Testing Normality of Functional Time Series

17 Pages Posted: 12 Jun 2018

See all articles by Tomasz Górecki

Tomasz Górecki

Adam Mickiewicz University

Siegfried Hörmann

Graz University of Technology

Lajos Horváth

University of Utah - Department of Mathematics

Piotr Kokoszka

Utah State University - Department of Mathematics & Statistics

Date Written: July 2018

Abstract

We develop tests of normality for time series of functions. The tests are related to the commonly used Jarque–Bera test. The assumption of normality has played an important role in many methodological and theoretical developments in the field of functional data analysis. Yet, no inferential procedures to verify it have been proposed so far, even for i.i.d. functions. We propose several approaches which handle two paramount challenges: (i) the unknown temporal dependence structure and (ii) the estimation of the optimal finite‐dimensional projection space. We evaluate the tests via simulations and establish their large sample validity under general conditions. We obtain useful insights by applying them to pollution and intraday price curves. While the pollution curves can be treated as normal, the normality of high‐frequency price curves is rejected.

Keywords: Functional data, Jarque–Bera test, normal distribution, time series

Suggested Citation

Górecki, Tomasz and Hörmann, Siegfried and Horváth, Lajos and Kokoszka, Piotr, Testing Normality of Functional Time Series (July 2018). Journal of Time Series Analysis, Vol. 39, Issue 4, pp. 471-487, 2018. Available at SSRN: https://ssrn.com/abstract=3192254 or http://dx.doi.org/10.1111/jtsa.12281

Tomasz Górecki (Contact Author)

Adam Mickiewicz University

Wieniawskiego 1
Poznan, 61-712
Poland

Siegfried Hörmann

Graz University of Technology

Kopernikusgasse 24/IV
Graz University of Technology,
GRAZ, A-8010
Austria

Lajos Horváth

University of Utah - Department of Mathematics ( email )

1645 E. Campus Center
Salt Lake City, UT 84112
United States
801 581-8159 (Phone)

Piotr Kokoszka

Utah State University - Department of Mathematics & Statistics ( email )

3900 Old Main Hill
Logan, UT 84322-3530
United States
435-797-0746 (Phone)
435-797-1822 (Fax)

HOME PAGE: http://www.math.usu.edu/~piotr/

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