A randomness test for functional panels

TL;DR

This paper introduces a new statistical test for assessing independence in functional panel data, accommodating growing dimensions and providing reliable results for high-frequency multivariate datasets.

Contribution

It develops a portmanteau style test with a novel central limit theorem for increasing dimension vectors, applicable to various functional data analysis contexts.

Findings

Test has correct size and high power in simulations.

Applicable to climate, finance, ecology, economics, and geophysics datasets.

Successfully applied to real-world temperature and precipitation data.

Abstract

Functional panels are collections of functional time series, and arise often in the study of high frequency multivariate data. We develop a portmanteau style test to determine if the cross-sections of such a panel are independent and identically distributed. Our framework allows the number of functional projections and/or the number of time series to grow with the sample size. A large sample justification is based on a new central limit theorem for random vectors of increasing dimension. With a proper normalization, the limit is standard normal, potentially making this result easily applicable in other FDA context in which projections on a subspace of increasing dimension are used. The test is shown to have correct size and excellent power using simulated panels whose random structure mimics the realistic dependence encountered in real panel data. It is expected to find application in climatology, finance, ecology, economics, and geophysics. We apply it to Southern Pacific sea surface temperature data, precipitation patterns in the South-West United States, and temperature curves in Germany.