Estimation of the Risk Measure under a Nuisance Autoregression

Fuente: arXiv
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Autori principali: Jurečková, Jana, Picek, Jan
Natura: Preprint
Pubblicazione: 2026
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author Jurečková, Jana
Picek, Jan
author_facet Jurečková, Jana
Picek, Jan
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_10553
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Estimation of the Risk Measure under a Nuisance Autoregression
Jurečková, Jana
Picek, Jan
Methodology
62M10, 62G08, 62J05
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.
title Estimation of the Risk Measure under a Nuisance Autoregression
topic Methodology
62M10, 62G08, 62J05
url https://arxiv.org/abs/2605.10553