On trend and its derivatives estimation in repeated time series with subordinated long-range dependent errors

TL;DR

This paper investigates the performance of kernel smoothing methods for estimating trend and derivatives in irregularly spaced time series with dependent, long-range dependent errors, providing theoretical results and bandwidth selection insights.

Contribution

It extends kernel smoothing analysis to irregular time series with subordinated Gaussian long memory errors, deriving functional CLTs and addressing bandwidth selection.

Findings

Functional CLTs for trend and derivative estimators

Bandwidth selection strategies for dependent errors

Performance analysis under irregular sampling

Abstract

For temporal regularly spaced datasets, a lot of methods are available and the properties of these methods are extensively investigated. Less research has been performed on irregular temporal datasets subject to measurement error with complex dependence structures, while this type of datasets is widely available. In this paper, the performance of kernel smoother for trend and its derivatives is considered under dependent measurement errors and irregularly spaced sampling scheme. The error processes are assumed to be subordinated Gaussian long memory processes and have varying marginal distributions. The functional central limit theorem for the estimators of trend and its derivatives are derived and bandwidth selection problem is addressed.