Bootstrap procedures for AR (∞) — processes
Bootstrap procedures for AR (∞) — processes
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AR (∞) 的引导程序 — 过程
DOI：
10.1007/978-3-642-48850-4_14
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
Jens
中科院分区：
文献类型：
--
作者：
Jens
In this paper we will deal with an application of Efron’s 1979 bootstrap to stationary stochastic processes in discrete time. In many applications it is assumed that these processes are of autoregressive or more generally of autoregressive moving average type, i.e. the underlying stationary process X = (X t: t ∈ Z = {0, ±1, ±2,…}) is assumed to satisfy the following stochastic difference equation
$$ {X_t} = \sum\limits_{{v = 1}}^p {{a_v}{X_{{t - v}}} + {\varepsilon_t} + \sum\limits_{{\mu = 1}}^q {{b_{\mu }}{\varepsilon_{{t - \mu }}},\;t \in Z} } $$
Here e = (e t: t ∈ Z) denotes a white noise, that is a sequence of uncorrelated, zero mean random variables with finite variance σ 2 .
In this paper we will deal with an application of Efron’s 1979 bootstrap to stationary stochastic processes in discrete time. In many applications it is assumed that these processes are of autoregressive or more generally of autoregressive moving average type, i.e. the underlying stationary process X = (X t: t ∈ Z = {0, ±1, ±2,…}) is assumed to satisfy the following stochastic difference equation
$$ {X_t} = \sum\limits_{{v = 1}}^p {{a_v}{X_{{t - v}}} + {\varepsilon_t} + \sum\limits_{{\mu = 1}}^q {{b_{\mu }}{\varepsilon_{{t - \mu }}},\;t \in Z} } $$
Here e = (e t: t ∈ Z) denotes a white noise, that is a sequence of uncorrelated, zero mean random variables with finite variance σ 2 .