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自回归依赖回归中基于变量选择的参数变化检验AI 解读

We consider a regression model with autoregressive terms and propose significance tests for the detection of change points in this model. Our tests are applicable to both low- or moderate dimension and to high-dimension with sparse regressors. The dimension may be high from the practical point of view of economic and business applications, but in our theoretical framework it is fixed. To accommodate practically high dimension, variable selection is incorporated as an…

分布序列变点的在线监测AI 解读

We propose a method for the detection of a change point in a sequence {Fi} of distributions, which are available through a large number of observations at each i≥1. Under the null hypothesis, the distributions Fi are equal. Under the alternative hypothesis, there is a change point i∗>1, such that Fi=G for i≥i∗ and some unknown distribution G, which is not equal to F1. The change point, if it exists, is unknown, and the distributions before and after the potential change…

空间索引函数的主成分分析AI 解读

We develop an expansion, similar in some respects to the Karhunen–Loève expansion, but which is more suitable for functional data indexed by spatial locations on a grid. Unlike the traditional Karhunen–Loève expansion, it takes into account the spatial dependence between the functions. By doing so, it provides a more efficient dimension reduction tool, both theoretically and in finite samples, for functional data with moderate spatial dependence. For such data, it also…

函数型时间序列的周期性检验AI 解读

We derive several tests for the presence of a periodic component in a time series of functions. We consider both the traditional setting in which the periodic functional signal is contaminated by functional white noise, and a more general setting of a weakly dependent contaminating process. Several forms of the periodic component are considered. Our tests are motivated by the likelihood principle and fall into two broad categories, which we term multivariate and fully…

Motivated by the problem of the detection of a change point in the mean structure of yield curves, we introduce several methods to test the null hypothesis that the mean structure of a time series of curves does not change. The mean structure does not refer merely to the level of the curves, but also to their range and other aspects of their shape, most prominently concavity. The performance of the tests depends on whether possible break points in the error structure, which…

时空均值函数变化的检测AI 解读

Summary The paper develops inferential methodology for detecting a change in the annual pattern of an environmental variable measured at fixed locations in a spatial region. Using a framework built on functional data analysis, we model observations as a collection of function-valued time sequences available at many sites. Each sequence is modelled as an annual mean function, which may change, plus a sequence of error functions, which are spatially correlated. The tests…

函数型时间序列的平稳性检验AI 解读

Economic and financial data often take the form of a collection of curves observed consecutively over time. Examples include, intraday price curves, yield and term structure curves, and intraday volatility curves. Such curves can be viewed as a time series of functions. A fundamental issue that must be addressed, before an attempt is made to statistically model such data, is whether these curves, perhaps suitably transformed, form a stationary functional time series. This…

函数型时间序列的均值估计与两样本检验AI 解读

Summary The paper is concerned with inference based on the mean function of a functional time series. We develop a normal approximation for the functional sample mean and then focus on the estimation of the asymptotic variance kernel. Using these results, we develop and asymptotically justify testing procedures for the equality of means in two functional samples exhibiting temporal dependence. Evaluated by means of a simulation study and application to a real data set, these…

长记忆分数阶单整过程的脉冲响应AI 解读

Fractionally integrated time series, which have become an important modeling tool over the last two decades, are obtained by applying the fractional filter $(1 - L)^{ - d} = \sum\nolimits_{n = 0}^\infty {b_n } L^n$ to a weakly dependent (short memory) sequence. Weakly dependent sequences are characterized by absolutely summable impulse response coefficients of their Wold representation. The weights b n decay at the rate n d −1 and are not absolutely summable…

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…

弱依赖函数型数据AI 解读

Functional data often arise from measurements on fine time grids and are obtained by separating an almost continuous time record into natural consecutive intervals, for example, days. The functions thus obtained form a functional time series, and the central issue in the analysis of such data consists in taking into account the temporal dependence of these functional observations. Examples include daily curves of financial transaction data and daily patterns of geophysical…

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),…

函数型观测独立性的 Portmanteau 综合检验AI 解读

In various fields, observations are curves over some natural time interval. These curves often arise from finely spaced measurements (e.g., in physical sciences and finance) or from smoothing unequally spaced sparse measurements. Recent years have seen the development of tools for analyzing such data in the growing field of functional data analysis. To validate the assumptions underlying these tools, it is important to verify that the functional observations form a simple…

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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…

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(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…

摘要暂缺

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.

平稳 ARCH 模型：依赖结构与中心极限定理AI 解读

This paper studies a broad class of nonnegative ARCH(∞) models. Sufficient conditions for the existence of a stationary solution are established and an explicit representation of the solution as a Volterra type series is found. Under our assumptions, the covariance function can decay slowly like a power function, falling just short of the long memory structure. A moving average representation in martingale differences is established, and the central limit theorem is proved.