基于力学矢量加法的二维PAR过程及其实证研究

Two-Dimensional PAR Process and Its Empirical Research Based on Kinetic Vector Addition

经济系统由于受到了许多复杂因素的影响,通常是非线性的,因而时间序列分析中常用的线性AR过程不能描述序列中的非线性特征。借鉴经典物理学中的矢量加法,用不同大小和方向的作用力对应经济系统中指标受到的众多影响因素,展现经济系统的复杂性。创立时间序列的矢量分析方法,并与AR过程相结合,提出具有二维矢量形式的PAR过程。在平面直角坐标系中对矢量经济指标进行正交化分解,进而给出矢量AR过程的二维坐标方程,然后用离差平方和的最小二乘法推导出矢量AR坐标方程的系数。对SP500收益率建模的实证结果表明:PAR过程的预测精度显著高于传统的AR过程,证明了PAR过程的可行性。

The economic system is usually nonlinear due to many complex factors,so the traditional linear AR process cannot depict the nonlinear features in time series analysis. Referring to the vector addition in classical physics,the complexity of the economic system was showed with that different size and direction of the force corresponding index was affected by many factors in the economic system. A phasor analysis method was proposed. Then,we combined it with AR process and built the two-dimensional PAR process. In plane rectangular coordinate system,we had the orthogonalization decomposition of vector economic indicators,which are vector AR two-dimensional coordinate equation of the process,and then used the sum of squared residuals of least squares to deduce coefficientvector AR coordinate equation. Finally,the empirical results show that the PAR process forecasts more accuracy than the traditional AR process,indicating the applicability of the proposed PAR process.