论文标题
具有锥形创新和过滤器的线性过程的功能限制定理
Functional limit theorems for linear processes with tapered innovations and filters
论文作者
论文摘要
在本文中，我们考虑部分总和过程$ \ sum_ {k = 1}^{[nt]} x_k^{（n）} $，其中$ \ {x_k^{（n）} = \ sum_ {j = 0} k \ in \ bz \}，\ n \ ge 1，$是一系列带有锥形滤波器$ a_ {J}^{（n）} = a_ {j} \ ind {[0 \ le j \ le j \ le j \ le j \ le le（n）} $ and tapered tapered tapered innovation $ j n n n Ince的线性过程。 \ bz $。两个锥度参数$ b（n）$和$ \（n）$将$ n \ to $ n \ to \ infty $增长。我们考虑$ b（n）$相对较慢（软锥度）且迅速（硬锥度）的案例，以及所有三种增长$ b（n）$（n）$（强，弱和中度渐变）。
In the paper we consider the partial sum process $\sum_{k=1}^{[nt]}X_k^{(n)}$, where $\{X_k^{(n)}=\sum_{j=0}^{\infty} a_{j}^{(n)}ξ_{k-j}(b(n)), \ k\in \bz\},\ n\ge 1,$ is a series of linear processes with tapered filter $a_{j}^{(n)}=a_{j}\ind{[0\le j\le ł(n)]}$ and heavy-tailed tapered innovations $ξ_{j}(b(n), \ j\in \bz$. Both tapering parameters $b(n)$ and $ł(n)$ grow to $\infty$ as $n\to \infty$. The limit behavior of the partial sum process (in the sense of convergence of finite dimensional distributions) depends on the growth of these two tapering parameters and dependence properties of a linear process with non-tapered filter $a_i, \ i\ge 0$ and non-tapered innovations. We consider the cases where $b(n)$ grows relatively slow (soft tapering) and rapidly (hard tapering), and all three cases of growth of $ł(n)$ (strong, weak, and moderate tapering).
