基于等时圆矢量差分的ARVMA组合模型及其实证研究

ARVMA PROCESS AND ITS EMPIRICAL RESEARCH BASED ON VECTOR DIFFERENCE IN AN ISOCHRONAL CIRCLE

对于非平稳的时间序列,直接差分会丢失很多有价值的信息,增大建模误差.采用与传统的数学改进方法不同的物理模型,对非平稳时间序列提出了基于矢量差分的ARVMA(Autoregressive Vectorized Moving Average Model)组合模型.借助矢量三角形非线性的可加性以及等时圆中质点沿弦下滑的等时性,构建等时圆中的矢量差分方法和由点出发的时间序列,并用作用力函数的极大值阐释了最大价格的产生机制.然后,利用矢量差分可以减弱过度差分的优良性及差分时一阶自相关系数的自适应性,充分论证了非线性的矢量差分在消除非平稳趋势时可以最大程度地保留原始数据的信息量.最后,对IBM股票日收盘价数据进行实证研究.实证结果表明:等时圆矢量差分方法与直接差分相比预测误差更小.

A direct difference method may make data lost a lot of valuable information for non-stationary time series, and it will increase the modelling error. In this paper, the ARVMA （Autoregressive Vectorized Moving Average Model） process is proposed for the modelling of non-stationary time series, which is different from traditional mathematical improvement method. Firstly, with the help of nonlinear additivity for the vector triangle and isochronism for the circle, a vectorial difference method is created and the time series which is from a point is built. Then the maximum value of the power function is used to explain the generation mechanism of the largest price. Next, we employ the effectiveness of reducing the excessive difference and the adjustability of the first order autocorrelation coefficient to demonstrate that the amount of information of the original data is fully preserved when eliminating the non-stationary trend term compared to direct difference method. Finally, IBM stock closing price data are used for empirical research and the empirical results show that the forecast error of vectorial difference method based on isochronal circle is smaller than that of direct difference method.