Detecting the Change of Variance by Using Conditional Distribution with Diverse Copula Functions

2018 ◽  
pp. 145-154 ◽  
Author(s):  
Jong-Min Kim ◽  
Jaiwook Baik ◽  
Mitch Reller
Keyword(s):  
Conditional Distribution ◽  
Copula Functions

scholarly journals MIXED CAUSAL-NONCAUSAL AR PROCESSES AND THE MODELLING OF EXPLOSIVE BUBBLES

2019 ◽  
Vol 35 (6) ◽  
pp. 1234-1270 ◽  
Author(s):  
Sébastien Fries ◽  
Jean-Michel Zakoian
Keyword(s):  
Conditional Distribution ◽  
Stable Distribution ◽  
Financial Time Series ◽  
Domain Of Attraction ◽  
Real Data ◽  
Autoregressive Processes ◽  
Financial Time ◽  
Causal Representation ◽  
Heavy Tailed ◽  
Non Gaussian

Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.

NONLINEAR PANEL DATA MODELS WITH DISTRIBUTION-FREE CORRELATED RANDOM EFFECTS

2021 ◽  
pp. 1-25
Author(s):  
Yu-Chin Hsu ◽  
Ji-Liang Shiu
Keyword(s):  
Panel Data ◽  
Data Model ◽  
Conditional Distribution ◽  
Unobserved Heterogeneity ◽  
Random Effect ◽  
Data Models ◽  
Panel Data Model ◽  
Panel Data Models ◽  
Likelihood Functions ◽  
Correlated Random Effects

Under a Mundlak-type correlated random effect (CRE) specification, we first show that the average likelihood of a parametric nonlinear panel data model is the convolution of the conditional distribution of the model and the distribution of the unobserved heterogeneity. Hence, the distribution of the unobserved heterogeneity can be recovered by means of a Fourier transformation without imposing a distributional assumption on the CRE specification. We subsequently construct a semiparametric family of average likelihood functions of observables by combining the conditional distribution of the model and the recovered distribution of the unobserved heterogeneity, and show that the parameters in the nonlinear panel data model and in the CRE specification are identifiable. Based on the identification result, we propose a sieve maximum likelihood estimator. Compared with the conventional parametric CRE approaches, the advantage of our method is that it is not subject to misspecification on the distribution of the CRE. Furthermore, we show that the average partial effects are identifiable and extend our results to dynamic nonlinear panel data models.

Effects of covariates on alternating recurrent events in accelerated failure time models

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Moumita Chatterjee ◽  
Sugata Sen Roy
Keyword(s):  
Recurrent Events ◽  
Failure Time ◽  
Likelihood Method ◽  
Model Parameters ◽  
Accelerated Failure Time ◽  
Survival Times ◽  
Copula Functions ◽  
Event Time ◽  
Accelerated Failure Time Models ◽  
Accelerated Failure

AbstractIn this article, we model alternately occurring recurrent events and study the effects of covariates on each of the survival times. This is done through the accelerated failure time models, where we use lagged event times to capture the dependence over both the cycles and the two events. However, since the errors of the two regression models are likely to be correlated, we assume a bivariate error distribution. Since most event time distributions do not readily extend to bivariate forms, we take recourse to copula functions to build up the bivariate distributions from the marginals. The model parameters are then estimated using the maximum likelihood method and the properties of the estimators studied. A data on respiratory disease is used to illustrate the technique. A simulation study is also conducted to check for consistency.

scholarly journals HEYDE’S CHARACTERIZATION THEOREM FOR DISCRETE ABELIAN GROUPS

2010 ◽  
Vol 88 (1) ◽  
pp. 93-102 ◽  
Author(s):  
MARGARYTA MYRONYUK
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
Gaussian Distributions ◽  
Discrete Abelian Group

AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.

scholarly journals Asymptotic normality of conditional distribution estimation in the single index model

2017 ◽  
Vol 9 (1) ◽  
pp. 162-175
Author(s):  
Diaa Eddine Hamdaoui ◽  
Amina Angelika Bouchentouf ◽  
Abbes Rabhi ◽  
Toufik Guendouzi
Keyword(s):  
Distribution Function ◽  
Confidence Interval ◽  
Asymptotic Normality ◽  
Conditional Distribution ◽  
Conditional Distribution Function ◽  
Single Index ◽  
Index Model ◽  
Single Index Model ◽  
Distribution Estimation

AbstractThis paper deals with the estimation of conditional distribution function based on the single-index model. The asymptotic normality of the conditional distribution estimator is established. Moreover, as an application, the asymptotic (1 − γ) confidence interval of the conditional distribution function is given for 0 < γ < 1.

ON DEFAULT CORRELATION AND PRICING OF COLLATERALIZED DEBT OBLIGATION BY COPULA FUNCTIONS

2006 ◽  
Vol 05 (03) ◽  
pp. 483-493 ◽  
Author(s):  
PING LI ◽  
HOUSHENG CHEN ◽  
XIAOTIE DENG ◽  
SHUNMING ZHANG
Keyword(s):  
Credit Derivatives ◽  
Copula Function ◽  
Dependence Structure ◽  
Default Correlation ◽  
Specific Kind ◽  
Copula Functions ◽  
Recovery Rates ◽  
Collateralized Debt Obligation ◽  
Collateralized Debt ◽  
Debt Obligation

Default correlation is the key point for the pricing of multi-name credit derivatives. In this paper, we apply copulas to characterize the dependence structure of defaults, determine the joint default distribution, and give the price for a specific kind of multi-name credit derivative — collateralized debt obligation (CDO). We also analyze two important factors influencing the pricing of multi-name credit derivatives, recovery rates and copula function. Finally, we apply Clayton copula, in a numerical example, to simulate default times taking specific underlying recovery rates and average recovery rates, then price the tranches of a given CDO and then analyze the results.

Sign in / Sign up

Export Citation Format

Share Document