All Times ET
Keywords: Air pollution, Time series, B-spline, Kernel estimator, Prediction interval
With the increasingly prominent problem of air pollution, effective and precise prediction about air pollutants concentration has become a wide concern in recent years.Traditional methods such as time series or parametric linear models usually suffer from poor prediction since they fail to interpret the complex dynamic structure in the air pollutants concentration data.In our paper, we handle the above issue by extending the nonparametric regression model with auto-regressive errors for equally spaced design to the time series setup. To implement the model, we propose a B-spline estimator for the trend function as well as a kernel estimator for the variance function. Prediction interval for multi-step-ahead future observation is also constructed after fitting the auto-regressive model of errors and obtaining the quantile of residuals. The proposed method is illustrated by various simulation studies and an example of air pollutants data, which contains 8 years of daily air pollutants concentrations in Xi'an. Final results demonstrate that our method outperforms others for its higher prediction accuracy and wider applicability.