【作者】 姜仁娜；

【导师】 叶俊；

【作者基本信息】 清华大学 ， 数学， 2004， 硕士

【摘要】 Chib和Greenberg(1994)首次对非截尾的ARMA模型的参数估计提出了MCMC算法。在此之前,时间序列模型的参数估计方法主要集中在经典算法的使用,例如MLE方法,但对于复杂的时序模型,经典算法具有很大的局限性。MCMC算法与MLE方法相比,它避免了极值优化过程的复杂性和参数初值的选取问题,并且具有更好的稳定性。因此,MCMC算法已越来越受到统计界和计量经济界的广发重视。Nakatsuma, T. (2000a) 和Goldman, E.等 (2000b) 分别对ARMA模型和ARMA-GARCH模型做了MCMC算法研究,Goldman, E. 和 Tsurumi, S. (2001) 也使用MCMC算法对双截断的ARMA-GARCH模型进行了分析,结果都充分表明了MCMC算法的优越性。由于实际中的金融数据有时会受到一定的界限限制,例如各国的货币机构会对本国的汇率进行限制,因此研究截断模型具有很强的实际意义的。对于截断数据模型,如果采用的最小二乘法来估计参数,则容易忽略随机误差项实际上的异方差性,造成参数估计量的偏差。因此本文主要讨论用Metropolis-Hastings算法对双截尾的ARMA-GARCH-M模型进行参数估计。文中首先提出了双截尾的ARMA-GARCH-M模型,在详细的给出了其后验分布及参数的建议分布后,对此模型设计了M-H算法。作为算法的实际应用,我们做了模拟数据分析,并使用该算法对日元/美元汇率数据(1997.1.2-1998.12.31)的双截尾ARMA-GARCH-M模型的参数进行估计。论文的另一部分工作是讨论上证指数和深证成指的长记忆性问题,所采用的模型是研究长记忆性所常用的ARFIMA(p,d,q)模型,重点集中在对分整参数d的估计。文中使用Hurst指数方法估计参数d,分别用经典R/S方法、有偏修正R/S方法和无偏修正R/S方法进行研究,并结合国内的上指和深指的收益率数据,给出了三种方法的结果。在此基础上,给出ARFIMA模型的最优阶和全部参数估计值,进一步得出了上证指数和深证成指收益率所适合的最优ARFIMA模型。更多还原

【Abstract】 MCMC algorithms were developed by Chib and Greenberg(1994) for the untruncated ARMA model. The classical algorithms such as MLE were widely used to study time series models before, but they are limited for the complicated time series models. Compared to MLE procedures, MCMC algorithms are more stable and the problems such as searching the multiple maximal are avoided, and the rate of convergence is also faster than the classical methods. In recent years MCMC methods have been widely attended by the statistician, and have become an important subject in time series analysis. There are a lot of papers concerning about MCMC algorithms in time series models. Nakatsuma, T. (2000a) and Goldman, E. et al (2000b) developed MCMC procedures for ARMA models and ARMA-GARCH models separately, Goldman, E. and Tsurumi, S. (2001) developed MCMC algorithms for doubly-truncated ARMA-GRACH models, these results all showed the advantages of MCMC algorithms. In this paper we develop a MCMC procedure for the doubly-truncated ARMA-GARCH-M model which maybe become increasingly important for estimating volatility returns and exogenous shocks for finance data.Because the practical financial data are always limitary, for example the monetary authorities manage to limit the exchange rate to control the market risk, it is very significant to study doubly-truncated models. On the other hand, using OLS to estimate the parameter of the doubly-truncated data is prone to neglect the heteroskedastic characteristic of stochastic errors, consequently result in the basis estimation of parameter. Therefore we develop a hybrid Metropolis-Hastings algorithms to estimate the parameter of doubly-truncated ARMA-GRACH-M models. In this paper, we construct doubly-truncated ARMA-GRACH-M models first. After giving the posterior distribution and proposal distribution of parameters we develop the iterative processes of the M-H algorithm. To illustrate the validity of M-H method, <WP=4>we consider an example with simulated data and finally doubly-truncated ARMA-GRACH-M models of exchange rate series are estimated.The other part of this paper is to discuss the long-time memory of return rate of shanghai and shenzhen stock market, and we use the ARFIMA(p,d,q) models. We discuss the estimation methods of parameters in ARFIMA(p,d,q) model, especially the estimation of the parameter d. We use Hurst Exponent method to estimate the parameter d, and study the classical R/S method, biased modified R/S method and unbiased modified R/S method. In particular, we analyze the return rate of shanghai and shenzhen stock market using those R/S methods and give the comparative results. The results indicate that Chinese stock market has shown long-term memory. On this condition, we give the optimum ranks and the estimations of all parameters in ARFIMA(p,d,q) model, accordingly we educe the optimum ARFIMA models for the return of shanghai and shenzhen stock market.更多还原