﻿ 基于Markov状态转换的期货铜价格预测及风险控制模型 Price Forecasting and Risk Control Model of Copper Futures Based on Markov State Transition Model

Statistics and Application
Vol.05 No.02(2016), Article ID:17935,11 pages
10.12677/SA.2016.52020

Price Forecasting and Risk Control Model of Copper Futures Based on Markov State Transition Model

Yongzhong Tian

Yunnan Copper Industry Limited by Share Ltd., Kunming Yunnan

Received: Jun. 9th, 2016; accepted: Jun. 25th, 2016; published: Jun. 30th, 2016

Copyright © 2016 by author and Hans Publishers Inc.

This work is licensed under the Creative Commons Attribution International License (CC BY).

http://creativecommons.org/licenses/by/4.0/

ABSTRACT

Copper as a kind of important non-ferrous metals, has a strong influence on other non-ferrous metal prices, so the stable development of the copper futures market not only has an important role in spot copper market development, but also has great significance in other non-ferrous metals market stability and promoting sound and rapid development of the national economy. In this paper, the two-state Markov state transformation model is used to predict the yield and volatility of copper futures with good results.

Keywords:Copper Futures, Markov Transformation Model, Composite Likelihood Function

1. 引言

Markov状态换模型由Hamilton (1989) [1] 首先提出，他在研究美国的经济周期时，运用三状态两阶滞后的Markov机制转换模型研究了美国1953~1984年间季度实际产出增长的波动，模型回归效果良好。Cai (1994) [2] 、Hamilton、Susmel (1994) [3] 几乎同时提出了将Markov状态换模型引入ARCH模型中的方法，这一创举使得对变结构金融资产序列的波动性建模取得了显著的进步和发展。孙金丽、张世英(2003) [4] 将MS-GARCH模型运用到中国股票市场的分析中，证明具有结构转换功能的MS-GARCH模型的分析结果由于单一状态条件下的GARCH模型。朱钧钧 [5] (2011)利用马尔科夫状态转换–门限GARCH模型的MCMC估计对我国股市波动率的双重不对称性进行了解释，得到了稳定并且可信的结果。

2. 理论方法综述

2.1. Markov链

2.2. Markov模型

Markov模型中需要估计的参数有转移概率, ,。我们采用EM算法去进行参数估计，关于似然函数的选择有两种方式：完全似然函数Zucchini (2009) [6] 、复合似然函数Zou (2013) [7] 。不过在Zou (2013) [7] 已经说明复合似然函数效果要好于完全似然函数。

,

,

3. 模型分析

3.1. 日收益率数据分析

Figure 1. 2001~2015 Shanghai futures copper’s daily index return rate

3.2. 模型构建

3.3. 模型效果

3.3.1. 模型的收益率

3.3.2. 模型的准确率

Table 1. 2001~2015 three model yields

Figure 2. Prediction accuracy of the model (training time equals 100 trading days)

Figure 3. Prediction accuracy of the model (training time equals 150 trading days)

Figure 4. Prediction accuracy of the model (training time equals 200 trading days)

3.3.3. 模型对大幅波动的预判

4. 模型的缺陷和不足

5. 总结

Table 2. The predict situation of model to large fluctuations

Figure 5. Comparison of actual yield and forecast yield

Price Forecasting and Risk Control Model of Copper Futures Based on Markov State Transition Model[J]. 统计学与应用, 2016, 05(02): 203-213. http://dx.doi.org/10.12677/SA.2016.52020

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