Bootstrapping continuous-time autoregressive processes
Bootstrapping continuous-time autoregressive processes
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DOI：
10.1007/s10463-013-0406-0
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发表时间：
2013-05
影响因子：
1
通讯作者：
P. Brockwell;Jens-Peter Kreiss;Tobias Niebuhr
中科院分区：
文献类型：
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作者：
P. Brockwell;Jens-Peter Kreiss;Tobias Niebuhr
对于离散规则时间间隔的L驱动的连续时间自回归(CAR)过程，我们发展了一个Bootstrap过程。众所周知，定期抽样的平稳Ornstein-Uhlenbeck过程[即CAR(1)过程]具有带I.I.D.的离散时间自回归表示。噪音。基于该表示，可以找到一个简单的自举过程。由于高阶规则抽样的CAR过程满足具有不相关(但通常是相关的)噪声的ARMA方程，因此对于这种过程需要更一般的Bootstrap过程。我们考虑依赖于均匀间隔时间的CAR过程的观测的统计量，以及在更精细的网格上的辅助观测，这给出了连续时间过程的导数的近似。这使得我们能够逼近CAR过程的状态向量，它是向量值CAR(1)过程，其采样版本在均匀间隔网格上是具有I.I.D.的多元AR(1)过程。噪音。这导致了基于残差的有效引导，该引导允许在底层离散时间网格上复制CAR过程。我们证明了这种方法对于经验自协方差和自相关是一致的。
We develop a bootstrap procedure for Lévy-driven continuous-time autoregressive (CAR) processes observed at discrete regularly-spaced times. It is well known that a regularly sampled stationary Ornstein–Uhlenbeck process [i.e. a CAR(1) process] has a discrete-time autoregressive representation with i.i.d. noise. Based on this representation a simple bootstrap procedure can be found. Since regularly sampled CAR processes of higher order satisfy ARMA equations with uncorrelated (but in general dependent) noise, a more general bootstrap procedure is needed for such processes. We consider statistics depending on observations of the CAR process at the uniformly-spaced times, together with auxiliary observations on a finer grid, which give approximations to the derivatives of the continuous time process. This enables us to approximate the state-vector of the CAR process which is a vector-valued CAR(1) process, and whose sampled version, on the uniformly-spaced grid, is a multivariate AR(1) process with i.i.d. noise. This leads to a valid residual-based bootstrap which allows replication of CARprocesses on the underlying discrete time grid. We show that this approach is consistent for empirical autocovariances and autocorrelations.