On Local Trigonometric Regression Under Dependence
研究了在残差过程存在相依性时，将时间序列分解为长期趋势和季节性成分的非参数估计方法，发现季节性成分的收敛速度不受相依性影响，而趋势成分的收敛速度取决于长记忆参数，并提出了自适应带宽选择算法。
We consider nonparametric estimation of an additive time series decomposition into a long‐term trend μ and a smoothly changing seasonal component S under general assumptions on the dependence structure of the residual process. The rate of convergence of local trigonometric regression estimators of S turns out to be unaffected by the dependence, even though the spectral density of the residual process has a pole at the origin. In contrast, the rate of convergence of nonparametric estimators of μ depends on the long‐memory parameter d . Therefore, in the presence of long‐range dependence, different bandwidths for estimating μ and S should be used. A data adaptive algorithm for optimal bandwidth choice is proposed. Simulations and data examples illustrate the results.