This paper introduces the statistical analysis of Jacobi frequency varying Long Range Dependence (LRD) functional time series in connected and compact two-point homogeneous spaces. The convergence to zero, in the Hilbert-Schmidt operator norm, of the integrated bias of the periodogram operator is proved under alternative conditions to the ones considered in Ruiz-Medina (2022). Under this setting of conditions, weak-consistency of the minimum contrast parameter estimator of the LRD operator holds. The case where the projected manifold process can display Short Range Dependence (SRD) and LRD at different manifold scales is also analyzed. The estimation of the spectral density operator is addressed in this case. The performance of both estimation procedures is illustrated in the simulation study undertaken within the families of multifractionally integrated spherical functional autoregressive-moving average (SPHARMA) processes.

翻译：本文件介绍对连接和紧凑的两点同质空间的雅各比频率不同长距离依赖性(LRD)功能时间序列的统计分析,在Hilbert-Schmidt操作员规范中,用不同于Ruiz-Medina(2022年)考虑的条件,证明周期图操作员综合偏差的趋同为零,在这一条件设置下,LRD操作员最低对比参数估计值的不一致性保持不变,还分析了预测的多过程在不同多尺度显示短距离依赖性和LRD的情况,对光谱密度操作员的估算在本例中涉及,两种估计程序的业绩在多偏差综合功能自重平均(SPHARMA)流程中进行的模拟研究中加以说明。