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高频投资组合贝塔稳定性的序贯检验AI 解读

Despite substantial criticism, variants of the capital asset pricing model (CAPM) remain to this day the primary statistical tools for portfolio managers to assess the performance of financial assets. In the CAPM, the risk of an asset is expressed through its correlation with the market, widely known as the beta. There is now a general consensus among economists that these portfolio betas are time-varying and that, consequently, any appropriate analysis has to take this…

利用趋势回归分割均值非平稳时间序列AI 解读

In this paper, we provide a segmentation procedure for mean-nonstationary time series. The segmentation is obtained by casting the problem into the framework of detecting structural breaks in trending regression models in which the regressors are generated by suitably smooth functions. As test statistics we propose to use the maximally selected likelihood ratio statistics and a related statistics based on partial sums of weighted residuals. The main theoretical contribution…

函数型线性模型中的误差相关检验AI 解读

The paper proposes two inferential tests for error correlation in the functional linear model, which complement the available graphical goodness-of-fit checks. To construct them, finite dimensional residuals are computed in two different ways, and then their autocorrelations are suitably defined. From these autocorrelation matrices, two quadratic forms are constructed whose limiting distribution are chi-squared with known numbers of degrees of freedom (different for the two…

多元时间序列模型协方差结构的突变检测AI 解读

In this paper, we introduce an asymptotic test procedure to assess the stability of volatilities and cross-volatilites of linear and nonlinear multivariate time series models. The test is very flexible as it can be applied, for example, to many of the multivariate GARCH models established in the literature, and also works well in the case of high dimensionality of the underlying data. Since it is nonparametric, the procedure avoids the difficulties associated with parametric…

函数型观测均值变化的检测AI 解读

Summary Principal component analysis has become a fundamental tool of functional data analysis. It represents the functional data as Xi(t) = μ(t)+Σ1≤l<∞ηi, l+ vl(t), where μ is the common mean, vl are the eigenfunctions of the covariance operator and the ηi, l are the scores. Inferential procedures assume that the mean function μ(t) is the same for all values of i. If, in fact, the observations do not come from one population, but rather their mean changes at some point(s),…

多元时间序列回归模型序贯程序的检测延迟AI 解读

We consider a multiple regression model in which the explanatory variables are specified by time series. To sequentially test for the stability of the regression parameters in time, we introduce a detector which is based on the first excess time of a CUSUM-type statistic over a suitably constructed threshold function. The aim of this paper is to study the delay time associated with this detector. As our main result, we derive the limit distribution of the delay time and…

区分随机游走与均值变化备择AI 解读

We study test procedures that detect structural breaks in underlying data sequences. In particular, we wish to discriminate between different reasons for these changes, such as (1) shifting means, (2) random walk behavior, and (3) constant means but innovations switching from stationary to difference stationary behavior. Almost all procedures presently available in the literature are simultaneously sensitive to all three types of alternatives. The test statistics under…

非参数前沿估计量的渐近性质AI 解读

Aragon, Daouia, and Thomas-Agnan (2005, Econometric Theory 21, 358–389) introduced a new nonparametric frontier estimation. We prove the weak convergence of the empirical conditional quantile function. The distribution of the limit depends on the unknown conditional quantile density function. We provide a method to construct uniform confidence bands without estimating the conditional quantile density.

具有稳定型误差的温和爆炸自回归的极限定理AI 解读

We discuss the limiting behavior of the serial correlation coefficient in mildly explosive autoregression, where the error sequence is in the domain of attraction of an α-stable law, α ∈ (0,2]. Therein, the autoregressive coefficient ρ = ρn > 1 is assumed to satisfy the condition ρn → 1 such that n(ρn − 1) → ∞ as n → ∞. In contrast to the vast majority of existing literature in the area, no specific form of ρ is required. We show that the serial correlation coefficient…

摘要暂缺

区分长程依赖与均值变化AI 解读

We develop a testing procedure for distinguishing between a long-range dependent time series and a weakly dependent time series with change-points in the mean. In the simplest case, under the null hypothesis the time series is weakly dependent with one change in mean at an unknown point, and under the alternative it is long-range dependent. We compute the CUSUM statistic Tn, which allows us to construct an estimator k̂ of a change-point. We then compute the statistic Tn,1…

条件异方差时间序列的方差恒定性监测AI 解读

We propose several methods of on-line detection of a change in unconditional variance in a conditionally heteroskedastic time series. We follow the paradigm of Chu, Stinchcombe, and White (1996, Econometrica 64, 1045–1065) in which the first m observations are assumed to follow a stationary process and the monitoring scheme has asymptotically controlled probability of falsely rejecting the null hypothesis of no change. Our theory is applicable to broad classes of GARCH-type…

基于 GARCH 创新密度的拟合优度检验AI 解读

Testing goodness (or lack) of fit for distributions of observable and nonobservable random variables is one of the main topics in statistics. When they exist, the corresponding density functions and their shapes allow researchers to easily recognize the underlying distribution functions. The present paper is concerned with the densities of (unobservable) generalized autoregressive conditional heteroskedasticity (GARCH) innovations and also with developing goodness-of-fit…

随机过程积分泛函的收敛AI 解读

We investigate the convergence in distribution of integrals of stochastic processes satisfying a functional limit theorem. We allow a large class of continuous Gaussian processes in the limit. Depending on the continuity properties of the underlying process, local Lebesgue or Riemann integrability is required.We are grateful to the referees and Benedikt Pötscher for their helpful and constructive comments. The research of the first author was partially supported by OTKA…

GARCH(p,q) 模型的序贯变点检测AI 解读

We suggest a sequential monitoring scheme to detect changes in the parameters of a GARCH(p,q) sequence. The procedure is based on quasi-likelihood scores and does not use model residuals. Unlike for linear regression models, the squared residuals of nonlinear time series models such as generalized autoregressive conditional heteroskedasticity (GARCH) do not satisfy a functional central limit theorem with a Wiener process as a limit, so its boundary crossing probabilities…

GARCH 过程参数估计量的效率AI 解读

We propose a class of estimators for the parameters of a GARCH(p,q) sequence. We show that our estimators are consistent and asymptotically normal under mild conditions. The quasi-maximum likelihood and the likelihood estimators are discussed in detail. We show that the maximum likelihood estimator is optimal. If the tail of the distribution of the innovations is polynomial, even a quasi-maximum likelihood estimator based on exponential density performs better than the…

GARCH(1,1) 序列最大矩指数的估计AI 解读

We propose an estimator for the maximal moment exponent of a GARCH(1,1) sequence. We establish its consistency asymptotic normality with rate n−1/2. Finite sample properties are investigated by means of a small simulation study.The research for this paper was partially supported by NSF grant INT-0223262. István Berkes and Lajos Horváth were supported by the Hungarian National Foundation for Scientific Research, grant T 29621. Piotr Kokoszka and Lajos Horváth were supported…

GARCH 平方残差相关性的渐近理论AI 解读

We develop an asymptotic theory for quadratic forms of the autocorrelations of squared residuals from a GARCH(p,q) model. Denoting by , k ≥ 1, these autocorrelations computed from a realization of length n, we show that the statistic is a matrix computed from the data, converges to the chi-square distribution with K degrees of freedom for any 1 ≤ i1 < ··· < iK. Our results are valid under weak assumptions on the innovations and model coefficients that admit that arbitrary…

ARCH序列平方残差的经验过程AI 解读

We derive the asymptotic distribution of the sequential empirical process of the squared residuals of an ARCH(p) sequence. Unlike the residuals of an ARMA process, these residuals do not behave in this context like asymptotically independent random variables, and the asymptotic distribution involves a term depending on the parameters of the model. We show that in certain applications, including the detection of changes in the distribution of the unobservable innovations, our…

ARCH(p) 平方残差相关加权和的大样本分布AI 解读

We develop asymptotic theory for linear statistics of sample autocorrelations of squared residuals from an ARCH( p ) model. Our results are valid for most estimators used in practice and do not depend on the assumption of normality of the errors; the existence of the fourth moment is required. In several special cases, we identify the limit distributions as well-known functionals of a Brownian motion.

标准化 U 统计量最大值的极限定理及其应用AI 解读

We show that the maximally selected standardized U-statistic goes in distribution to an infinite sum of weighted chi-square random variables in the degenerate case. The result is applied to the detection of possible changes in the distribution of a sequence observation.

随机删失的 Koziol–Green 模型AI 解读

In the Koziol–Green (1976) model of random censorship the survival distribution of the censoring variables is some power, the censoring parameter, of the survival distribution of the lifetimes. Using a strong approximation result of Burke, Csörgó and Horv´th, we construct empirical exact confidence bands for the life distribution of the censored variable, and a randomly Efron-transformed variant of the usual product-limit process is shown to converge weakly to the Brownian…