Abstract

We propose portmanteau tests for functional white noise utilizing the sum of squared

empirical autocorrelation functions of functional time series. By applying a Hilbert space approach,

we establish the limiting properties of the test under the null hypothesis of uncorrelated but not

necessarily independent processes.

The test is non-pivotal due to unknown dependence within

the sequence. To address this issue, we employ the blockwise random weighting bootstrap to obtain critical values and justify its validity. Furthermore, we extend this method for diagnostics of

functional autoregressive model and demonstrate its effectiveness through extensive Monte Carlo

simulations and a real data application. An accompanying R package is provided to facilitate checks

for general functional white noise.

Information

Preprint No.SS-2024-0316
Manuscript IDSS-2024-0316
Complete AuthorsYu Miao, Muyi Li, Wai Keung Li, Xingbai Xu
Corresponding AuthorsMuyi Li
Emailslimuyi@xmu.edu.cn

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Acknowledgments

Muyi Li acknowledges the financial support of NSFC (72073112, 72033008, 71988101),

Natural Science Foundation of Fujian Province (2025J01036), and Key program of National Bureau of Statistics (2023LZ019). Wai Keung Li would like to thank the partial

support of EdUHK grant RG44/2019-2020R. Xingbai Xu acknowledges the financial support of NSFC (72073110, 72473118). The authors thank for Yuhan Chi (Xiamen Univer-

sity) providing technical support.

Supplementary Materials

All technical details and additional numerical studies can be found in the Supplementary Material.

Supplementary materials are available for download.