销售收入时间序列在销售价格与销售数量之间的矩阵分解

Matrix Decomposition on Times Series of Sales Revenue between Sales Price and Sales Volume

为更好地反映销售价格与销售数量对销售收入的作用特征与规律,本文在将销售收入时间序列在销售价格与销售数量之间的乘法分解基础上,进一步提出矩阵分解。将销售价格乘以销售数量等于销售收入这一基本逻辑关系纳入销售收入的时间序列分解中来,将销售收入分解为由销售价格和数量各自的趋势性、周期性、季节性、随机性分量双边交叉相乘所得的销售收入,依次得到销售收入与销售价格、销售数量之间在水平绝对量、水平相对量、变动绝对量、变动相对量上的分解矩阵和分解定理,并将该矩阵分解理论与方法在百度公司付诸实践发现,可以设计出一些标准化的报表来集中体现业绩分解结果,以助提高企业业绩分析效果。

To better reflect the characteristics and rules of the sales price and sales volume to the sales revenue, matrix decomposition is proposed based on Xu （2017） multiplicative decomposition between the sales price and the sales volume. The basic relation, ＂The sales price multiplied by the sales volume equals to the sales revenue＂, was included in the decomposition of the time series. The original sales revenue was decomposed and a new result is produced by cross-multiplying sales price and sales volume of trend, cyclical, seasonal, and irregular component bilaterally. The decomposition matrices and theorems of sales revenue between sales price and sales volume on the absolute amount, the relative amount, changes in the absolute amount, changes in the relative amount are proposed in turn. The matrix decomposition theory and method are put into practice in Baidu Inc. Findings show that certain standardized reports can be designed to reflect the decomposition results of performance which may help improve the performance analysis results.