Abstract
Generalized Cross Validation (GCV) has been considered a popular model for choosing the complexity of statistical models, it is also well known for its optimal properties. Mallow’s CP criterion (MCP) has been considered a powerful tool which is used to select smoothing parameters for spline estimates with non-Gaussian data. Most of the past works applied Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP) smoothing methods to time series data, this methods over fits data in the presence of Autocorrelation error. A new Smoothing method is proposed by taking the hybrid of Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP). The predicting performance of the Hybrid GCV-MCP is compared with Generalized Cross Validation (GCV) and Mallow’s CP criterion (MCP) using data generated through a simulation study and real-life data on all SITC export and import price index in Nigeria between the years, 2001-2018, performed by using a program written in R and based on the predictive Mean Score Error (PMSE) criterion. Experimental results obtained show that the predictive mean square error (PMSE) of the three smoothing methods decreases as the sample size and smoothing parameters increases. The study discovered that the Hybrid GCV-MCP smoothing methods performed better than the classical GVV and MCP for both the simulated and real life data.
Highlights
There are several ways of modeling time-series observations through nonparametric regression techniques to make predictions, one such nonparametric technique is the spline smoothing method [1]
It was discovered that for the Generalized Cross-Validation (GCV) smoothing method, the predictive mean square error decreases as the time increases; when T = 50 the PMSE decreased from 0.053273 to 0.027264 when T = 100 and further decreases from 0.027264 to 0.025485 when T = 150 for smoothing function λ = 1
For the Mallow’s CP criterion (MCP) smoothing method, the predictive mean square error decreases as the time increases; when T = 50 the PMSE decreased from 0.048021 to 0.034561 when T = 100 and further decreases from 0.034561 to 0.025485 when T = 150 for smoothing function λ = 1
Summary
There are several ways of modeling time-series observations through nonparametric regression techniques to make predictions, one such nonparametric technique is the spline smoothing method [1]. Smoothing spline is a solution to a nonparametric regression problem with the function i.e. Є C2 [a, b] in the model that minimizes the penalized residual sum of squares with two continuous derivatives, as given below;. . The solution based on smoothing spline for a minimum problem in equation (2) is known as a “natural cubic spline” with knots at x1, ..., xn. From this point of view, a specially structured spline interpolation which depends on a chosen value λ develops into a suitable approach of function g in a model (2). Samuel Olorunfemi Adams and Yahaya Haruna Umar: Comparative Study of GCV-MCP Hybrid Smoothing
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