We propose an information criterion for determining an unknown number of periodic components in functional time series. Identifying the number of frequencies in large-scale time series has been a central focus. To achieve this goal, we suggest an iterative procedure, utilizing the residual process obtained through least squares fitting. This iterative approach demonstrates broad applicability. We establish the consistency of the estimated number of periodic components by minimizing the information criterion. The efficacy of the procedure is illustrated through numerical simulations. In real data analysis, we apply this information criterion to temperature data and sunspot data.

翻译：我们提出一种用于确定函数型时间序列中未知周期成分个数的信息准则。在大规模时间序列中识别频率个数一直是研究的核心焦点。为实现这一目标，我们建议采用迭代程序，利用通过最小二乘拟合得到的残差过程。该迭代方法具有广泛适用性。通过最小化信息准则，我们验证了所估计周期成分个数的一致性。数值模拟实验证实了该方法的有效性。在实际数据分析中，我们将此信息准则应用于温度数据和太阳黑子数据。