An empirical likelihood goodness-of-fit test for time series

Summary. Standard goodness-of-fit tests for a parametric regression model against a series of nonparametric alternatives are based on residuals arising from a fitted model. When a parametric regression model is compared with a nonparametric model, goodness-of-fit testing can be naturally approached by evaluating the likelihood of the parametric model within a nonparametric framework. We employ the empirical likelihood for an α -mixing process to formulate a test statistic that measures the goodness of fit of a parametric regression model. The technique is based on a comparison with kernel smoothing estimators. The empirical likelihood formulation of the test has two attractive features. One is its automatic consideration of the variation that is associated with the nonparametric fit due to empirical likelihood's ability to Studentize internally. The other is that the asymptotic distribution of the test statistic is free of unknown parameters, avoiding plug-in estimation. We apply the test to a discretized diffusion model which has recently been considered in financial market analysis.     

Uniformly strong consistency and Berry-Esseen bound of frequency polygons for α-mixing samples

In this article, the frequency polygon investigated by Scott is studied as a nonparametric estimator for α-mixing samples. By some known exponent and moment inequalities, we obtain the uniformly strong consistency and Berry-Esseen bound of the estimator. The present results relax the relevant conditions used by Carbon et al. Furthermore, the convergence rate of the uniformly asymptotic normality is derived, which is O(n^{? 1/11}) under the given conditions.     

Wavelet Estimator in Nonparametric Regression Model with Dependent Error’s Structure

In this article, we consider a nonparametric regression model with replicated observations based on the dependent error’s structure, for exhibiting dependence among the units. The wavelet procedures are developed to estimate the regression function. The moment consistency, the strong consistency, strong convergence rate and asymptotic normality of wavelet estimator are established under suitable conditions. A simulation study is undertaken to assess the finite sample performance of the proposed method.     

Precise large deviations for φ-mixing and UND random variables with long-tailed distributions

In this paper, we investigate the precise large deviations for sums of φ-mixing and UND random variables with long-tailed distributions. The asymptotic relations for non random sum and random sum of random variables with long-tailed distributions are obtained.     

Semiparametric Regression Smoothing of Non-linear Time Series

In this paper, we consider using a semiparametric regression approach to modelling non-linear autoregressive time series. Based on a finite series approximation to non-parametric components, an adaptive selection procedure for the number of summands in the series approximation is proposed. Meanwhile, a large sample study is detailed and a small sample simulation for the Mackey–Glass system is presented to support the large sample study.     

Normalité asymptotique d'estimateurs convergents du mode conditionnel

We state sufficient conditions for asymptotic normality of convergent estimates of the conditional mode, irrespective of data dependence, and give an application to α-mixing stationary processes.     

Distribution of the cross-correlations of squared residuals in ARIMA models

ABSTRACT The distribution of the cross-correlations of squared residuals from Box-Jenkins models is considered in very general conditions, and the asymptotic distribution is derived. A test for a lagged relationship in volatility for economic time series under instantaneous causality is proposed, and its empirical behaviour is studied. An example involving the international stock market's volatility is studied, and an interesting result is observed.     

Strong Consistency of Conditional Value-at-risk Estimate for ϕ-mixing Samples

In this article, we investigate the strong consistency of conditional value-at-risk estimate for ? ?mixing samples under mild conditions. Moreover, the corresponding strong consistency rate is also obtained.