Time changes and stationarity issues for extended scalar autoregressive models

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
V. Girardin , R. Senoussi
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引用次数: 0

Abstract

A scalar discrete or continuous time process is reducible to stationarity (RWS) if its transform by some smooth time change is weakly stationary. Different issues linked to this notion are here investigated for autoregressive (AR) models. AR models are understood in a large sense and may have time-varying coefficients. In the continuous time case the innovation may be of the semi-martingale type–such as compound Poisson noise; in the discrete case, the noise may not be Gaussian.

Necessary and sufficient conditions for scalar AR models to be RWS are investigated, with explicit formulas for the time changes. Stationarity reduction issues for discrete sequences sampled from time continuous AR processes are also considered. Several types of time changes, RWS processes and sequences are studied with examples and simulation, including the classical multiplicative stationary AR models.

扩展标量自回归模型的时间变化和平稳性问题
如果标量离散或连续时间过程通过某种平滑时间变化进行的变换是弱平稳的,则该过程可归结为平稳性(RWS)。本文针对自回归(AR)模型研究了与这一概念相关的不同问题。AR模型在很大意义上被理解,并且可以具有时变系数。在连续时间的情况下,创新可能是半鞅型的——例如复合泊松噪声;在离散的情况下,噪声可能不是高斯的。研究了标量AR模型为RWS的充要条件,给出了时间变化的显式公式。还考虑了从时间连续AR过程中采样的离散序列的静态约简问题。通过实例和仿真研究了几种类型的时间变化、RWS过程和序列,包括经典的乘性平稳AR模型。
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来源期刊
Journal of Statistical Planning and Inference
Journal of Statistical Planning and Inference 数学-统计学与概率论
CiteScore
2.10
自引率
11.10%
发文量
78
审稿时长
3-6 weeks
期刊介绍: The Journal of Statistical Planning and Inference offers itself as a multifaceted and all-inclusive bridge between classical aspects of statistics and probability, and the emerging interdisciplinary aspects that have a potential of revolutionizing the subject. While we maintain our traditional strength in statistical inference, design, classical probability, and large sample methods, we also have a far more inclusive and broadened scope to keep up with the new problems that confront us as statisticians, mathematicians, and scientists. We publish high quality articles in all branches of statistics, probability, discrete mathematics, machine learning, and bioinformatics. We also especially welcome well written and up to date review articles on fundamental themes of statistics, probability, machine learning, and general biostatistics. Thoughtful letters to the editors, interesting problems in need of a solution, and short notes carrying an element of elegance or beauty are equally welcome.
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