The Test For Heteroscedasticity Of Partially Linear Autoregressive Models With An Exogenous Variable

Forecasting to the forest resources is now one of forest ecology construction research area newest tasks. According to the current forest conditions, the prediction about future development is extremely important to the forest resources plan and the ecology construction. However, the forest system has the following characteristic: wide spatial distribution, long growth cycle, multitudinous influencing factors, complex structure, and comprehensive function; And it also has renewability, the uncertainty of the trend, which is random dynamic large-scale system with a dispersed structure. According to the forest resources characteristics we may use the random time-variable dynamic models to conduct the research.The observations'variance homogeneity is a very basic hypothesis in the classic regression analysis. Only under this hypothesis, can the conventional statistical inference be carried on. If the variance is not homogeneous and unknown, the regression analysis will meet many questions. Therefore it is necessary to test the variance homogeneity of the models. This article mainly has conducted the comprehensive research on the forest resources'partially linear autoregressive models with an exogenous variable. And it has obtained A series of good results. This article's main work summarizes as follows:Variance structured method has been taken to study the partially linear autoregressive models'variance homogeneity examination systematically. We obtain the likelihood ratio test statistic and the Score test statistic. And then, based on using the parameter orthogonalization method we gain the model's revised likelihood ratio test statistic and revised Score test statistic to test the variance homogeneity. Finally, we investigate the test power by Monte Carlo simulations, which display the effectiveness of the proposed test, and an practical example is also given to illustrate the application of our results. The results indicate: The revised likelihood ratio test is better than the likelihood ratio test and the revised score test surpasses the score test. This method is concise, effective.