非等间距多变量模型在数乘变换下的特性

Characteristics of Non-equidistant Model Based on Multiple Transformation

讨论了原始序列在数乘变换下非等间距MGM(1,m)模型的特性问题。利用矩阵相关的运算性质,推导出非等间距MGM(1,m)模型在数乘变换后参数向量、模拟预测值及相对误差的计算公式,并比较了在数乘变换前后的变化情况。研究结果表明:对各原始序列作相同倍数的数乘变换,不会改变模型的模拟预测效果,还能缩小数据的量级,使计算过程更简洁。该结果还适用于等间距模型,使结果应用更广。

The characteristics of non-equidistant MGM(1,m) model was discussed under the original sequence made by multiple transformation.The calculation formula of parameter vector,simulation prediction values and the relative errors of the non-equidistant MGM(1,m) model after multiple transformations were derived by using the operation nature about matrix.The changes of parameter vector,simulation prediction values and the relative errors after multiple transformations were compared.The results show that simulative and predicative effect of the model is not changed,the magnitude of the data is reduced and the calculating process is simplified when the original data series are made the same times of multiple transformation.The results are also applied to equally spaced model.