基于状态转移模型的条件期望与方差--从2状态到N状态的推广

THE CONDITIONAL MEANS AND VARIANCES BASED ON REGIME-SWITCHING MODEL—GENERALIZATION FROM TWO-STATE TO N-STATE

基于状态转移模型计算的条件期望与方差,可以应用到金融领域,计算和度量市场在不同状态下的收益与风险.Nielson基于2状态转移模型,计算了2状态下股市的收益率的条件期望与方差.然而,实际研究中,常需要用到3状态、甚至多状态的状态转移模型.因此,基于Nielson的研究,从2状态推广到了N状态.基于N状态转移模型计算了条件期望、条件方差及无条件期望、无条件方差,该结果更具普遍性且形式更为简洁.最后,采用计算期望与方差的方法,分析中国股市收益率与波动率.实证结果表明,中国股市除存在牛市、熊市外,还存在政策市,且其具有"低风险,高收益"的特点.利用N状态转移模型计算的期望与方差可以更合理地度量金融市场在不同情况下的收益与风险.

The conditional means and variances via regime-switching model could be applied to measure the return and risk of financial market in different situations. Therefore, Nielson （2000） estimated the unconditional and conditional means as well as variances of stock returns via two-state regime switching model. However, three-state, even N-state regime switching model is needed always. Consequently, in this paper, the two-state regime-switching model is extended to N-state. A simple and general form of unconditional and conditional means as well as variances based on N-state regime-switching model is given. The result of this paper is applied to investigate the return and volatility of Chinese stock market. Empirical results show that there is not only bull market and bear market, but also ＂ policy market＂ in Chinese stock market, and the characteristic of ＂ low risk, high return＂ exists in Chinese ＂ policy market＂. Thus, the conditional means and variances based on n-state regime-switching model is a better tool to measure the return and risk of financial market in different situations.