Characteristics of Critical Fluctuations Caused by Self-Modulation and its Application

我分析了所谓的自调制系统，它是一种动态随机过程，其参数由其自身轨迹的移动平均值给出。在这三年里，我研究了自调节系统的基本性质和应用。最典型的例子是公开市场上的交易间隔，如日元兑美元汇率市场。我已经证明，由最优移动平均归一化的区间的时间序列可以很好地用纯泊松过程来近似。这里，最优移动平均数由特征时间指数衰减约30秒的加权移动平均数给出，然后将自调节的基本思想推广到市场价格，特别是在我拥有10多年高质量数据的日元兑美元市场。我首先介绍了市场价格的最优移动平均数，然后观察了这个降噪市场价格的动态。发现这种动态并不像金融技术假设的那样纯粹是随机的，我发现了明确的证据，表明存在着潜在的市场力量。这个势力不是一个常数，但它的中心以更大尺度的移动平均线移动，势的曲率也在从正稳定状态到负不稳定状态缓慢变化。这种动力学性质可以用势系数来表征。由于这一分析方法适用于市场风险评估，本人开发了一种可应用于真实公开市场的实时数据分析算法，并从理论上证明了势能公式表示为对价差的一种自调制过程，从而大大扩大了自调制的适用性。

I analyzed so-called the self-modulation systems which are dynamical stochastic processes whose parameters are given by the moving averages of their own traces. In these 3 years I have studied the basic properties and also applications.The most typical example of the self-modulation systems is the transaction intervals in open markets such as the Yen-Dollar exchange market. I have shown that the time sequence of the intervals normalized by an optimal moving average is quite well approximated by a pure Poisson process. Here, the optimal moving average is given by a weighted moving average with exponential decay of characteristic time about 30 seconds.Then the basic idea of self-modulation is generalized to the market prices especially to the Yen-Dollar market which I have the high quality data for more than 10 years. I firstly introduced an optimal moving average for the market prices and then observed the dynamics of this noise-reduced market price. It is found that the dynamics is not purely random as assumed by the financial technology, I found clear evidence that there exists a potential force of market. This potential force is not a constant but its center is moving with a larger scale moving average and the curvature of the potential is also changing slowly between a positive stable state to a negative unstable state. This dynamical property can be characterized by the potential coefficient. As this analysis is suitable for risk evaluation of markets, I developed a real time data analysis algorithm which is ready to be applied to the real open market.It is also shown theoretically that the potential force formulation is expressed as a kind of self-modulation process for the price difference, so the applicability of the self-modulation has been enlarged considerably.