TY - JOUR
T1 - Asymptotic normality of the principal components of functional time series
AU - Kokoszka, Piotr
AU - Reimherr, Matthew
N1 - Funding Information:
The first author was partially supported by the NSF grant DMS 0931948 .
PY - 2013
Y1 - 2013
N2 - We establish the asymptotic normality of the sample principal components of functional stochastic processes under nonrestrictive assumptions which admit nonlinear functional time series models. We show that the aforementioned asymptotic depends only on the asymptotic normality of the sample covariance operator, and that the latter condition holds for weakly dependent functional time series which admit expansions as Bernoulli shifts. The weak dependence is quantified by the condition of L4-m-approximability which includes all functional time series models in practical use. We also demonstrate convergence of the cross covariance operators of the sample functional principal components to their counterparts in the normal limit.
AB - We establish the asymptotic normality of the sample principal components of functional stochastic processes under nonrestrictive assumptions which admit nonlinear functional time series models. We show that the aforementioned asymptotic depends only on the asymptotic normality of the sample covariance operator, and that the latter condition holds for weakly dependent functional time series which admit expansions as Bernoulli shifts. The weak dependence is quantified by the condition of L4-m-approximability which includes all functional time series models in practical use. We also demonstrate convergence of the cross covariance operators of the sample functional principal components to their counterparts in the normal limit.
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U2 - 10.1016/j.spa.2012.12.011
DO - 10.1016/j.spa.2012.12.011
M3 - Article
AN - SCOPUS:84873382257
VL - 123
SP - 1546
EP - 1562
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
SN - 0304-4149
IS - 5
ER -