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Subordinated continuous-time AR processes and their application to modeling behavior of mechanical system

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  • Gajda, Janusz
  • Wyłomańska, Agnieszka
  • Zimroz, Radosław

Abstract

Many real data exhibit behavior adequate to subdiffusion processes. Very often it is manifested by so-called “trapping events”. The visible evidence of subdiffusion we observe not only in financial time series but also in technical data. In this paper we propose a model which can be used for description of such kind of data. The model is based on the continuous time autoregressive time series with stable noise delayed by the infinitely divisible inverse subordinator. The proposed system can be applied to real datasets with short-time dependence, visible jumps and mentioned periods of stagnation. In this paper we extend the theoretical considerations in analysis of subordinated processes and propose a new model that exhibits mentioned properties. We concentrate on the main characteristics of the examined subordinated process expressed mainly in the language of the measures of dependence which are main tools used in statistical investigation of real data. We present also the simulation procedure of the considered system and indicate how to estimate its parameters. The theoretical results we illustrate by the analysis of real technical data.

Suggested Citation

  • Gajda, Janusz & Wyłomańska, Agnieszka & Zimroz, Radosław, 2016. "Subordinated continuous-time AR processes and their application to modeling behavior of mechanical system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 123-137.
    • Handle: RePEc:eee:phsmap:v:464:y:2016:i:c:p:123-137
    DOI: 10.1016/j.physa.2016.07.041
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    References listed on IDEAS

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    1. P. Brockwell, 2001. "Lévy-Driven Carma Processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 113-124, March.
    2. Rosinski, Jan, 2007. "Tempering stable processes," Stochastic Processes and their Applications, Elsevier, vol. 117(6), pages 677-707, June.
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    Cited by:

    1. 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.
    2. 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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