Assessing worst weather by estimating value-at-risk using Heteroscedastic process

Abstract

A substantial issue in modern risk management is the measurement of risks. Specify, the requirement to quantify risk discovers in many different contexts. For instance, a regulator measures the risk exposure of a government institution in order determining the maximum value from any phenomenon occurred as a tool against unexpected losses. Particularly attention will be given to Value-at-Risk (V@R). Mostly, implementation of V@R is in financial cases, as potential alarm of institution to anticipate the magnitude of risk. Combining V@R with the forecast function of AR-ARCH processes, this paper proposes a new implementation of estimative-V@R and improved-V@R to compute heavy rain as representation of worst weather, which has the same future goal providing funds to anticipate financial losses. There are limited researches related to heavy rain forecast based on constructing a process by considering risk of with modifying some mathematics equations. We consider an overview of the existing approaches to measure V@R of weather data involving time series process and some stochastic expansion. We present V@R using AR and heteroscedastic processes ARCH considering the changes of data volatility. We consider an estimative prediction limit to determine an improved prediction limit with better conditional coverage properties. The parameter estimator of AR-ARCH is assumed to have the same asymptotic distribution as the conditional maximum likelihood estimator. This paper deals with calculation coverage probability to validate α-V@R performance.