The generalized fluctuation test: A unifying view

In this paper, a general principle of constructing tests for parameter constancy without assuming a specific alternative is introduced. A unified asymptotic result is established to analyze this class of tests. As applications, tests based on the range of recursive and moving estimates are considered, and their asymptotic distributions are characterized analytically. Our simulations show that different tests have quite different behavior under various alternatives and that no test uniformly dominates the other tests.     

Fisher Information for Fractional Brownian Motion Under High-Frequency Discrete Sampling

We investigate the issue of the validation of the local asymptotic normality property of three characterizing parameters of the fractional Brownian motion under high-frequency discrete sampling. We prove that the local asymptotic normality property holds true for the likelihood only when at least one of the volatility parameter and the Hurst exponent is known. We provide optimal rates of convergence of the three parameters and Fisher information matrix in closed form.     

Estimation for the three-parameter inverse gaussian distribution

The three-parameter inverse Gaussian distribution is defined and moment estimators and maximum likelihood estimators are obtained. The moment estimators are found in closed form and their asymprotic normality is proven. A sufficient condition is provided for the existence of the maximum likelihood estimators.     

Alternative forms of fractional Brownian motion

It is pointed out that two contradictory definitions of fractional Brownian motion are well-established, one prevailing in the probabilistic literature, the other in the econometric literature. Each is associated with a different definition of nonstationary fractional time series, arising in functional limit theorems based on such series. These various definitions have occasionally led to some confusion. The paper discusses the definitions and attempts a clarification.     

An invariance principle for triangular arrays of dependent variables with application to autocovariance estimation

The invariance principle for triangular arrays of dependent variables is studied. We use the concept of mixingale, proposed by McLeish (1975). Uniform bounds are imposed on the growth of conditional expectations with respect to distant predecessors. The theorem is applied to invariance principles for autocovariance estimates based on triangular arrays of time-series data for weak mixing sequences and linear processes. Such results are required for bootstrap applications.     

Maximum likelihood estimation of linear continuous time long memory processes with discrete time data

Summary.  We develop a new class of time continuous autoregressive fractionally integrated moving average (CARFIMA) models which are useful for modelling regularly spaced and irregu-larly spaced discrete time long memory data. We derive the autocovariance function of a stationary CARFIMA model and study maximum likelihood estimation of a regression model with CARFIMA errors, based on discrete time data and via the innovations algorithm. It is shown that the maximum likelihood estimator is asymptotically normal, and its finite sample properties are studied through simulation. The efficacy of the approach proposed is demonstrated with a data set from an environmental study.     

非完整相对运动动力学系统的非等时变分方程和积分不变量

首先给出非完整相对运动动力学系统的非等时变分方程,然后研究它们的解,并证明在一定条件下可利用第一积分来得到非等时变分方程的特解.最后利用正则方程和变分方程证明,可由第一积分直接构造系统的积分不变量.