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

TL;DR

This paper demonstrates how the value of information can guide algorithm selection and tuning in machine learning, specifically for minimizing mean-square error in financial time-series forecasting, exemplified with cryptocurrency data.

Contribution

It introduces a method to use the value of information to determine the theoretical performance bounds and information requirements for machine learning models in finance.

Findings

V(I) provides an upper bound on model performance.

I(V) indicates the minimum information needed for desired accuracy.

Application to cryptocurrency forecasts shows practical utility.

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.