Wavelet Estimation of Semi-parametric Regression Model

Abstract

The semi-parametric regression model combines parametric and nonparametric regression. However, non-parametric estimation may provide flexible solutions to the problems suffers by the regression model, but the problem of dimensionality that this estimator suffers, which occurs due to the increasing number of explanatory variables, still remain, this, in turn, may reduce the accuracy of the estimation process. Estimate the non-parametric part of the semi-parametric models that can be studied using conventional non-parametric methods such as the Spline Smoothing and Kernel Smoothing. However, there are other non-parametric methods that can be used, therefore, in this paper, the semi-parametric regression model was estimated by employing the wavelet estimate for the soft threshold, according to the "Speckman" method, and then comparing it with the two methods, Nadaraya-Watson and Local Linear, through the implementation of simulation experiments that included different sample sizes and threshold values. The parametric part estimation of the partially linear model according to the least-squares method was not identical to those estimates using the Speckman method, that is because the least-squares method was not appropriate for the uneven nature of the number of weekly work hours. Simulation experiments have demonstrated the efficiency of the wavelet estimation method and its superiority over other methods. The above estimation methods were applied to real data related to the study of the production value for the public industrial sector in Iraq, and some factors affect it, such as the value of industrial supplies, the total wages of workers, and the number of workers.

Comparison of the two hybrid models, Wavelet-ARIMA and Wavelet-ES, to predict the prices of the US dollar index

“…Through the comparison criteria AIC, RMSE and MAPE, the best HWA hybrid models were obtained using the filter D16, followed by the model with the filter D4, then the model with the filter D8, while the best HWE models was the model with the filter D8, followed by the model with the filter D4, then the model with the filter D16, and therefore the best hybrid model for the dollar index price series is the HWA hybrid model with filter D16. Based on the foregoing, the final model that will be applied to estimate the dollar index price series is the ARIMA (5,1,2) model, defined according to the following mathematical formula: y t = β 1 y t−1 + β 2 y t−2 + β 3 y t−3 + β 4 y t−4 + β 5 y t−5 + a t + δ 1 a t−1 + δ 2 a t−2 (15) The estimated formula is as following: Through figure (8), which relates to the residual test of the final model, it was found that the values of the autocorrelation function were within confidence limits, and that these residuals are random and follow a normal distribution. The weekly values of the dollar index were predicted according to the (D16)-ARIMA(5,1,2) hybrid model for a period of ( 16) weeks, Table 4 and Figure 9 show the predictive values and confidence limits at the level of significance (0.05).…”