语言数据的自回归模型及其在上证综指预测中的应用

Autoregressive Models for Linguistic Data and Its Application in the Forecast of Shanghai Composite Index (SCI)

专家对金融证券市场的感知和判断是一相对重要的信息资源,应在系统建模中结合实际数据加以适当吸收和利用。本文给出基于随机模糊结合方法的一类移动平均自回归模型,并将其用于上证综指月度数据的趋势预测中。由于专家的感知或判断通常以语言形式表达,而语言通常具有模糊性特征。基于模糊随机变量对此类语言数据定义其均值、方差、协方差以及误差标准化过程,并得到模型在一种集间距离下的最小二乘估计及其渐近性质。给出了该模型在上证综指预测中的实证结果,其表明本文的自回归模型不仅较好地适用于语言数据环境并给出良好的模糊值预测结果,而且同时带来对原始股价序列的较准确预测结果,其精度对比基于实际数据的自回归模型的预测结果有显著提高。

The expert’s perception or judgment on the financial security market is relatively a valuable financial information resource, which ought to be utilized in a proper way combining with the real original data. In this paper, we propose autoregressive moving average models with a random fuzzy combinatory method and apply the models to the prediction of the trends of the monthly Shanghai Composite Index(SCI). Since the human’s perception or judgment is usually expressed in a linguistic way, which is considered to be characterized with fuzziness. The expectation, variance and covariance as well as a standardized process of errors are defined for such linguistic data based on the fuzzy random variables, and a least square estimation formula as well as its asymptotic properties for the model are obtained. Some empirical results from the prediction of the monthly Shanghai Composite Index(SCI) with this model are given. A comparison of the real linguistic SCI with the prediction values shows that the proposed forecasting model is suitable to the environments of the linguistic data, which not only gives us an accurate fuzzy-valued prediction result for linguistic SCI, but also brings a good forecast for the original monthly SCI, and the prediction precision is greatly raised comparing with a prediction from the real original data based autoregressive model.