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Value of Information in the Mean-Square Case and its Application to the Analysis of Financial Time-Series Forecast

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  • Roman Belavkin
  • Panos Pardalos
  • Jose Principe

Abstract

The advances and development of various machine learning techniques has lead to practical solutions in various areas of science, engineering, medicine and finance. The great choice of algorithms, their implementations and libraries has resulted in another challenge of selecting the right algorithm and tuning their parameters in order to achieve optimal or satisfactory performance in specific applications. Here we show how the value of information (V(I)) can be used in this task to guide the algorithm choice and parameter tuning process. After estimating the amount of Shannon's mutual information between the predictor and response variables, V(I) can define theoretical upper bound of performance of any algorithm. The inverse function I(V) defines the lower frontier of the minimum amount of information required to achieve the desired performance. In this paper, we illustrate the value of information for the mean-square error minimization and apply it to forecasts of cryptocurrency log-returns.

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  • Roman Belavkin & Panos Pardalos & Jose Principe, 2024. "Value of Information in the Mean-Square Case and its Application to the Analysis of Financial Time-Series Forecast," Papers 2410.01831, arXiv.org.
    • Handle: RePEc:arx:papers:2410.01831
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    File URL: http://arxiv.org/pdf/2410.01831
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    References listed on IDEAS

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    1. Roman Belavkin, 2013. "Optimal measures and Markov transition kernels," Journal of Global Optimization, Springer, vol. 55(2), pages 387-416, February.
    2. Roman V. Belavkin, 2010. "Information Trajectory of Optimal Learning," Springer Optimization and Its Applications, in: Michael J. Hirsch & Panos M. Pardalos & Robert Murphey (ed.), Dynamics of Information Systems, chapter 0, pages 29-44, Springer.
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    1. Roman V. Belavkin, 2014. "Asymmetry of Risk and Value of Information," SEET Working Papers 2014-03, BELIS, Istanbul Bilgi University.

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