Factorization and discrete-time representation of multivariate CARMA processes

IF 0.6 4区 数学 Q4 STATISTICS & PROBABILITY
Vicky Fasen-Hartmann, Markus Scholz
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引用次数: 1

Abstract

In this paper we show that stationary and non-stationary multivariate continuous-time ARMA (MCARMA) processes have the representation as a sum of multivariate complexvalued Ornstein-Uhlenbeck processes under some mild assumptions. The proof benefits from properties of rational matrix polynomials. A conclusion is an alternative description of the autocovariance function of a stationary MCARMA process. Moreover, that representation is used to show that the discrete-time sampled MCARMA(p,q) process is a weak VARMA(p, p− 1) process if second moments exist. That result complements the weak VARMA(p, p− 1) representation derived in Chambers and Thornton [8]. In particular, it relates the right solvents of the autoregressive polynomial of the MCARMA process to the right solvents of the autoregressive polynomial of the VARMA process; in the one-dimensional case the right solvents are the zeros of the autoregressive polynomial. Finally, a factorization of the sample autocovariance function of the noise sequence is presented which is useful for statistical inference.
多元CARMA过程的因子分解和离散时间表示
本文证明了在一些温和的假设下,平稳和非平稳的多元连续时间ARMA(MCARMA)过程具有多元复值Ornstein-Uhlenbeck过程的和的表示。证明受益于有理矩阵多项式的性质。结论是对平稳MCARMA过程的自协方差函数的一种替代描述。此外,该表示用于表明,如果存在二阶矩,则离散时间采样的MCARMA(p,q)过程是弱VARMA(p,p−1)过程。该结果补充了Chambers和Thornton[8]中得出的弱VARMA(p,p−1)表示。特别地,它将MCARMA过程的自回归多项式的右溶剂与VARMA过程中的自回归方程的右溶剂联系起来;在一维情况下,正确的溶剂是自回归多项式的零。最后,给出了噪声序列的样本自协方差函数的因子分解,这对统计推断是有用的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.10
自引率
0.00%
发文量
48
期刊介绍: ALEA publishes research articles in probability theory, stochastic processes, mathematical statistics, and their applications. It publishes also review articles of subjects which developed considerably in recent years. All articles submitted go through a rigorous refereeing process by peers and are published immediately after accepted. ALEA is an electronic journal of the Latin-american probability and statistical community which provides open access to all of its content and uses only free programs. Authors are allowed to deposit their published article into their institutional repository, freely and with no embargo, as long as they acknowledge the source of the paper. ALEA is affiliated with the Institute of Mathematical Statistics.
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