Partially Observed Functional Data: The Case of Systematically Missing Parts

TL;DR

This paper introduces new estimators for mean and covariance functions in partially observed functional data, especially when data is systematically missing, improving estimation accuracy in practical market scenarios.

Contribution

The paper proposes novel estimators that handle systematic missingness in functional data, relaxing the missing-completely-at-random assumption and enabling consistent estimation.

Findings

New estimators outperform classical ones in missing data scenarios.

Estimation procedures can be tested with a sequential multiple hypothesis test.

Methodology applied to German Control Reserve Market data.

Abstract

New estimators for the mean and the covariance function for partially observed functional data are proposed using a detour via the fundamental theorem of calculus. The new estimators allow for a consistent estimation of the mean and covariance function under specific violations of the missing-completely-at-random assumption. The requirements of the estimation procedure can be tested using a sequential multiple hypothesis test procedure. An extensive simulation study compares the new estimators with the classical estimators from the literature in different missing data scenarios. The proposed methodology is motivated by the practical problem of estimating the mean price curve in the German Control Reserve Market. In this auction market, price curves are only partially observable and the underlying missing data mechanism depends on systematic trading strategies which clearly violate the missing-completely-at-random assumption. In contrast to the classical estimators, the new estimators lead to useful estimates of the mean and covariance functions. Supplementary materials are provided online.