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Summary The paper is concerned with testing normality in samples of curves and error curves estimated from functional regression models. We propose a general paradigm based on the application of multivariate normality tests to vectors of functional principal components scores. We examine finite sample performance of a number of such tests and select the best performing tests. We apply them to several extensively used functional data sets and determine which can be treated as normal, possibly after a suitable transformation. We also offer practical guidance on software implementations of all tests we study and develop large sample justification for tests based on sample skewness and kurtosis of functional principal component scores.
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TESTING NORMALITY OF FUNCTIONAL TIME SERIES
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.
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- Award ID(s):
- 1737795
- PAR ID:
- 10059530
- Date Published:
- Journal Name:
- Journal of time series analysis
- Volume:
- 39
- ISSN:
- 0143-9782
- Page Range / eLocation ID:
- 471-487
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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