This paper investigates statistical inference methods for autocovariance estimation in functional time series under the presence of conditional heteroscedasticity. Functional time series data, which are characterized by observations evolving over continuous time or space, often exhibit complex dependencies and time-varying volatility patterns. In the presence of conditional heteroscedasticity, traditional autocovariance estimators may be biased or inefficient, necessitating the development of robust inference techniques. We propose a novel approach based on robust covariance estimation and bootstrap resampling to account for heteroscedasticity and provide reliable estimates of autocovariance. The efficacy of the proposed methodology is demonstrated through simulations and applications to real-world functional time series data, highlighting its ability to capture dynamic dependencies and volatility patterns under varying conditions.

Functional time series, autocovariance, conditional heteroscedasticity

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