European Journal of Statistics and Probability (EJSP)

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Smoothing Spline of Arma Observations in the Presence of Autocorrelation Error


Given a set of observations x1, . . . xn , Spline Smoothing is of great importance in non-parametric regression because it is the fitting of smoothing function to filter out noise in an observation. Many methods of selecting smoothing parameters including; the Cross Validation (CV), Generalized Cross-Validation (GCV), Unbiased Risk (UBR) and Generalized Maximum Likelihood (GML) are developed under the assumption of independent observations. In this study, GML, GCV and UBR methods were extended to ARMA time series observations in the presence of autocorrelation at four levels, i.e. 0.1, 0.3, 0.5 and 0.8. Mean Bias, Mean Square Error and Variance were used to evaluate the performance of the three selection methods. Data were simulated to compare the performances of these three selection methods based on six sample sizes i.e. 20, 60, 200, 350, 500 and 750.GML method was computationally more effective and consistent than the UBR and GCV selection methods because it worked well for all samples sizes and at all levels of autocorrelation.

Keywords: B-spline, Least Square Spline, Non-parametric regression, P-Spline

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