Samuel Olorunfemi Adams (ISSN: 2643-9603)

Description

Spline Smoothing is a technique under the Non-parametric regression used to filter out noise in observations, it is one of
the most popular methods used for the prediction of non-parametric regression models and its performance depends on the choice
of smoothing parameters. Most of the past works applied to smooth methods to time series data, this method over fits data in the
presence of Autocorrelation error. There are many methods of estimating smoothing parameters; most popular among them are;
Generalized Maximum Likelihood (GML), Generalized Cross-Validation (GCV), and Unbiased Risk (UBR), these methods tend to
overfit smoothing parameters in the presence of autocorrelation error. An efficient new Spline Smoothing estimation method is
proposed and compared with three classical methods to eliminate the problem of overfitting associated with the presence of
Autocorrelation in the error term. It is demonstrated through a simulation study performed by using a program written in R based
on the predictive Mean Score Error criteria. The result indicated that the predictive mean square error (PMSE) of the four
smoothing methods decreases as the smoothing parameters increases and decrease as the sample sizes increases. This study
discovered that the proposed smoothing method is the best for time-series observations with Autocorrelated error because it
doesn't overfit and works well for large sample sizes. This study will help researchers overcome the problem of overfitting
associated with applying Smoothing spline method time series observation.