1,171 research outputs found
Regenerative block empirical likelihood for Markov chains
Empirical likelihood is a powerful semi-parametric method increasingly
investigated in the literature. However, most authors essentially focus on an
i.i.d. setting. In the case of dependent data, the classical empirical
likelihood method cannot be directly applied on the data but rather on blocks
of consecutive data catching the dependence structure. Generalization of
empirical likelihood based on the construction of blocks of increasing
nonrandom length have been proposed for time series satisfying mixing
conditions. Following some recent developments in the bootstrap literature, we
propose a generalization for a large class of Markov chains, based on small
blocks of various lengths. Our approach makes use of the regenerative structure
of Markov chains, which allows us to construct blocks which are almost
independent (independent in the atomic case). We obtain the asymptotic validity
of the method for positive recurrent Markov chains and present some simulation
results
Robust Inference of Risks of Large Portfolios
We propose a bootstrap-based robust high-confidence level upper bound (Robust
H-CLUB) for assessing the risks of large portfolios. The proposed approach
exploits rank-based and quantile-based estimators, and can be viewed as a
robust extension of the H-CLUB method (Fan et al., 2015). Such an extension
allows us to handle possibly misspecified models and heavy-tailed data. Under
mixing conditions, we analyze the proposed approach and demonstrate its
advantage over the H-CLUB. We further provide thorough numerical results to
back up the developed theory. We also apply the proposed method to analyze a
stock market dataset.Comment: 45 pages, 2 figure
Model Checks Using Residual Marked Empirical Processes
This paper proposes omnibus and directional tests for testing the goodness-of-fit of a parametric regression time series model. We use a general class of residual marked empirical processes as the building-blocks for estimation and testing of such models. First, we establish a weak convergence theorem under mild assumptions, which allows us to study in a unified way the asymptotic null distribution of the test statistics and their asymptotic behavior against Pitman's local alternatives. To approximate the asymptotic null distribution of test statistics we justify theoretically a bootstrap procedure. Also, some asymptotic theory for the estimation of the principal components of the residual marked processes is considered. This asymptotic theory is used to derive optimal directional tests and efficient estimation of regression parameters. Finally, a Monte Carlo study shows that the bootstrap and the asymptotic results provide good approximations for small sample sizes and an empirical application to the Canadian lynx data set is considered.
Estimation of Copula-Based Semiparametric Time Series Models
This paper studies the estimation of a class of copula-based semiparametric stationary Markov models. These models are characterized by nonparametric invariant (or marginal) distributions and parametric copula functions that capture the temporal dependence of the processes; the implied transition distributions are all semiparametric. Models in this class are easy to simulate, and can be expressed as semiparametric regression transformation models. One advantage of this copula approach is to separate out the temporal dependence(such as tail dependence) from the marginal behavior (such as fat tailedness) of a time series. We present conditions under which processes generated by models in this class are -mixing; naturally, these conditions depend only on the copula specification. Simple estimators of the marginal distribution and the copula parameter are provided, and their asymptotic properties are established under easily verifiable conditions. Estimators of important features of the transition distribution such as the (nonlinear) conditional moments and conditional quantiles are easily obtained from estimators of the marginal distribution and the copula parameter; their consistency and asymptotic normality can be obtained using the Delta method. In addition, the semiparametric conditional quantile estimators are automatically monotonic across quantiles.Copula; Nonlinear Markov models; Semiparametric estimation;Conditional quantile
Testing for Changes in Kendall's Tau
For a bivariate time series we want to detect
whether the correlation between and stays constant for all . We propose a nonparametric change-point test statistic based on
Kendall's tau and derive its asymptotic distribution under the null hypothesis
of no change by means a new U-statistic invariance principle for dependent
processes. The asymptotic distribution depends on the long run variance of
Kendall's tau, for which we propose an estimator and show its consistency.
Furthermore, assuming a single change-point, we show that the location of the
change-point is consistently estimated. Kendall's tau possesses a high
efficiency at the normal distribution, as compared to the normal maximum
likelihood estimator, Pearson's moment correlation coefficient. Contrary to
Pearson's correlation coefficient, it has excellent robustness properties and
shows no loss in efficiency at heavy-tailed distributions. We assume the data
to be stationary and P-near epoch dependent on an
absolutely regular process. The P-near epoch dependence condition constitutes a
generalization of the usually considered -near epoch dependence, , that does not require the existence of any moments. It is therefore very
well suited for our objective to efficiently detect changes in correlation for
arbitrarily heavy-tailed data
An overview of the goodness-of-fit test problem for copulas
We review the main "omnibus procedures" for goodness-of-fit testing for
copulas: tests based on the empirical copula process, on probability integral
transformations, on Kendall's dependence function, etc, and some corresponding
reductions of dimension techniques. The problems of finding asymptotic
distribution-free test statistics and the calculation of reliable p-values are
discussed. Some particular cases, like convenient tests for time-dependent
copulas, for Archimedean or extreme-value copulas, etc, are dealt with.
Finally, the practical performances of the proposed approaches are briefly
summarized
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