Nonparametric Estimation of Periodic Characteristic Sequences and Its Practical Application
Considering the time series with unknown period length,a nonparametric model with trend term and period term is established.Firstly,the period length is determined by the regression residual with penalty,and then the trend function and period sequence are estimated based on profile least square method and local linear approximation.The asymptotic properties of estimators are discussed,including the consistency of periodic length estimation and the asymptotic normality of periodic sequence and trend estimation.Numerical simulation shows the advantages of this method in improving the interpretability of the model.Finally,our method is applied to urban carbon dioxide concentration and urban PM2.5.The fitting of concentration data shows the practicability of this method.
cycle lengthsmooth trendperiodic sequenceidentification conditionsprofile least squares
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