## MATHEMATICS • MAY 24, 2021
# *Noise is commonly discarded, but identifying patterns in noise can be very useful.*
*Generalize the Hearst exponent by adding more coefficients in order to get a more complete description of the changing data. This makes it possible to find patterns in the data that are usually considered noise and were previously impossible to analyze.*
*The development of this mathematical apparatus can solve the issue of parameterisation and analysis of processes for which there is no exact mathematical description. This opens up enormous prospects in describing, analyzing and forecasting complex systems.*
*by moscow institute of physics and technology*
One of the metrics used in economics and natural sciences in time series analysis is the Hurst exponent. It suggests whether the trend present in the data will persist: for example, whether values will continue to increase, or whether growth will turn to decline. This assumption holds for many natural processes and is explained by the inertia of natural systems. For example, lake level change, which is consistent with predictions derived from analysis of the Hurst exponent value, is determined not only by the current amount of water, but also by evaporation rates, precipitation, snowmelt, etc. All of the above is a time-consuming process.
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