长记忆理论及其在金融市场建模中的应用

【作者】 邓露；

【导师】 张晓峒；

【作者基本信息】 南开大学 ， 数量经济学， 2009， 博士

【摘要】 上个世纪80年代以来,长记忆理论开始在计量经济学领域中得到迅速发展,并逐渐在金融领域中得到广泛应用。然而到目前为止,理论界关于如何准确检验一个时间序列是I(0),I(d)还是I(1)过程的问题,在检验方法和统计量上仍存在很多争论。当前的估计和检验方法也只适用于较为简单的情形,对于模型中存在短记忆成分和结构突变成分的研究方法还很不完善,迫切需要从理论上进一步深化。此外,在实证研究中,有证据表明,金融市场如股票市场中的回报率及其波动性都具有长记忆特征,这就意味着市场有效性假定不复存在。不仅如此,政府宏观政策的冲击还有可能改变市场的长期特征,忽略这一问题很可能影响到市场有效性的判定和相应政策的制定。因此,对金融市场长记忆性的精确建模对于投资组合与风险管理就有着非常重要的意义。要实现上述目的,就必须从理论上对这一领域的研究进行系统和完善,并在实践中加以正确运用。本文立足于目前理论研究和实践应用中存在的具体问题,在总结前人研究成果基础上,对长记忆理论及其在金融市场建模中的应用进行深入了研究。其贡献主要体现在以下几点:第一,基于一个ARFIMA(p,d,q)过程,对三种分数单积参数的半参数估计方法的有限样本性质进行了比较,并用蒙特卡罗方法对备择假设下短期项对分数单积参数估计和长记忆性判别的影响进行了模拟。第二,基于一个误差项是分数白噪声过程的AO模型,对小样本下不同突变形式对分数单积参数估计和检验的影响进行了分析,并对上述情形下多个未知突变点BP检验的有限样本性质给出了模拟证据。第三,分析了结构突变对中国股市长记忆性的影响,将长记忆参数改变看作市场有效性的变化,就政府干预对股市有效性的影响进行了科学评价,并提出了政策建议。本文对于长记忆理论及其在金融市场中应用的研究是按照一定的逻辑思路逐步展开的。全文共分为六章,第一章是引言,阐述论文的选题背景及意义、研究思路与方法、主要创新点。接下来三章是理论研究部分,其中第二章是长记忆过程及其模型研究,主要对长记忆过程的定义与特征,两种长记忆模型即ARFIMA和FIGARCH模型的设定及其估计方法进行分析。在此基础上,第三、四章分别探讨了短期项和结构突变项对于长记忆建模的影响。第五章作为实证研究部分,首先运用长记忆模型对石油期货市场中的“约瑟夫效应”进行了验证。接下来运用长记忆性与结构突变分析方法对我国股市的有效性与政府干预问题进行了研究。最后一章是结论以及对未来研究方向的展望。通过各章的分析,我们得到的主要结论有:第一,当数据生成过程是一个一般的ARFIMA(p,d,q)而不是分数白噪声过程时,各半参数方法得到的分数单积参数估计量仍能服从正态分布,但其分布的均值却明显偏离了真实值,这就造成分数单积参数估计的偏差和长记忆性的误判。同时,自回归参数和移动平均参数往往具有不同的短期效应。此外,基于小样本下不同带宽的模拟,建议在实践中应该选择较大的带宽。第二,通过对一个带有结构突变的长记忆过程检验其长记忆性,发现模型中的结构突变尤其是趋势突变会造成对分数单积参数的高估,导致长记忆性检验的功效和尺度扭曲都很高。这时,在各种半参数方法中,GPH方法的稳健性相对较高,造成的偏差最小。接下来,将Bai和Perron(1998,2003)多个未知突变点估计和检验方法推广到误差项是长记忆过程的情形中,发现除d接近于0.5的情形外,该方法对突变点的估计和检验具有比较好的效果。尤其是当d＜0时,突变点估计量的分布、以及相应的检验功效和实际检验水平也更优。该检验对于突变点的位置、突变幅度的变化也表现的比较稳健。第三,对石油期货市场的实证研究发现,该市场的投资风险对新息冲击的响应是一个长记忆过程。因此在实践中,建议采用FIGARCH等模型对未来的石油价格及其波动进行预测,并采取相应策略确保宏观经济平稳运行。通过对我国股市有效性的再审视,发现我国股票价格走势的改变常常是政府政策的出台造成的。而在不同阶段,政策对于股票市场有效性的影响也不同。因此,在今后的发展中,政府要逐步抛弃依靠政策引导股市的观念,这是中国股市走向有效性的必由之路。更多还原

【Abstract】 Since 1980s, the long memory theory has been developed very fast in the Econometrics area, and been put into application in the Finance widely. However, as far as the theoretical research is concerned, there is no consensus among the question on how to test a stochastic process is I(0), I(d), or I(1) . Moreover, the estimation and test method is only fit for the simple model, and there is no mature analysis when there is affection of short memory term and structural break. Therefore, theoretical improvement is highly needed. As to the empirical research, there is evidence that the return series and its volatility show long memory properties in the financial market, for example, the stock market, which means that the Efficient Market Hypothesis (EMH) is no longer existed. In addition, shock from government policy may change the long term characteristics of the market, lose sight of which may influence the EMH judgment and the related policy. So it is great importance of exact model specification on the investment portfolio and risk management. To make all of the above goals into realization, the research on long memory theory must be systematical improved and then put into application in a correct way.Based on the available literatures, this thesis aims at the solution of the present theoretical and empirical problems and makes research on the long memory theory with its application in the financial market. The main contribution of the thesis are as follows: Firstly, based on an AKFIMA(p, d, q) process, it compares the finite sample properties of three semiparametic estimator on the fractional integration parameter d, and makes simulations on the influence of the short memory term on the estimation of d and the test of long memory under the alternative hypothesis by Monte Carlo approach. Secondly, the influence of the different structural breaks terms is analyzed based on an AO model in which the error term is a fractional noise. And then, the performance of BP test on unknown muli-break points is simulated via Monte Carlo method under small samples. Thirdly, taking the change of the long memory parameter as the market efficiency’s altering, the latent impact of structural breaks to China’s stock market is studied. At last, the effect of the government policy is evaluated and advices are given.The study on the long memory theory with its application on financial market is deployed gradually. The whole thesis comprises six chapters. The first one is introduction, which briefly demonstrates the background and significance of the research, the goals and method used, and the innovations. The next three are theoretical study. Thereinto, the second chapter is the long memory process and model study in which we introduce the definition, characteristics, and ARFIMA and FIGARCH model with the estimation. Above on this, the third and forth chapter analyze the impact of short term and structural breads on the modeling of long memory process. The fifth chapter is empirical research which starts with an verification of the "Joseph effect" in the oil futures market, and then the EMH in China’s stock and government intervention is researched via the long memory and struck breaks approach. The last chapter is conclusion and future research interest. The main conclusions of the thesis are as follows:Firstly, When the process is a general ARFIMA(p, d, q) rather than fractional noise, the distributions of the semi-estimators are still normal, however, the mean has some deviation from the real value, which cause power and size problems in the test. And the AR and MA parameters have different short term effects. Moreover, we suggest chose longer bandwidth in the practice.Secondly, through the long memory test on an AO model with fractional noise errors, we find that the structural breaks especially the trend breaks can cause overestimate of the long memory parameter, and lead to high power and size. In this situation, the GPH estimator is more robust with smaller bias. Next, the Bai and Perron(1998, 2003) test is extended into long memory conditions and shows a fairly well performance except that d is close to 0.5. Especially when d<0, the distribution of the estimator and the test are even better. Besides, the test is relatively robust to the location and change of the break points.Lastly, through the empirical research on the oil futures market, it is indicated that the shock of innovation to the investment risk is a long memory process. Therefore, the FIGARCH model should be used in practice to forecast the oil futures price and its volatility and the related policy should be make to keep the stable economic growth. Through the retest of the long memory properties in our stock market, it shows that the change of the price have something to do with the government policy, which has different impact to the market efficiency in different periods. Therefore, the policy-leading way on management of the stock market should be abandoned in the future which is the exact way for the market to go to efficiency.更多还原