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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…