Infinitely Stochastic Micro Forecasting

TL;DR

This paper introduces a novel stochastic forecasting method for future expenses based on individual event developments, applicable across various fields, and develops inference techniques for infinitely stochastic processes.

Contribution

It proposes a new approach for predicting future subevent flows from reported and unreported events using infinitely stochastic processes, including non-homogeneous Poisson processes.

Findings

Developed inference methods for infinitely stochastic processes.

Illustrated methodology on quantitative risk assessment.

Applicable to diverse areas like epidemics, war damages, and digital payments.

Abstract

Forecasting costs is now a front burner in empirical economics. We propose an unconventional tool for stochastic prediction of future expenses based on the individual (micro) developments of recorded events. Consider a firm, enterprise, institution, or state, which possesses knowledge about particular historical events. For each event, there is a series of several related subevents: payments or losses spread over time, which all leads to an infinitely stochastic process at the end. Nevertheless, the issue is that some already occurred events do not have to be necessarily reported. The aim lies in forecasting future subevent flows coming from already reported, occurred but not reported, and yet not occurred events. Our methodology is illustrated on quantitative risk assessment, however, it can be applied to other areas such as startups, epidemics, war damages, advertising and commercials, digital payments, or drug prescription as manifested in the paper. As a theoretical contribution, inference for infinitely stochastic processes is developed. In particular, a non-homogeneous Poisson process with non-homogeneous Poisson processes as marks is used, which includes for instance the Cox process as a special case.