Oracally efficient estimation and consistent model selection for auto-regressive moving average time series with trend
Oracally efficient estimation and consistent model selection for auto-regressive moving average time series with trend
复制标题
具有趋势的自回归移动平均时间序列的 Oracally 高效估计和一致模型选择
DOI：
10.1111/rssb.12170
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
Yang Lijian
中科院分区：
文献类型：
--
作者：
Shao Qin;Yang Lijian
在实践中遇到的大多数时间序列都包含非零趋势，然而教科书上的时间序列分析方法通常集中在零均值平稳自回归移动平均（ARMA）过程上。趋势通常是用随机方法估计并从时间序列中减去，残差作为真ARMA噪声用于数据分析和推断，包括参数估计、滞后选择和预测。我们提出了一种理论上合理的由平滑趋势函数和ARMA误差项组成的两步时间序列分析方法，该方法计算效率高，易于实践。趋势是通过b样条回归估计的，基于残差的最大似然估计量被证明是有效的，因为它是渐近有效的，就好像真正的趋势函数是已知的，然后去除以获得ARMA误差。此外，建立了去趋势残差序列模型选择贝叶斯信息准则的一致性。通过仿真研究和实际数据分析，说明了该程序的有限样本性能。
Most time series that are encountered in practice contain non-zero trend, yet textbook approaches to time series analysis are typically focused on zero-mean stationary auto-regressive moving average (ARMA) processes. Trend is often estimated byad hocmethods and subtracted from time series, and the residuals are used as the true ARMA noise for data analysis and inference, including parameter estimation, lag selection and prediction. We propose a theoretically justified two-step method to analyse time series consisting of a smooth trend function and ARMA error term, which is computationally efficient and easy for practitioners to implement. The trend is estimated byB-spline regression, and the maximum likelihood estimator based on residuals is shown to be oracally efficient in the sense that it is asymptotically as efficient as if the true trend function were known and then removed to obtain the ARMA errors. In addition, consistency of the Bayesian information criterion for model selection is established for the detrended residual sequence. Finite sample performance of the procedure is illustrated by simulation studies and real data analysis.