# TESTING EQUALITY OF MEANS WHEN THE OBSERVATIONS ARE FROM FUNCTIONAL TIME SERIES

*Lajos Horvath* and
*Gregory Rice*

*Journal of Time Series Analysis*, 2015, vol. 36, issue 1, 84-108

**Abstract:**
type="main" xml:id="jtsa12095-abs-0001"> There are numerous examples of functional data in areas ranging from earth science to finance where the problem of interest is to compare several functional populations. In many instances, the observations are obtained consecutively in time, and thus, the classical assumption of independence within each population may not be valid. In this article, we derive a new, asymptotically justified method to test the hypothesis that the mean curves of multiple functional populations are the same. The test statistic is constructed from the coefficient vectors obtained by projecting the functional observations into a finite dimensional space. Asymptotics are established when the observations are considered to be from stationary functional time series. Although the limit results hold for projections into arbitrary finite dimensional spaces, we show that higher power is achieved by projecting onto the principle components of empirical covariance operators that diverge under the alternative. Our method is further illustrated by a simulation study as well as an application to electricity demand data.

**Date:** 2015

**References:** View references in EconPapers View complete reference list from CitEc

**Citations:** View citations in EconPapers (3) Track citations by RSS feed

**Downloads:** (external link)

http://hdl.handle.net/10.1111/jtsa.12095 (text/html)

Access to full text is restricted to subscribers.

**Related works:**

This item may be available elsewhere in EconPapers: Search for items with the same title.

**Export reference:** BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text

**Persistent link:** https://EconPapers.repec.org/RePEc:bla:jtsera:v:36:y:2015:i:1:p:84-108

**Ordering information:** This journal article can be ordered from

http://www.blackwell ... bs.asp?ref=0143-9782

Access Statistics for this article

Journal of Time Series Analysis is currently edited by *M.B. Priestley*

More articles in Journal of Time Series Analysis from Wiley Blackwell

Bibliographic data for series maintained by Wiley Content Delivery ().