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Stable continuous-time autoregressive process driven by stable subordinator

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  • Wyłomańska, Agnieszka
  • Gajda, Janusz

Abstract

In this paper we examine the continuous-time autoregressive moving average process driven by α-stable Lévy motion delayed by inverse stable subordinator. This process can be applied to high-frequency data with visible jumps and so-called “trapping-events”. Those properties are often visible in financial time series but also in amorphous semiconductors, technical data describing the rotational speed of a machine working under various load regimes or data related to indoor air quality. We concentrate on the main characteristics of the examined subordinated process expressed in the language of the measures of dependence which are main tools used in statistical investigation of real data. However, because the analyzed system is based on the α-stable distribution therefore we cannot consider here the correlation (or covariance) as a main measure which indicates at the dependence inside the process. In the paper we examine the codifference, the more general measure of dependence defined for wide class of processes. Moreover we present the simulation procedure of the considered system and indicate how to estimate its parameters. The theoretical results we illustrate by the simulated data analysis.

Suggested Citation

  • Wyłomańska, Agnieszka & Gajda, Janusz, 2016. "Stable continuous-time autoregressive process driven by stable subordinator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 1012-1026.
    • Handle: RePEc:eee:phsmap:v:444:y:2016:i:c:p:1012-1026
    DOI: 10.1016/j.physa.2015.10.081
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    Citations

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    Cited by:

    1. Peter J. Brockwell & Alexander Lindner, 2021. "Aspects of non‐causal and non‐invertible CARMA processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 777-790, September.
    2. Sikora, Grzegorz & Michalak, Anna & Bielak, Łukasz & Miśta, Paweł & Wyłomańska, Agnieszka, 2019. "Stochastic modeling of currency exchange rates with novel validation techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1202-1215.
    3. Szarek, Dawid & Bielak, Łukasz & Wyłomańska, Agnieszka, 2020. "Long-term prediction of the metals’ prices using non-Gaussian time-inhomogeneous stochastic process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).

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