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The Application of Kernel Smoothing to Time Series Data

The Application of Kernel Smoothing to Time Series Data
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摘要 There are already a lot of models to fit a set of stationary time series, such as AR, MA, and ARMA models. For the non-stationary data, an ARIMA or seasonal ARIMA models can be used to fit the given data. Moreover, there are also many statistical softwares that can be used to build a stationary or non-stationary time series model for a given set of time series data, such as SAS, SPLUS, etc. However, some statistical softwares wouldn't work well for small samples with or without missing data, especially for small time series data with seasonal trend. A nonparametric smoothing technique to build a forecasting model for a given small seasonal time series data is carried out in this paper. And then, both the method provided in this paper and that in SAS package are applied to the modeling of international airline passengers data respectively, the comparisons between the two methods are done afterwards. The results of the comparison show us the method provided in this paper has superiority over SAS's method. There are already a lot of models to fit a set of stationary time series, such as AR, MA, and ARMA models. For the non-stationary data, an ARIMA or seasonal ARIMA models can be used to fit the given data. Moreover, there are also many statistical softwares that can be used to build a stationary or non-stationary time series model for a given set of time series data, such as SAS, SPLUS, etc. However, some statistical softwares wouldn't work well for small samples with or without missing data, especially for small time series data with seasonal trend. A nonparametric smoothing technique to build a forecasting model for a given small seasonal time series data is carried out in this paper. And then, both the method provided in this paper and that in SAS package are applied to the modeling of international airline passengers data respectively, the comparisons between the two methods are done afterwards. The results of the comparison show us the method provided in this paper has superiority over SAS's method.
机构地区 School of Mathematics
出处 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2006年第2期219-226,共8页 应用数学学报(英文版)
基金 Supported by the National Natural Science Foundation of China(No.10371034)
关键词 Nonparametric regression kernel smoothing seasonal time series ARIMA model SAS package international airline passengers Nonparametric regression, kernel smoothing, seasonal time series, ARIMA model, SAS package, international airline passengers
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参考文献5

  • 1Box, G.E.P, Jenkins, G.W, Reinsel, G.C. Time series analysis: Forecasting and control, 3rd Ed, Prentice- Hall, Inc, 1994
  • 2Brockewell, P.J, Davis, R.A. Time series: Theory and methods, 2nd ed, Springer-Verlag, New York, 1996
  • 3Eubank, R.L. Nonparametric regression and spline smoothing. Marcel Dekker, Inc, New York, 1999
  • 4Hart, J.D. Nonparametric smoothing and Lack-of-Fit Tests. Springer-Verlag, New York, 1997
  • 5Wu, X.Z, Wang, Z.J. Nonparametric statistical Methods. Chinese High Education Press, Beijing, 1996

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