Estimation of the Risk Measure under a Nuisance Autoregression

TL;DR

This paper develops a method to estimate quantile functions of unobservable error terms in autoregressive models using R-estimators, aiding risk measurement in economic and physical experiments.

Contribution

It introduces a novel approach combining R-estimators with autoregression quantiles to estimate unobservable error quantiles from observed data.

Findings

Successfully estimates risk measures from observed autoregressive data.

Provides a new methodology for quantile estimation in the presence of nuisance autoregression.

Enhances risk assessment accuracy in economic and physical experiments.

Abstract

The goal of an experiment is to evaluate the profit, loss, or the amount of a physical entity over a period. The measurements $X_t$ can be influenced by the values measured in the past; hence we describe the situation with an autoregression model, whose autoregression coefficients are generally unknown. The variable of interest is the error term $Z_t$ of the model, which is the increment of $X_t$ with respect to the past, but itself unobservable. The problem is to estimate various quantile functions of $Z$, as the risk measure of the loss or the related economic indicators. We construct an estimate of quantile functions of $Z$ in the situation that the inference is possible only by means of observations $X$. The proposed estimates are based on the R-estimators of autoregression coefficients, combined with the autoregression quantiles.