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Search Results: 1 - 10 of 9333 matches for " Xiaofeng Shao "
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Testing for white noise under unknown dependence and its applications to goodness-of-fit for time series models
Xiaofeng Shao
Mathematics , 2009,
Abstract: 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's 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 the dependent white noise. Due to recent popularity of conditional heteroscedastic models (e.g., GARCH models), which imply nonlinear dependence with zero autocorrelation, there is a need to understand the asymptotic properties of the existing test statistics under unknown dependence. In this paper, we showed that the asymptotic null distribution of Box-Pierce's test statistic with general weights still holds under unknown weak dependence so long as the lag truncation number grows at an appropriate rate with increasing sample size. Further applications to diagnostic checking of the ARMA and FARIMA models with dependent white noise errors are also addressed. Our results go beyond earlier ones by allowing non-Gaussian and conditional heteroscedastic errors in the ARMA and FARIMA models and provide theoretical support for some empirical findings reported in the literature.
Nonstationarity-extended Whittle Estimation
Xiaofeng Shao
Mathematics , 2009,
Abstract: 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 FARIMA models with GARCH-type innovations. To cover nonstationary fractionally integrated processes, we extend the idea of Abadir, Distaso and Giraitis (2007, Journal of Econometrics 141, 1353-1384) and develop the nonstationarity-extended Whittle estimation. The resulting estimator is shown to be asymptotically normal and is more efficient than the tapered Whittle estimator. Finally, the results from a small simulation study are presented to corroborate our theoretical findings.
A generalized portmanteau test of independence between two stationary time series
Xiaofeng Shao
Mathematics , 2008,
Abstract: 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 Chen and Deo (2004, Econometric Theory 20, 382-416), who extended the applicability of 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 derived under fairly mild conditions. In particular, each time series is allowed to possess short memory, long memory or anti-persistence. A simulation study shows that the tests have reasonable size and power properties.
A self-normalized approach to confidence interval construction in time series
Xiaofeng Shao
Statistics , 2010,
Abstract: 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 choosing 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 normalizing matrix is computed using recursive estimates. Under mild conditions, we establish the theoretical validity of our method for a broad class of statistics that are functionals of the empirical distribution of fixed or growing dimension. From a practical point of view, our method is conceptually simple, easy to implement and can be readily used by the practitioner. Monte-Carlo simulations are conducted to compare the finite sample performance of the new method with those delivered by the normal approximation and the block bootstrap approach.
Method Research of Earthquake Prediction and Volcano Prediction in Italy  [PDF]
Lijun Chen, Xiaofeng Chen, Lei Shao
International Journal of Geosciences (IJG) , 2015, DOI: 10.4236/ijg.2015.69076
Abstract: This paper adopts the earthquake catalogue of the European Mediterranean Seismological Centre (EMSC), in accordance with the principles of Seismo-Geothermics Theory and the concept of seismic cone; it discusses the integrity of the earthquake catalogue and the overview of Mediterranean seismic cones; it focuses on the structural details and structural feature of the Italian branch of the Mediterranean seismic cone; it deduces the precursory process of subcrustal earthquake activities before two earthquakes magnitude over 6 and the eruptions of Etna volcano since 2005; then it summarizes the prediction working method of Seismo-Geothermics on estimating the general shell strength, the general period, and the rough location of future earthquake or volcano activities; and finally it discusses and explains some possible problems. The principle and working process of this method were testified in card No. 0419 in 2012, the author’s prediction card, which can apply to predict for intracrustal strong earthquakes and volcano activities within the global twenty four seismic cones. The purpose of this paper is to develop the tools and methods of the prediction of future earthquake and volcano.
Fixed-smoothing asymptotics for time series
Xianyang Zhang,Xiaofeng Shao
Statistics , 2012, DOI: 10.1214/13-AOS1113
Abstract: 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 correctness of a new bootstrap method, the Gaussian dependent bootstrap, in the context of Gaussian location model.
On the Coverage Bound Problem of Empirical Likelihood Methods For Time Series
Xianyang Zhang,Xiaofeng Shao
Statistics , 2014,
Abstract: The upper bounds on the coverage probabilities of the confidence regions based on blockwise empirical likelihood [Kitamura (1997)] and nonstandard expansive empirical likelihood [Nordman et al. (2013)] methods for time series data are investigated via studying the probability for the violation of 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 the fixed-b asymptotics, which has been recently shown to provide a more accurate approximation to the finite sample distribution than the conventional chi-square approximation. Our theoretical and numerical findings suggest that both the finite sample and large sample upper bounds for coverage probabilities are strictly less than one and the blockwise empirical likelihood confidence region can exhibit serious undercoverage when (i) the dimension of moment conditions is moderate or large; (ii) the time series dependence is positively strong; or (iii) the block size is large relative to sample size. A similar finite sample coverage problem occurs for the nonstandard expansive empirical likelihood. To alleviate the coverage bound problem, we propose to penalize both empirical likelihood methods by relaxing the convex hull constraint. Numerical simulations and data illustration demonstrate the effectiveness of our proposed remedies in terms of delivering confidence sets with more accurate coverage.
Two sample inference for the second-order property of temporally dependent functional data
Xianyang Zhang,Xiaofeng Shao
Statistics , 2015, DOI: 10.3150/13-BEJ592
Abstract: Motivated by the need to statistically quantify the difference between two spatio-temporal datasets that arise in climate downscaling studies, we propose new tests to detect the differences of the covariance operators and their associated characteristics of two functional time series. Our two sample tests are constructed on the basis of functional principal component analysis and self-normalization, the latter of which is a new studentization technique recently developed for the inference of a univariate time series. Compared to the existing tests, our SN-based tests allow for weak dependence within each sample and it is robust to the dependence between the two samples in the case of equal sample sizes. Asymptotic properties of the SN-based test statistics are derived under both the null and local alternatives. Through extensive simulations, our SN-based tests are shown to outperform existing alternatives in size and their powers are found to be respectable. The tests are then applied to the gridded climate model outputs and interpolated observations to detect the difference in their spatial dynamics.
A general approach to the joint asymptotic analysis of statistics from sub-samples
Stanislav Volgushev,Xiaofeng Shao
Statistics , 2013,
Abstract: In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such statistics is challenging since it typically involves a nontrivial verification of technical conditions and tedious case-by-case asymptotic analysis. In this paper, we provide a novel technique that allows to circumvent those problems in a general setting. Our approach consists of two major steps: a probabilistic part which is mainly concerned with weak convergence of sequential empirical processes, and an analytic part providing general ways to extend this weak convergence to functionals of the sequential empirical process. Our theory provides a unified treatment of asymptotic distributions for a large class of statistics, including recently proposed self-normalized statistics and sub-sampling based p-values. In addition, we comment on the consistency of bootstrap procedures and obtain general results on compact differentiability of certain mappings that seem to be of independent interest.
Comparative Study of Global Seismicity on the Hot Engine Belt and the Cooling Seismic Belt—Improvement on Research Ideas of Earthquake Prediction  [PDF]
Lijun Chen, Xiaofeng Chen, Fangfang Wan, Pinzhong Li, Lei Shao
International Journal of Geosciences (IJG) , 2015, DOI: 10.4236/ijg.2015.67060
Abstract: The study in this paper analyzes and compares the distribution on the global engine active seismic zone and cooling seismic belt basing on the ANSS earthquake catalog from Northern California Earthquake Data Center. An idea of the seismogenesis and earthquake prediction research is achieved by showing the stratigraphic structure in the hot engine belt. The results show that the main engine and its seismic cones are the global seismic activity area, as well as the subject of global geological disaster. Based on the conjecture of other stratum structure, the energy of crustal strong earthquake and volcano activities probably originates from the deep upper mantle. It is suggested that the research on earthquake and volcano prediction should focus on the monitor and analysis on the sub-crustal earthquake activities.
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