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局部时密度估计与非参数协整回归的渐近理论AI 解读

Asymptotic theory is developed for local time density estimation for a general class of functionals of integrated and fractionally integrated time series. The main result provides a convenient basis for developing a limit theory for nonparametric cointegrating regression and nonstationary autoregression. The treatment directly involves local time estimation and the density function of the processes under consideration, providing an alternative approach to the Markov chain…

最小条件下 U 统计量的 Edgeworth 展开AI 解读

Berry-Esseen bounds for U -statistics under the optimal moment conditions were derived by Koroljuk and Borovskich and Friedrich.Under the same optimal moment assumptions with an additional nonlattice condition, we establish a one-term Edgeworth expansion with remainder o(n -1/2 ) for U -statistics.

一般分数阶单整过程的渐近理论及单位根检验应用AI 解读

In this paper, functional limit theorems for general fractional processes are established under quite weak conditions. The results are then used to derive weak convergence of general nonstationary fractionally integrated processes and to characterize unit root distribution in a model with error being a fractional autoregressive moving average process or a nonstationary fractionally integrated process.The authors thank three referees and an associate editor for their detailed…

线性过程的不变性原理及其应用AI 解读

Let X t be a linear process defined by X t = [sum ] k=0 ∞ ψ k ε t − k , where {ψ k , k ≥ 0} is a sequence of real numbers and {ε k , k = 0,±1,±2,...} is a sequence of random variables. Two basic results, on the invariance principle of the partial sum process of the X t converging to a standard Wiener process on [0,1], are presented in this paper. In the first result, we assume that the innovations ε k are independent and identically distributed random variables but do not…