Shibin Zhang

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• Professor
• Professor (Full) at Shanghai Normal University

Central limit theorems (CLTs) for frequency-domain statistics are fundamental tools in frequency domain analysis. However, for irregularly spaced data, they are still limited. In both the pure increasing domain and the mixed increasing domain asymptotic frameworks, three CLTs of frequency-domain statistics are established for the observations at un...

In this paper, we propose a novel frequency-domain test for multivariate time series white noise. The proposed test statistic is constructed by maximizing two normalized cumulative sums of frequency-domain series. Under the null hypothesis, each normalized cumulative sum converges in distribution to a standard Brownian bridge. The numerical results...

In this paper, we propose a new frequency domain test for pairwise time reversibility at any specific couple of quantiles of two-dimensional marginal distribution. The proposed test is applicable to a very broad class of time series, regardless of the existence of moments and Markovian properties. By varying the couple of quantiles, the test can de...

Based on periodogram-ratios of two univariate time series at different frequency points, two tests are proposed for comparing their spectra. One is an Anderson-Darling-like statistic for testing the equality of two time-invariant spectra. The other is the maximum of Anderson-Darling-like statistics for testing the equality of two time-varying spect...

Spectra are frequently used to depict the dependence features of a second-order stationary process. In this paper, the spatial log-spectral density is expressed by a new type of smoothing splines in the form of the summation of a linear expression of univariate bases and two quadratic forms of univariate bases. Based on this new type of smoothing s...

This paper is concerned with testing the second-order stationarity of a time series. By using a blockwise scheme, the test is transformed to compare local spectra of different segments of the blocked time series. Based on periodogram-ratios of each pair of segments at the same frequency points, an Anderson-Darling-like statistic is constructed to c...

In modelling spatial data, it is a crucial aspect to specify the covariance function of the random field appropriately. For the sake of simplicity, the spatial isotropy is often assumed. By approximating the isotropy by a composite hypothesis containing the rotational invariance and axial symmetry of the covariance function, a maximum statistic is...

Various approaches for spectral analysis based on regularly spaced data have already been well-established, but the spectral inference based on irregularly spaced data are still essentially limited. Under the Bayesian framework, a detouring approach for spectral estimation is proposed for analyzing irregularly spaced data. The detouring process is...

Recently, quantile-based spectral analysis has drawn much attention due to that it can capture serial dependence more than covariance-related. One of typical quantile-based spectra is the copula spectral density kernel (CSDK) proposed by Dette et al. (2015), which is more informative than the traditional spectral density. To avoid smoothing all CSD...

Based on periodogram-ratios of two univariate time series at different frequency points, two tests are proposed for comparing their spectra. One is an Anderson-Darling-like statistic for testing the equality of two time-invariant spectra. The other is the maximum of Anderson-Darling-like statistics for testing the equality of two spectra no matter...

Based on periodogram-ratios of two univariate time series at different frequency points, two tests are proposed for comparing their spectra. One is an Anderson-Darling-like statistic for testing the equality of two time-invariant spectra. The other is the maximum of Anderson-Darling-like statistics for testing the equality of two spectra no matter...

Following the nonstationary univariate time series model of Rosen et al. (2012), we propose an adaptive estimation of time-varying spectra and cross-spectra for analyzing possibly nonstationary multivariate time series. Under the Bayesian framework, the estimation is implemented by smoothing stochastic approximation Monte Carlo (SSAMC) methods. We...

Probability transform-based inference, for example, characteristic function-based inference, is a good alternative to likelihood methods when the probability density function is unavailable or intractable. However, a set of grids needs to be determined to provide an effective estimator based on probability transforms. This paper is concerned with p...

This paper is concerned with parametric estimation, model specification and autocorrelation diagnosis for stationary moving averages driven by a Wiener process. By incorporating the analysis of the spectral densities of the discretely observed trajectory, empirical likelihood methods based on moment conditions are developed to the dependent sequenc...

This article is concerned with a least squares estimator (LSE) of the kernel function parameter  for a Lévy-driven moving average of the form X(t) = ∫t − ∞K((t − s)) dL(s), where is a Lévy process without the Brownian motion part, K is a kernel function and  > 0 is a parameter. Let h be the time span between two consecutive observations and let...

We study the problem of parameter estimation for Ornstein–Uhlenbeck processes driven by symmetric α-stable motions, based on discrete observations. A least squares estimator is obtained by minimizing a contrast function based on the integral form of the process. Let h be the length of time interval between two consecutive observations. For both the...

In this paper, we consider the problem of testing for an autocorrelation change in discretely observed Ornstein-Uhlenbeck processes driven by Lévy processes. For a test, we propose a class of test statistics constructed by an iterated cumulative sums of squares of the difference between two adjacent observations. It is shown that each of the test s...

The Lévy copula can describe the dependence structure of a multidimensional Lévy process or a multivariate infinitely divisible random variable. Suppose the Lévy copula of a multidimensional Lévy process is known. We present the Lévy copula of the Lévy measure of the moving average driven by the multidimensional Lévy process. If there exist some sp...

Based on a representation of a stochastic integral of Ornstein–Uhlenbeck (O–U) type, the exact simulation algorithm of the tempered stable O–U process is given in this paper. The algorithm employs the double rejection method and the general acceptance–rejection technique. The time complexity of the double rejection method is uniformly bounded over...

In this paper, a stochastic integral of Ornstein–Uhlenbeck type is represented to be the sum of three independent random variables—one follows a distribution whose density is a deconvolution of the densities of two generalized inverse Gaussian distributions, and the two others all have compound Poisson distributions. Based on the representation of...

O-U compound Poisson processes, as a new category of processes of Ornstein--Uhlenbeck type, are put forward in this paper. These processes are a generalization of gamma O--U processes. By dealing with the characteristic function of the transition distribution function, the transition law of the O--U compound Poisson process is expressed by a sum of...

Convolutions of exponential distributions have widely used in stochastic process and queuing network. In this paper, the closed-form of the probability density function of the sum of exponential random variables is obtained. And we fit convolutions of exponential distributions to the daily realized volatility data of the SSE Composite Index. Furthe...

Processes of Ornstein-Uhlenbeck type, driven by positive compound Poisson processes, are considered. We are interested in parametric estimation of these processes based on discrete observations. The parameter of the stationary distribution is estimated by the method of moments, and a consistent and asymptotically normal estimator is provided. The t...

In this paper, a stochastic integral of Ornstein--Uhlenbeck type is represented to be the sum of two independent random variables: one has a tempered stable distribution and the other has a compound Poisson distribution. In distribution, the compound Poisson random variable is equal to the sum of a Poisson-distributed number of positive random vari...

In this paper, a stochastic integral of Ornstein–Uhlenbeck type is represented to be the sum of two independent random variables: one has a tempered stable distribution and the other has a compound Poisson distribution. In distribution, the compound Poisson random variable is equal to the sum of a Poisson-distributed number of positive random varia...

IG-OU processes are a subclass of the non-Gaussian processes of Ornstein–Uhlenbeck type, which are important models appearing in financial mathematics and elsewhere. The simulation of these processes is of interest for its applications in statistical inference. In this paper, a stochastic integral of Ornstein–Uhlenbeck type is represented to be the...

The stationary Gamma-OU processes are recommended to be the volatility of the financial assets. A parametric estimation for the Gamma-OU processes based on the discrete observations is considered in this paper. The estimator of an intensity parameter λ and its convergence result are given, and the simulations show that the estimation is quite accur...