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TESTING EQUALITY OF MEANS WHEN THE OBSERVATIONS ARE FROM FUNCTIONAL TIME SERIES
Author(s) -
Horváth Lajos,
Rice Gregory
Publication year - 2015
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12095
Subject(s) - mathematics , series (stratigraphy) , independence (probability theory) , covariance , test statistic , limit (mathematics) , functional data analysis , population , statistical hypothesis testing , characterization (materials science) , statistic , econometrics , mathematical analysis , statistics , paleontology , materials science , demography , sociology , biology , nanotechnology
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.