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A discrete autoregressive process as a model for short-range correlations in DNA sequences

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  • Dehnert, M.
  • Helm, W.E.
  • Hütt, M.-Th.

Abstract

We present a direct way to model short- and medium-range correlations in DNA sequences and to separate them from long-range correlations. To do so, we discuss symbol sequences generated by a discrete autoregressive process of order p, DAR(p). These sequences display higher-order Markov properties but are based on very few parameters. The aim of our investigation is (1) to introduce with such DAR(p) processes a parameter-efficient tool for generating higher-order Markov processes on a discrete alphabet, (2) to study, how the parameters of the process determine the statistical properties of the sequence and (3) to provide the mathematical tools for estimating the parameters from a given experimental sequence. The statistical properties of the generated sequences, expressed in terms of parameters in the DAR(p) process, are monitored with methods from information theory. The implications of our findings for DNA sequences are discussed and some application is given. In particular, it is shown, how short-range correlations in DNA sequences can be parameterised by such a process.

Suggested Citation

  • Dehnert, M. & Helm, W.E. & Hütt, M.-Th., 2003. "A discrete autoregressive process as a model for short-range correlations in DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 327(3), pages 535-553.
    • Handle: RePEc:eee:phsmap:v:327:y:2003:i:3:p:535-553
    DOI: 10.1016/S0378-4371(03)00399-6
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    References listed on IDEAS

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    1. Trifonov, E.N., 1998. "3-, 10.5-, 200- and 400-base periodicities in genome sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 249(1), pages 511-516.
    2. Herzel, Hanspeter & Große, Ivo, 1995. "Measuring correlations in symbol sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 216(4), pages 518-542.
    3. P. A. Jacobs & P. A. W. Lewis, 1983. "Stationary Discrete Autoregressive‐Moving Average Time Series Generated By Mixtures," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(1), pages 19-36, January.
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    Cited by:

    1. Kosmidis, Kosmas & Hütt, Marc-Thorsten, 2023. "DNA visibility graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
    2. Marc A. Scott & Kaushik Mohan & Jacques‐Antoine Gauthier, 2020. "Model‐based clustering and analysis of life history data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1231-1251, June.
    3. Möller, Simon & Hameister, Heike & Hütt, Marc-Thorsten, 2014. "A genome signature derived from the interplay of word frequencies and symbol correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 216-226.
    4. Jeongsim Kim & Bara Kim & Khosrow Sohraby, 2008. "Mean queue size in a queue with discrete autoregressive arrivals of order p," Annals of Operations Research, Springer, vol. 162(1), pages 69-83, September.

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