A randomness test for functional panels

Piotr Kokoszka, Matthew Logan Reimherr, Nikolas Wölfing

Research output: Contribution to journalArticle

1 Citation (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)37-53
Number of pages17
JournalJournal of Multivariate Analysis
Volume151
DOIs
StatePublished - Oct 1 2016

Fingerprint

Randomness
Time series
Projection
Climatology
High-frequency Data
Random Structure
Geophysics
Sea Surface Temperature
Panel Data
Multivariate Data
Ecology
Finance
Random Vector
Justification
Central limit theorem
Identically distributed
Normalization
Sample Size
Cross section
Subspace

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Cite this

Kokoszka, Piotr ; Reimherr, Matthew Logan ; Wölfing, Nikolas. / A randomness test for functional panels. In: Journal of Multivariate Analysis. 2016 ; Vol. 151. pp. 37-53.
@article{a1d7a0f5691e453f9b316a0cfb2d669d,
title = "A randomness test for functional panels",
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.",
author = "Piotr Kokoszka and Reimherr, {Matthew Logan} and Nikolas W{\"o}lfing",
year = "2016",
month = "10",
day = "1",
doi = "10.1016/j.jmva.2016.07.002",
language = "English (US)",
volume = "151",
pages = "37--53",
journal = "Journal of Multivariate Analysis",
issn = "0047-259X",
publisher = "Academic Press Inc.",

}

A randomness test for functional panels. / Kokoszka, Piotr; Reimherr, Matthew Logan; Wölfing, Nikolas.

In: Journal of Multivariate Analysis, Vol. 151, 01.10.2016, p. 37-53.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A randomness test for functional panels

AU - Kokoszka, Piotr

AU - Reimherr, Matthew Logan

AU - Wölfing, Nikolas

PY - 2016/10/1

Y1 - 2016/10/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84980012108&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84980012108&partnerID=8YFLogxK

U2 - 10.1016/j.jmva.2016.07.002

DO - 10.1016/j.jmva.2016.07.002

M3 - Article

AN - SCOPUS:84980012108

VL - 151

SP - 37

EP - 53

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

ER -