A new nonlinear unit root test with Fourier function

Abstract

Traditional unit root tests display a tendency to be nonstationary in the case of structural breaks and nonlinearity. To eliminate this problem this paper proposes a new flexible Fourier form nonlinear unit root test. This test eliminates this problem to add structural breaks and nonlinearity together to the test procedure. In this test procedure, structural breaks are modeled by means of a Fourier function and nonlinear adjustment is modeled by means of an exponential smooth threshold autoregressive (ESTAR) model. The simulation results indicate that the proposed unit root test is more powerful than the Kruse and KSS tests.     

Simulation of stationary Gaussian vector fields

In earlier work we described a circulant embedding approach for simulating scalar-valued stationary Gaussian random fields on a finite rectangular grid, with the covariance function prescribed. Here, we explain how the circulant embedding approach can be used to simulate Gaussian vector fields. As in the scalar case, the simulation procedure is theoretically exact if a certain non-negativity condition is satisfied. In the vector setting, this exactness condition takes the form of a nonnegative definiteness condition on a certain set of Hermitian matrices. The main computational tool used is the Fast Fourier Transform. Consequently, when implemented appropriately, the procedure is highly efficient, in terms of both CPU time and storage.     

小波变换在雷达信号处理中的应用

，小波变换理论是傅里叶分析的重大进展，它已成为当今从应用数学到信号与图像处理等众多领域的研究热点。本文综述了傅里叶变换、加窗傅氏变换、小波变换的特性，讨论了将小波变换应用于雷达领域的前景。     

Hartley变换法地震波成像原理

建立了基于Hartly变换的地震波成像理论。理论分析和模拟计算表明,该方法比F-K地震波偏移成像法的计算速度更快,并使所需內存减半,是一个颇具工业价值的地震波成像新体制。     

FOURIER SERIES ESTIMATION FOR LENGTH BIASED DATA

This paper proposes and investigates Fourier series estimators for length biased data. Specifically, two Fourier series estimators are constructed and studied based on ideas of Jones (1991) and Bhattacharyya et al. (1988) in the case of kernel density estimation. Approximate expressions for mean squared errors and integrated mean squared errors are obtained and compared, and some simulated examples are investigated. The Fourier series estimator based on the proposal of Jones seems to have the more desirable properties of the two. The paper concludes with some comments that put this work in a wider context.     

DATA-BASED CHOICE OF THE SMOOTHING PARAMETER FOR A KERNEL DENSITY ESTIMATOR

The problem of optimally choosing the smoothing parameter of a Fourier integral density estimator (FIE) is addressed. A new data-based method of so doing is shown to be related to, but an improvement over, the method of Davis (1981). It is shown that Davis' method does not lead to consistent estimation of certain, principally multimodal, densities. In a simulation study involving the bimodal mixture of two normal densities, the new method is seen to represent a substantial improvement.     

关于Fourier级数收敛性问题一个新条件的注记

在实函数空间中，对用于判定Fourier级数收敛性的一个能同时包含O-正则变化拟单调类和剩余有界变差类的GBV条件作了进一步推广．这一条件能用于处理一类缺项三角级数的收敛性．     

基于FPGA的超高速FFT硬件实现

介绍了频域抽取基二快速傅里叶运算的基本原理;讨论了基于FPGA达4 096点的大点数超高速FFT硬件系统设计与实现方法,当多组大点数进行FFT运算时,利用FPGA内部大容量存储资源,采用乒乓结构进行流型运算,提高FFT运算速度,同时保证结果的准确性;对实际硬件进行了FFT运算测试,测试结果证明了系统的可行性和正确性,并且利用该硬件系统成功完成了星载SAR实时成像处理。     

Laplace transform approach to option pricing for time-changed Brownian models

In this article, we consider European option pricing for time-changed Brownian models using Laplace transform. We obtain a general formula for the option price as the integral of a real-valued function involving the Laplace transform of the random time change. Unlike the usual Fourier transform technique, our method does not suffer from difficulties specific to complex integration, such as the evaluation of multiple-valued functions, and allows for a model-independent analysis of the truncation error. In the numerical analysis part, we compare option prices in variance gamma (VG), normal inverse Gaussian (NIG), and generalized hyperbolic (GH) models obtained by Laplace transform with those obtained by the Fourier transform method introduced by Carr and Madan in 1999. The results show that our method converges faster than the Fourier approach when the Laplace transforms of the subordinators decay exponentially, for examples like NIG and GH models.