  
Function Estimation ◽  
Conditional Covariance ◽  
Monotonic Transformation ◽  
Covariance Functions ◽  
Latent Space ◽  
Latent Ability

The local dependence of item pairs is investigated via a conditional covariance function estimation procedure. The conditioning variable used in the procedure is obtained by a monotonic transformation of total score on the remaining items. Intuitively, the conditioning variable corresponds to the unidimensional latent ability that is best measured by the test. The conditional covariance functions are estimated using kernel smoothing, and a standardization to adjust for the confounding effect of item difficulty is introduced. The particular standardization chosen is an adaptation of Yule’s coefficient of colligation. Several models of local dependence are discussed to explain special situations, such as speededness and latent space multidimensionality, in which the assumptions of unidimensionality and local independence are violated.

High-quantile regression for tail-dependent time series

Biometrika ◽  
2020 ◽  
Author(s):  
Ting Zhang
Keyword(s):  
Time Series ◽  
Quantile Regression ◽  
Limit Theorems ◽  
Tail Dependence ◽  
Serial Dependence ◽  
Response Distribution ◽  
Tail Region ◽  
Strongly Mixing ◽  
Regression Estimators ◽  
High Quantile

Summary Quantile regression is a popular and powerful method for studying the effect of regressors on quantiles of a response distribution. However, existing results on quantile regression were mainly developed for cases in which the quantile level is fixed, and the data are often assumed to be independent. Motivated by recent applications, we consider the situation where (i) the quantile level is not fixed and can grow with the sample size to capture the tail phenomena, and (ii) the data are no longer independent, but collected as a time series that can exhibit serial dependence in both tail and non-tail regions. To study the asymptotic theory for high-quantile regression estimators in the time series setting, we introduce a tail adversarial stability condition, which had not previously been described, and show that it leads to an interpretable and convenient framework for obtaining limit theorems for time series that exhibit serial dependence in the tail region, but are not necessarily strongly mixing. Numerical experiments are conducted to illustrate the effect of tail dependence on high-quantile regression estimators, for which simply ignoring the tail dependence may yield misleading $p$-values.

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