论文标题
最小值的预测对定期固定的长度记忆的序列预测多个季节性增量
Minimax-robust forecasting of sequences with periodically stationary long memory multiple seasonal increments
论文作者
论文摘要
我们介绍了随机序列$ζ（k）$，并定期固定的概括性多个分数顺序，结合了环固化，多季节，集成和分分集成的模式。我们根据其观察值$ k <0 $解决了由随机序列$ζ（k）$构建的线性函数的最佳估计问题。对于具有已知光谱密度的序列，我们获得了用于计算均方根误差值的公式和功能最佳估计值的光谱特性。在序列频谱密度尚不清楚的情况下，提出了确定功能最佳线性估计值的最低光谱密度和最小值光谱特性的公式，而在给出了一些可允许的光谱密度。
We introduce stochastic sequences $ζ(k)$ with periodically stationary generalized multiple increments of fractional order which combines cyclostationary, multi-seasonal, integrated and fractionally integrated patterns. We solve the problem of optimal estimation of linear functionals constructed from unobserved values of stochastic sequences $ζ(k)$ based on their observations at points $ k<0$. For sequences with known spectral densities, we obtain formulas for calculating values of the mean square errors and the spectral characteristics of the optimal estimates of functionals. Formulas that determine the least favorable spectral densities and minimax (robust) spectral characteristics of the optimal linear estimates of functionals are proposed in the case where spectral densities of sequences are not exactly known while some sets of admissible spectral densities are given.
