连续时间局部平稳时间序列模型

IF 0.9 4区数学 Q3 STATISTICS & PROBABILITY

Advances in Applied Probability Pub Date : 2021-04-28 DOI:10.1017/apr.2022.64

Annemarie Bitter, R. Stelzer, Bennet Ströh

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引用次数: 4

摘要

摘要我们将离散时间中局部平稳过程的经典定义（参见Dahlhaus，“局部平稳过程”，在时间序列分析：方法和应用（2012）中）应用于连续时间设置，并获得时域和频域中的等效表示。由此，使用Wigner–Ville谱导出了一个独特的时变谱密度。作为一个例子，我们研究了时变Lévy驱动的状态空间过程，包括一类时变Lèvy驱动CARMA过程。首先，研究了这两类过程之间的联系。考虑一系列时变Lévy驱动的状态空间过程，我们给出了系数函数的充分条件，以确保相对于给定定义的局部平稳性。

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Continuous-time locally stationary time series models

Abstract We adapt the classical definition of locally stationary processes in discrete time (see e.g. Dahlhaus, ‘Locally stationary processes’, in Time Series Analysis: Methods and Applications (2012)) to the continuous-time setting and obtain equivalent representations in the time and frequency domains. From this, a unique time-varying spectral density is derived using the Wigner–Ville spectrum. As an example, we investigate time-varying Lévy-driven state space processes, including the class of time-varying Lévy-driven CARMA processes. First, the connection between these two classes of processes is examined. Considering a sequence of time-varying Lévy-driven state space processes, we then give sufficient conditions on the coefficient functions that ensure local stationarity with respect to the given definition.

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来源期刊

Advances in Applied Probability 数学-统计学与概率论

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Advances in Applied Probability has been published by the Applied Probability Trust for over four decades, and is a companion publication to the Journal of Applied Probability. It contains mathematical and scientific papers of interest to applied probabilists, with emphasis on applications in a broad spectrum of disciplines, including the biosciences, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.