External Shocks and the Law of Carbon Price Fluctuation —Based on the Framework of CWT and EEMD

This paper focused on researching the fluctuation of carbon trading price caused by the external shocks through analyzing the data of three-phase carbon spot price from Blue Next Environmental Exchange and the European Climate Exchange (ECX). The results are the following: 1) released important information and events will seriously affect the carbon price fluctuations; some important information are released that cause sharp fluctuations in a short period of time; the Sudden events lead to long-term, drastic fluctuations in carbon price and its influence over the impact of important information; 2) the impact of external events is always corresponding to the low-frequency component of time sequence; this is because the low-frequency component usually reflects the data signal amplitude which is severer, and the high-frequency component represents the data signal amplitude which is a smaller part; it has random fluctuations of the time sequence.


Introduction
In order to respond to the challenge brought by global climate change, the European Commission established European Union Emission Trading Scheme (EU ETS) in Jan. 2005, with market mechanism as a new path to address greenhouse gas emission reduction issue, making carbon credit tradable intangible goods and gradually transit to a financial asset. EU ETS is the first major carbon trading market worldwide, also the biggest carbon trading market currently worldwide. The practice of 11-year operation of EU carbon credit trading market Since EU ETS was established, the price of carbon credit has experienced several dramatic fluctuation: due to imbalance of supply and demand resulting from deviation of initial quota estimation by the government; the price of carbon credit suffered a cliff fall after the event of certification disclosure in the end of April 2006; when it was known in the end of Phase I that carbon quota cannot be used continuously, the price of carbon credit fell to near zero; due to influence of global financial crisis, the price of carbon credit fell dramatically again in later 2008; due to influence of European debt crisis and stagnation of global climate negotiation, the price of carbon credit fell once again in early 2011. Wide ranged fluctuation, especially nose dive of carbon credit price, fails to provide clear signal of market price for long-term emission reduction of enterprises, not conductive to promotion of long-term investment in emission reduction of enterprise.
In order to protect enterprises' enthusiasm of emission reduction, reduce investment risk of investors, and maintain stable operation of carbon market, dramatic price fluctuation shall be avoided as much as possible.
Through intuitive observation it was found that every dramatic price fluctuation of EU ETS actually related to impact of external shocks (disclosure of important information and sudden events). Major issue this paper will address is to observe fluctuation of carbon credit price after external event, empirically test whether impact of external event is a major factor influencing short term abnormal fluctuation of carbon credit price in some specific period and further analyze extend of these events influencing yield of carbon quota market in short time. Through analysis of such events, we try to arouse carbon market rule designer's attention to impact of external event to draw experience and learn lessons to constantly improve design of trading system and risk control system, promote solid development of carbon market, at the same time, to help instruct trading behavior of carbon market participant during recurrence of such events, providing reference for them to maximize profit and enhance ability to hedge risk. In addition, we also hope to provide reference for China building a national unified carbon market from 2017 to 2020.
With development of EU carbon financial industry and enhancement of commodity and financial attributes of carbon credit, carbon price fluctuation draws high attention of scholars, and research on influencing factor and fluctuating rule of carbon price becomes a hot spot increasingly.  [8] found that besides significant influence of energy price and air temperature on carbon price, policies and system influencing supply-demand change also hace significant influence; Zou Yasheng et al. [9] found that CER cash market price is positively influenced by macroeconomic indicator and climate indicator of environment factor by analyzing with VEC model and impulse response model: Zheng Chunmei et al. [10] found that carbon credit future price is not influenced by petroleum future price by analyzing with MS-VAR model. Factors influencing carbon credit future price are different in different period. As for factors influencing carbon credit price at home, Ding Yang [11], Zheng Yuhua et al. [12] found that carbon price is influenced by factors such as economic factor, energy price and exchange rate, etc. likewise at home. Research of Xu Jia, Tan Xiujie [13] shows that domestic carbon price is influenced significantly by impactive event represented by policy adjustment and market inherent mechanism.
With regards to research on carbon market price fluctuation, existing litera-  [17] used event study method to analyze the happened since the establishment of the EU ETS 50 policy issues affecting the price of carbon trading, unlike previous single policy research of events, but the 50 events can be divided into 6 types, classification inspects the influence degree of each type of event to the carbon price, the results show that the influence of the negative influence of slightly higher than the positive events, and some events have a long term and short term different influence on the carbon price. In addition, in financial area, event research is also widely used to discuss the influence of a specific economic event on market value. For example, Pan Huifeng et al. [18] used the method to research the influence of impactive supply impact on petroleum market; Guo Hongyu et al. [19] used event analysis to observe short term influence of QE policy on Japanese stock market.
In a word, this paper thinks existing researches have the following deficiency:

Wavelet Analysis and Signal Identification and Detection
Wavelet analysis is a kind of variable resolution time-frequency analysis, mainly used in signal processing, it can effectively process unsteady signal. The principle is to look at time sequence data as a group of signal to be processed, signal fre-   The yield adopts spot transaction logarithm yield of 3 phases, which is the first order difference of the log taken from price to ensure stability of data. Written as:

Source and Pre-Processing of Data
where, i = 1, 2, 3, represents yield of 3 phases respectively.

Wavelet Analysis Based Carbon Price Singularity Detection
Signal singularity typically has two cases: 1) Amplitude mutates at some point, causing discontinuity of signal, this kind of mutation is called discontinuity of the first kind; 2) signal appears smooth, its amplitude has no mutation, but the first order difference of the signal has mutation and first order derivative is discontinuous, this type of mutation is called discontinuity point of the second kind.
Step of singularity detection is as follows: Step I: Yield time sequence fluctuation analysis According to equation 1) calculate yields of 3 phases R 1 , R 2 , R 3 to plot, results are shown as Figures 1-3, the amplitude in phase 1, 3 has obvious mutation, there is no obvious mutation in phase 2， but its appearance is non smooth curve, so only need to detect discontinuity point of the first kind. Seeing from yield fluctuation of 3 phases, price fluctuation in phase 1, 3 is more violent, while phase 2 is relatively smooth. Long vertical line represents the part with relatively violent fluctuation.
Step II: Wavelet decomposition As for wavelet base selection of wavelet decomposition, combining results of multiple wavelet base fitting and referencing other similar research, it is found

Singular Points and Corresponding External Event
We analyzed several singular points with larger jump and found that every jump point has the background of external event. External events at the time corresponding to price fluctuation singular point of 3 phases are shown as Table 1.

Influence of External Event Impact on Carbon Market Yield
In order to further analyze how external event influences carbon price fluctuation and test the result of continuous wavelet singularity detection, this paper chose 7 events in phase 1 and 3 as research subject to analyze the influence of external event on carbon price fluctuation in detail by using EEMD based event analysis. It can be found from layer analysis of wavelet signal that yield fluctuation is mainly combined result of components of different frequency. From the angle of structure decomposition, this paper decomposes and restructure into dimensions of high frequency component and low frequency component to discuss the influence of external event on carbon market yield fluctuation. High frequency component reflects small amplitude fluctuation, and low frequency component reflect larger one. Through structural combination of yield of different frequency, we can improve accuracy of analysis of price fluctuation rule.

Decomposition and Restructuring under EEMD Algorithm
Referencing the setting rule on decomposition by Huang, Wu et al. [20], the amplitude ratio coefficient of white noise is set as 0.2, the number of population mean is set as 100. Decompose the yield of 2 phases into a trend component and 8 Intrinsic Mode Function (IMF s ) of different frequency respectively with EEMD, IMF 1 -IMF 8 are ranked from high frequency to low frequency respectively, combine MF 1 -IMF 4 to high frequency components, combine IMF 5 -IMF 8 to low frequency component, the result of combination is shown in Figure 7 and Figure 8.  The European Union's 2007 emissions report.
In early April 2012 The global financial crisis broke out.
In the middle of September 2008 The third phases: 2013.01.01-2020.12.31 The European Union's 2012 emissions report.
In early April 2013 The European Union's 2013 emissions report.
In early April 2014 The European Union's 2014 emissions report. In

Abnormal Yield Test of High and Low Frequency Component
Using the basic thoughts of event analysis, lock a test interval of the chosen external event. This test interval is divided into an estimate window and an event window. Estimate window is the period before occurrence of the event. This paper chose 70 days before occurrence of the event as the estimate window to estimate normal yield without event. Event window is the period when the event occurs. This paper chose the period when above mentioned singular point positioning occurred as event window to test abnormal yield variation during this period. Set mean yield of estimate window as normal yield without event, expressed as: I and t represent time t of No. i event; T 0 represents the start date of estimate window, T 1 represents the start date of event window; abnormal excess yield in event window is expressed as: Finally, took single sample t statistical test for abnormal yield variation of high and low frequency component in event widow respectively, compare significance of yield variation, and extent of influence before and after event. The result of test is as shown in Table 2.
The smaller statistical result P value is, the more significant the result is, that

Conclusions
Main conclusions of the paper are as follows: first, wavelet analysis is a excellent abnormal point detection tool, able to precisely find the singular point of EU External incident impact is an important factor influencing over fluctuation of carbon market, and EU ETX has incident effect, so, carbon market supervision department shall consider the impact of policy issuance on market stability, predict the influence of impactive social political and economic incidents on carbon price fluctuation when making management system, so as to increase response shall also pay attention to the impact of relevant incident to acquire maximum benefit from investment in carbon exchange. Contribution of this article is based on such mature events in the European carbon market analysis, which can cause the carbon market rules designers full attention to external shocks, draw lessons from experience and constantly improve the design of the trading system and risk control system, promote the development of the carbon market steady. At the same time it also can help to guide the carbon trading behaviors of market participants to happen again, as they seek to maximize income and improve the ability of avoiding risk for reference, which for the Chinese national unity will be from 2017 to 2017 construction carbon markets. Carbon market supervision departments formulate policy management system to consider the impact on the market stability, and can expect a major social and political and economic emergency on the fluctuation of the carbon price, improve the impact of the response speed of response to major events, and establish the elastic carbon rationing regulating mechanism, to keep carbon emissions moderating scarcity. Investors should also pay attention to the impact of relevant events to get the most out of the carbon trading market.
Due to the limit of the method in this paper, we can only demonstrate whether there is any impact of different events on EUA returns but cannot explain the causality for each policy.