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面向海量数据的子抽样双重自助法AI 解读

The bootstrap is a popular and powerful method for assessing precision of estimators and inferential methods. However, for massive datasets that are increasingly prevalent, the bootstrap becomes prohibitively costly in computation and its feasibility is questionable even with modern parallel computing platforms. Recently, Kleiner and co-authors proposed a method called BLB (bag of little bootstraps) for massive data, which is more computationally scalable with little…

时间序列经验似然方法的覆盖率上界问题AI 解读

Summary The upper bounds on the coverage probabilities of the confidence regions based on blockwise empirical likelihood and non-standard expansive empirical likelihood methods for time series data are investigated via studying the probability of violating the convex hull constraint. The large sample bounds are derived on the basis of the pivotal limit of the blockwise empirical log-likelihood ratio obtained under fixed b asymptotics, which has recently been shown to provide…

时间序列自归一化：近期进展综述AI 解读

This article reviews some recent developments on the inference of time series data using the self-normalized approach. We aim to provide a detailed discussion about the use of self-normalization in different contexts and highlight distinctive feature associated with each problem and connections among these recent developments. The topics covered include: confidence interval construction for a parameter in a weakly dependent stationary time series setting, change point…

弱依赖与异方差误差下时间序列回归模型的推断AI 解读

Motivated by the need to assess the significance of the trend in some macroeconomic series, this article considers inference of a parameter in parametric trend functions when the errors exhibit certain degrees of nonstationarity with changing unconditional variances. We adopt the recently developed self-normalized approach to avoid the difficulty involved in the estimation of the asymptotic variance of the ordinary least-square estimator. The limiting distribution of the…

鞅差相关及其在高维变量筛选中的应用AI 解读

In this article, we propose a new metric, the so-called martingale difference correlation, to measure the departure of conditional mean independence between a scalar response variable V and a vector predictor variable U. Our metric is a natural extension of distance correlation proposed by Székely, Rizzo, and Bahirov, which is used to measure the dependence between V and U. The martingale difference correlation and its empirical counterpart inherit a number of desirable…

时间序列的固定平滑渐近理论AI 解读

In this paper, we derive higher order Edgeworth expansions for the finite sample distributions of the subsampling-based $t$-statistic and the Wald statistic in the Gaussian location model under the so-called fixed-smoothing paradigm. In particular, we show that the error of asymptotic approximation is at the order of the reciprocal of the sample size and obtain explicit forms for the leading error terms in the expansions. The results are used to justify the second-order…

具有相依误差的线性模型推断AI 解读

Summary The paper is concerned with inference for linear models with fixed regressors and weakly dependent stationary time series errors. Theoretically, we obtain asymptotic normality for the M-estimator of the regression parameter under mild conditions and establish a uniform Bahadur representation for recursive M-estimators. Methodologically, we extend the recently proposed self-normalized approach of Shao from stationary time series to the regression set-up, where the…

固定 b 子抽样与区块自助法：基于 p 值校准的改进置信集AI 解读

Summary Subsampling and block-based bootstrap methods have been used in a wide range of inference problems for time series. To accommodate the dependence, these resampling methods involve a bandwidth parameter, such as the subsampling window width and block size in the block-based bootstrap. In empirical work, using different bandwidth parameters could lead to different inference results, but traditional first-order asymptotic theory does not capture the choice of the…

未知依赖下借助自助法的白噪声谱检验AI 解读

To test for the white noise null hypothesis, we study the Cramér-von Mises test statistic that is based on the sample spectral distribution function. Since the critical values of the test statistic are difficult to obtain, we propose a blockwise wild bootstrap procedure to approximate its asymptotic null distribution. Using a Hilbert space approach, we establish the weak convergence of the difference between the sample spectral distribution function and the true spectral…

未知依赖下的白噪声检验及时间序列模型诊断AI 解读

Testing for white noise has been well studied in the literature of econometrics and statistics. For most of the proposed test statistics, such as the well-known Box–Pierce test statistic with fixed lag truncation number, the asymptotic null distributions are obtained under independent and identically distributed assumptions and may not be valid for dependent white noise. Because of recent popularity of conditional heteroskedastic models (e.g., generalized autoregressive…

时间序列变点检验AI 解读

This article considers the CUSUM-based (cumulative sum) test for a change point in a time series. In the case of testing for a mean shift, the traditional Kolmogorov–Smirnov test statistic involves a consistent long-run variance estimator, which is needed to make the limiting null distribution free of nuisance parameters. The commonly used lag-window type long-run variance estimator requires to choose a bandwidth parameter and its selection is a difficult task in practice.…

扩展至非平稳情形的 Whittle 估计AI 解读

For long memory time series models with uncorrelated but dependent errors, we establish the asymptotic normality of the Whittle estimator under mild conditions. Our framework includes the widely used fractional autoregressive integrated moving average models with generalized autoregressive conditional heteroskedastic-type innovations. To cover nonstationary fractionally integrated processes, we extend the idea of Abadir, Distaso, and Giraitis (2007, Journal of Econometrics…

时间序列置信区间构造的自归一化方法AI 解读

Summary We propose a new method to construct confidence intervals for quantities that are associated with a stationary time series, which avoids direct estimation of the asymptotic variances. Unlike the existing tuning-parameter-dependent approaches, our method has the attractive convenience of being free of any user-chosen number or smoothing parameter. The interval is constructed on the basis of an asymptotically distribution-free self-normalized statistic, in which the…

相依野生自助法AI 解读

We propose a new resampling procedure, the dependent wild bootstrap, for stationary time series. As a natural extension of the traditional wild bootstrap to time series setting, the dependent wild bootstrap offers a viable alternative to the existing block-based bootstrap methods, whose properties have been extensively studied over the last two decades. Unlike all of the block-based bootstrap methods, the dependent wild bootstrap can be easily extended to irregularly spaced…

两个平稳时间序列独立性的广义综合检验AI 解读

We propose generalized portmanteau-type test statistics in the frequency domain to test independence between two stationary time series. The test statistics are formed analogous to the one in the paper by Chen and Deo (2004, Econometric Theory 20, 382–416), who extended the applicability of the portmanteau goodness-of-fit test to the long memory case. Under the null hypothesis of independence, the asymptotic standard normal distributions of the proposed statistics are…

二次型的极限定理及其应用AI 解读

We consider quadratic forms of martingale differences and establish a central limit theorem under mild and easily verifiable conditions. By approximating Fourier transforms of stationary processes by martingales, our central limit theorem is applied to the smoothed periodogram estimate of spectral density functions. Our results go beyond earlier ones by allowing a variety of nonlinear time series and by avoiding strong mixing and/or summability conditions on joint…

非线性过程分数阶单整参数的局部 Whittle 估计AI 解读

We study asymptotic properties of the local Whittle estimator of the long memory parameter for a wide class of fractionally integrated nonlinear time series models. In particular, we solve the conjecture posed by Phillips and Shimotsu (2004, Annals of Statistics 32, 656–692) for Type I processes under our framework, which requires a global smoothness condition on the spectral density of the short memory component. The formulation allows the widely used fractional…

非线性时间序列的渐近谱理论AI 解读

We consider asymptotic problems in spectral analysis of stationary causal processes. Limiting distributions of periodograms and smoothed periodogram spectral density estimates are obtained and applications to the spectral domain bootstrap are given. Instead of the commonly used strong mixing conditions, in our asymptotic spectral theory we impose conditions only involving (conditional) moments, which are easily verifiable for a variety of nonlinear time series.