Multi-step-ahead Prediction Interval for Locally Stationary Time Series with Application to Air Pollutants Concentration Data
Multi-step-ahead Prediction Interval for Locally Stationary Time Series with Application to Air Pollutants Concentration Data
复制标题
局部平稳时间序列的多步超前预测区间及其在空气污染物浓度数据中的应用
作者：
Li Jie;Hu Qirui;Zhang Fengying
局部平稳时间序列经常出现在金融和环境科学中（例如，每日空气污染物浓度或财务收益）。然而，为这样的时间序列构建多步预测区间仍然是一个悬而未决的问题。因此，我们扩展了非参数回归模型与自回归误差等间距设计的时间序列设置。我们提出了一个B-样条估计的趋势函数和核估计的方差函数来实现模型。通过拟合误差的自回归模型，得到预测残差的分位数，构造了多步超前的未来观测值的预测区间。以西安市8年逐日空气污染物浓度数据为例，通过各种模拟研究，说明了所提出的方法。我们的结果表明，我们的方法优于其他由于其较高的预测精度和通用性。
Locally stationary time series frequently appears in both finance and environmental sciences (e.g., daily air pollutant concentration or financial returns). However, constructing the multi‐step‐ahead prediction interval for such time series remains an open question. Hence, we extend the nonparametric regression model with autoregressive errors for equally spaced designs to the time series setup. We propose a B‐spline estimator for the trend function and a kernel estimator for the variance function to implement the model. The prediction interval of multi‐step‐ahead future observations is also constructed after fitting the autoregressive model of errors and obtaining the quantile of prediction residuals. The proposed method is illustrated by various simulation studies and an example of air pollutant data, containing 8 years of daily air pollutant concentrations in Xi'an. Our results demonstrate that our method outperforms others owing to its higher prediction accuracy and versatility.