Functional conditional volatility modeling with missing data: inference and application to energy commodities

TL;DR

This paper develops a nonparametric method for estimating volatility in scalar-on-function models with missing data, providing theoretical guarantees and applying it to natural gas and exchange rate data.

Contribution

It introduces a simplified estimator for volatility with proven asymptotic properties and extends it to impute missing data, improving volatility estimation in energy commodities.

Findings

The estimators are consistent and asymptotically normal.

Imputation improves volatility estimation accuracy.

Application to real energy data demonstrates practical effectiveness.

Abstract

This paper explores the nonparametric estimation of the volatility component in a heteroscedastic scalar-on-function regression model, where the underlying discrete-time process is ergodic and subject to a missing-at-random mechanism. We first propose a simplified estimator for the regression and volatility operators, constructed solely from the observed data. The asymptotic properties of these estimators, including the almost sure uniform consistency rate and asymptotic distribution, are rigorously analyzed. Subsequently, the simplified estimators are employed to impute the missing data in the original process, enhancing the estimation of the regression and volatility components. The asymptotic behavior of these imputed estimators is also thoroughly investigated. A numerical comparison of the simplified and imputed estimators is presented using simulated data. Finally, the methodology is applied to real-world data to model the volatility of daily natural gas returns, utilizing intraday EU/USD exchange rate return curves sampled at a 1-hour frequency.