【作者】 王清生；

【导师】 陈敏；

【作者基本信息】 云南大学 ， 概率论与数理统计， 2013， 博士

【摘要】 首先,本文定义了一个刻画整个时间序列起伏波动特征的子序列,即交替的局部高低点列,由此二维点列可以导出另一关于高低水平和升降时间的二维点列。由定义可知,这一特殊子序列决定了整个序列局部趋势方向的转换、大小的调整及持续的时间,如果对这一导出的二维点列能够建立有效的统计模型,则对时间序列数据来说,尤其是金融数据,具有非常重要的理论价值和应用价值,例如研究金融市场的有效性、行为金融学、各种金融衍生产品的定价、证券投资及金融风险管理等。其次,关于此导出的二维点列,我们建立了两类体制转换模型：依赖于局部高低点的趋势转换模型和基于牛熊体制转换的局部高低点模型。前者刻画了动态过程的局部趋势在上升时受局部高点(高水平level,上升时间duration)的影响而转折向下,趋势在下降时受局部低点(低水平level,下降时间duration)的影响而转折向上,且这些交替的局部高低点列是前后依赖的。本质上,它是一类有别于固定门限的时变门限模型,此时变门限值(或点)就是数据序列的二维新子列(高低水平和升降时间),对此子序列建立了一个二维向量自回归的辅助模型,用此辅助模型来预测未来局部趋势方向的变化及大小的调整。又因当前二维门限值的预测吸收了过去门限值的信息,这些决定局部趋势的关键信息是过去较为长远的,而在建模局部趋势或均值的主模型中,局部趋势的大小不但吸收了局部短期的信息,而且吸收了辅助模型的中长期信息,所以当前局部趋势方向与大小既受局部短期因素的影响,也受较中长期因素的影响。此辅助模型与局部趋势主模型构成一个精美的对称结构,简称之为依赖于局部高低点(水平level,时间duration)的趋势转换模型(Trend-LD);为了更贴近于现实金融市场,后者在前者的基础上,对处于牛熊市下的局部高低点列分别进行建模,描述了金融数据在牛熊市下不对称的起伏波动行为。显然,它既吸收了局部的起伏波动信息,也吸收了牛熊趋势背景信息,是技术分析中的趋势理论和波浪理论思想的一个综合。我们认为这种动态行为是投资者的羊群效应对金融证券作用的直接反映。此外,我们还提出了一个体制弱平稳的定义,它是随机过程弱平稳的一个推广。再次,研究了金融市场中股指的局部高低波动水平和局部升降时间非对称地影响投资者的行为。结果表明起伏波动的高低水平比其升降时间更依赖于由前期的起伏波动(高低水平和升降时间),前后局部高低水平之间的依赖性要远大于前后局部升降时间之间的依赖性,而且前期局部高低水平对随后局部升降时间的影响要大于前期局部升降时间对随后局部高低水平的影响。这可能是因为局部高低水平波动幅度与投资者的短期盈亏有着直接的联系,而局部涨跌时间(周期)与投资者的短期盈亏关系相对弱些,因此二者对投资者的行为影响是不同的。最后,这两类模型应用于全球具有代表性的(发达和不发达)股票市场指数。前者应用于6个股票指数的建模,经验结果表明局部趋势方向和大小检验都显著地优于随机游走过程,这也意味着即使是如欧美这样发达的股票市场也是无效的,这与过去的许多经验研究是不同的；后者应用于建模16个股票指数,在考虑交易成本的条件下,基于此模型的结合顺势而为的低买高卖投资策略,模拟投资于起伏波动较大的不发达市场股票指数,本策略在到期末和整个模拟投资区间的业绩表现都显著地优于买入持有策略(即战胜市场),而模拟投资于起伏波动较小的发达市场股指,则业绩表现有分歧：(1)模拟投资于具有较长观测数据的北美地区的股指,本策略在到期末和整个模拟投资区间的业绩表现几乎都显著优于买入持有策略。(2)对于数据较少的欧洲和日本的股指,则本策略之业绩表现有些不如买入持有策略,而有些与买入持有策略没有明显差异。显然,基于本模型的模拟投资策略主要利用了局部高低点的信息,如果局部波动不大,加之频繁交易的成本,则很难战胜市场的。此经验结果进一步验证了不发达股票市场都是无效的和本模型是有应用价值的,即使对于发达的股票市场,长期来看,本策略也是有应用价值的,只是在局部长时间的强牛市中本策略表现不如买入持有策略。从行为金融的角度而言,这些经验结果表明了在不同市场发展程度中的投资者心理行为是不同的,尤其是羊群效应具有很大的差异,越是较为成熟的、法治更为完善的金融市场,投资者的羊群效应显得更为弱些,反之则相反。更多还原

【Abstract】 Firstly, in this paper we define a subseries of a time series, namely, a local alternate high-low point sequence, which characterize the rise-fall fluctuation of the whole series and is two-dimensional. It can be derived into another two-dimensional point sequence on the high-low level and up-down duration. By the definition, the particular subseries determine the direction change, the size correct and the duration of the local trend of the whole time series. If the new two-dimensional point sequence can be effectively builded a statistical model, it is a very important for the theoretical and practical value of time series data, especially financial data. For example, it is used to study the efficiency of financial market, behavioral finance, the pricing of the various derivatives of financial securities, the investment of securities and financial risk management and so on.Secondly, about the new two-dimensional point sequence, we build up two types of regime-switching models:one is a trend-switching model depended on the local high-low point, the other is the local high-low point model based on the regime-switching of bull-bear market. The former characterizes that the local trend of the dynamic process is resisted by the local high point (high level, upward duration) when the process rises, and supported by the local low point (low level, downward duration) when the process falls, meanwhile, the alternate local high-low points are before-after dependent and clustering. In essence, its thresholds are not fixed, but time-varying. The variable thresholds (or points) are a new two-dimensional sequence (high-low level, upward-downward duration). For the sequence, we set up an auxiliary model that is two-dimensional vector autoregressive. By means of the auxiliary model, we predict both the change of the direction and the correction of the size of the local trend. Moreover, because the forecast of the current two-dimensional thresholds (local high-low turning point) incorporate the information on the past thresholds, the critical information that controls the direction and the size of local trend is medium-and long-term. Furthermore, in the main model, which is also called for local trend (mean) model, the size of the local trend absorbs not only local short-term information, but also medium-and long-term information from the auxiliary model, so the switching of the direction and the correct of the size of the current local trend are impacted by both local short-term and medium-and long-term factors. We propose the beautiful, symmetric structure that the local trend (main) model is integrated with an auxiliary model. The specification can be also called the trend-switching model depends on the local high-low point or on both level and duration (Trend-LD); In order closer to real financial markets, the latter, based on the former, models local high-low points in bull and bear market respectively, and characterizes the dynamic behavior that the rise-fall fluctuation of local trend is not symmetric. Obviously, it incorporates not only the local information of rise-fall fluctuations, but also the large background information of bull-bear trend, so it is a blend of trend theory and wave theory in technology analysis. We believe that this dynamic behavior is a direct reflection of investors’ herding on security prices. In addition, we proposed a definition of weak stationarity of regime. It is a generalization of the common weak stationarity of stochastic process.Thirdly, this paper researches that investors’ behavior in the financial market asymmetrically affected by the local high-low levels and rise-fall durations of fluctuation of stock index. The results show that the dynamic behavior of the current high-low level of fluctuation is more dependent on the past fluctuations (high-low levels and rise-fall durations) than that of the rise-fall duration. The dependence between the high-low levels is much larger than that between the rise-fall durations. Moreover, the impact of the past local high-low levels on the subsequent rise-fall duration is greater than that of the past rise-fall durations on the subsequent local high-low level. This may result in the short-term profit of investors is more directly related to the local high-low level of fluctuation than to the local rise-fall duration (cycle). Therefore, the impact of the both on investors’ behavior is different.Finally, the two types of models are applied to the representative (developed and undeveloped) stock market indices. The former is used to model the six stock indices, the empirical result show that the forecasts of the direction and size of the local trend under the former’s hypothesis are significantly better than those under random walk hypothesis. It also means that even well-developed stock markets (e.g. Europe and North America) are not efficient, and the conclusion differs from those of the past many empirical studies. The latter is used to model the sixteen stock indices. Considering the transaction cost, By means of the model, we implement the buy-low-and-sell-high strategy along trend to invest the stock indices in the non-developed market with large rise-fall fluctuations. The findings show the performances of the strategy both at the end of the period and in the entire interval of investment simulation are significantly better than those of the buy-and-hold strategy (i.e., beat the market); However, to invest the stock indices in the developed markets with small rise-fall fluctuation, the performances are differences:(1) Implemented to invest in the stock index with a large observation data in North America, the performances of the strategy both at the end of the period and in the entire interval of investment simulation are almost significantly better than those of the buy-and-hold strategy;(2) With a less observation data in Europe and Japan, some are not significant as good as those of the buy-and-hold strategy, other are not significant different from those of the buy-and-hold strategy. Clearly, the simulating investment strategy based on the model, mainly takes advantage of the information of local high-low points. Nevertheless, if the local rise-fall fluctuation of the stock index is too small, taken the frequent trading cost into consideration, the simulating strategy is difficult to beat the market. The empirical result further shows that the non-developed stock markets are not weak efficient and the model-based strategy is practical for the non-developed stock markets, as even for the well-developed stock market in long-term view, except for the long-term strong bull market. From a behavioral finance perspective, the empirical results suggest that the psychological behaviors of investors in a different degree of development of the stock market are different, especially, herding behavior is a large difference. The more mature and sophisticated financial markets are, the more weak investors’ herding behavior is, and vice versa.更多还原