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Abstract

In this paper, the nonlinear vector autoregressive model is considered and a semiparametric method is proposed to estimate the nonlinear vector regression function. We use Taylor series expansion up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the parameters are estimated through the least squares method, the obtained nonlinear vector regression function is adjusted by a nonparametric diagonal matrix, and the proposed diagonal matrix is also estimated through the nonparametric smooth-kernel approach. Estimating the parameters can yield the desired estimate of the vector regression function based on the data. Under some conditions, the asymptotic consistency properties of the proposed semiparametric method are established. In this case, some simulated results for the semiparametric estimators in a nonlinear vector autoregressive function are presented. Mean Squares Error (MSE) criterion is also applied to verify the accuracy and the efficiency of the suggested model. The results of the study indicate the accuracy of the suggested model. Furthermore, the method is applied for the Retail Trade Survey to provide short-term economic indicators of the retail trade sector. The hypothesis of nonlinearity in the vector autoregression function model is also considered by the use of principal components. We use this test for the Retail Trade Survey (RTS) data which is considered to provide short-term economic indicators of the retail trade sector. Here, we use a nonlinear vector autoregression function model to forecast the sales of fresh, takeaway, supermarket, and café restaurant food in New Zealand during 2000 to 2010 on yearly basis. For our empirical example, the test of nonlinearity clearly indicates our model is nonlinear.

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