Mengatasi Error Berkorelasi Menggunakan Metode Transformasi Prewhitening pada Regresi Nonparametrik Kernel Bivariat

Abstract

Suppose that given 𝑛 data {(𝑋1𝑡, 𝑋2𝑡, 𝑌𝑡)}𝑛 with nonparametric regression model :𝑡=1𝑌𝑡  = 𝑚(𝑋1𝑡, 𝑋2𝑡) + 𝜀𝑡 ; 𝑡 = 1,2, ⋯ , 𝑛with 𝑚(𝑋𝑡) is a regression function and 𝜀𝑖 is a random errors. In nonparametric regression often found correlated errors, i.e. the error value does not meet the identical and independent assumptions. Correlated errors will adversely affect the estimation model. Correlated errors can be resolved by prewhitening transformation method, a method where the error is assumed to follow the model ARMA (𝑝, 𝑞). Applied on data is shown that regression model was obtained with correlated errors. The error obtained from the conventional Kernel regression model follows the AR(1) model with the value ∅1= 0.932. After the prewhitening transformation, the kernel regression model results from the prewhitening transformation with uncorrelated errors. The MSE value of the conventional Kernel estimation modal is 639203.308 smaller than the MSE value of the estimated Kernel prewhitening transformation model that is 290303.832, so the Kernel estimator resulting from prewhitening transformation is more efficient than conventional Kernel estimator.