Quantifying market efficiency of China’s regional carbon market by multifractal detrended analysis

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Applied Energy Symposium and Forum 2018: Low carbon cities and urban energy systems, CUE2018-Applied Energy andLow Forum 2018: Low carbon andsystems, Applied Energy Symposium andSymposium Forum 2018: carbon cities and urbancities energy CUE2018, 5–7 June 2018, Shanghai, China CUE2018, 5–7 June 2018,2018, Shanghai, ChinaChina urban energy systems, 5–7 June Shanghai,

Quantifying market efficiency of China’s regional carbon market by QuantifyingThe market efficiency of China’s regional carbon market by 15th International Symposium on District Heating and Cooling multifractal detrended analysis multifractal detrended analysis Assessing the feasibility of using the heat demand-outdoor Xinghua Fanaa, Xiangxiang Lvaa, Jiuli Yina,* , Jiaochen Liangbb a,* Xinghua Fan , Xiangxiang Lv , Jiulidistrict Yin , Jiaochen Liang temperature function for a long-term heat demand forecast Center for Energy Development and Environmental Protection Strategy Research, a a

Center for Energy Development and Environmental Protection Strategy Research, Jiangsu University,Zhenjiang,Jiangsu,212013,China

a a b c c University,Zhenjiang,Jiangsu,212013,China Department of Agricultural California State Fresno. , O. Le Corre I. Andrića,b,c*, A. PinaJiangsu , P. FerrãoBusiness, , J. Fournier ., University, B. Lacarrière b

b Department of Agricultural Business, California State University, Fresno. IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract a

Abstract

An efficient carbon market is important for mitigating carbon emissions. We investigate the efficiency of Chinese An efficient carbon is important for mitigating carbon emissions. We investigate Chinese carbon market usingmarket Multifractal Detrended Fluctuation Analysis. Data samples are basedtheonefficiency the returnofseries of Abstract carbon market Multifractal Fluctuation Analysis. Data samples are based on the series of seven pilots in using the Chinese carbonDetrended market. We find asymmetric distributions of carbon prices andreturn general Hurst seven pilots in the Chinese carbon market. find asymmetric distributions carbonmarkets prices and general exponent in the return series, both of whichWe suggest a lack of efficiency in theofcarbon under study.Hurst We then Districtanheating networks are commonly in the literature as one of most effective solutions forefficient decreasing exponent in the return series, both of which a lack of efficiency in the the carbon under study. We then define inefficiency indicator based onaddressed thesuggest generalized Hurst exponents, in which a markets zero value means andthe gasless emissions fromThe the building sector. Theseofsystems require high investments which are returned through theand heat define inefficiency indicator based on the generalized Hurst exponents, in which zero value means efficient agreenhouse higheranvalue efficient. inefficiency values the carbon markets pilots areaall greater than one, indicating sales. to less the changed climate conditions and policies, heathad demand in thethan future aubiquitous higherDue value efficient. The them. inefficiency values of therenovation carbon markets pilots are all greater one,could indicating inefficiencies among But there isbuilding evidence that the efficiencies been slightly improved asdecrease, the prolonging the investment return period. ubiquitous inefficiencies them. Butpilot. thereThe is evidence that the efficiencies been slightly improved markets developed exceptamong for the Tianjin efficiency ranking of the pilothad markets varies when usingas the The main scope of this paper is to assess theFor feasibility of using the ranking heat – outdoor temperature function for heat demand markets developed except for the Tianjin pilot. The efficiency of the pilot markets varies when using different time windows for the analysis. time scales shorter thandemand a month, the Chongqing pilot generally ranks forecast. The district of for Alvalade, infor Lisbon (Portugal), was used as a case study. Thepilot district is consisted of 665 different time the analysis. For time shorter than a amonth, the pilot generally the highest andwindows the Hubei pilot thelocated lowest; timescales scales longer than month, theChongqing Beijing performs theranks best buildings that vary in both construction period and Three weather scenarios (low, medium, high)with and market three district the highest andthe theworst. Hubei pilot the lowest; for timetypology. scalesthat longer than a month, Beijing pilot performs the best while Tianjin Regression results further show the inefficiency is the positively correlated renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were while Tianjin worst. Regression results thesuggestions inefficiencyfor is positively marketare activity in the the short run while negatively in further the longshow run. that Policy improvingcorrelated the tradingwith activities compared with results from a dynamic heat demand model, previously developed and validated by the authors. activity in the short run while negatively in the long run. Policy suggestions for improving the trading activities are also discussed based on the findings. Thediscussed results showed only weather change is considered, the margin of error could be acceptable for some applications also basedthat onwhen the findings.

(the error©in2018 annual demand 20% for all weather scenarios considered). However, after introducing renovation Copyright Elsevier Ltd.was Alllower rights than reserved. Copyright ©the 2018 Elsevier Ltd. All rights reserved. scenarios, error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). Copyright © 2018 Elsevierunder Ltd. All rights reserved. Selection and peer-review ofofthe committee of of Applied Energy Symposium and Forum 2018: Low Selection and peer-review underresponsibility responsibility thescientific scientific committee theup CUE2018-Applied Energy Symposium and The value of slope coefficient increased on average within the range of 3.8% to 8% per decade, that corresponds the Selection and peer-review under responsibility of the scientific committee of Applied Energy Symposium and Forum 2018: to Low carbon cities and urban energy systems, CUE2018. Forum 2018: Low carbon cities and urban energy systems. decrease in and the number of heating hours of 22-139h during the heating season (depending on the combination of weather and carbon cities urban energy systems, CUE2018. renovation scenarios considered). On the other trading hand, function intercept increasedDetrended for 7.8-12.7% pergeneral decadeHurst (depending Keywords: market efficiency; carbon market ; emission pilot;carbon price; Multifractal Analysis; exponent.on the coupled market scenarios). The values suggested couldtrading be used to modify theMultifractal function Detrended parameters for thegeneral scenarios Keywords: efficiency; carbon market ; emission pilot;carbon price; Analysis; Hurstconsidered, exponent. and improve the accuracy of heat demand estimations. 1. Introduction

1. Introduction © 2017 The Authors. Published by Elsevier Ltd. Carbon markets have played core mitigation roles both in major developed and developing economies. Since the Peer-review under responsibility ofcore the Scientific Committee of The 15th International Symposium on District Heating Since and the Carbon markets have played mitigation roles both in major developed and has developing economies. introduction of the European Emission Trading System (ETS), the number of ETSs more than tripled since 2012, Cooling. introduction of the European Emission Trading System (ETS), the number of ETSs has more than tripled since 2012, Keywords: Heat demand; Forecast; Climate change 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. 1876-6102 Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the Applied Energy Symposium and Forum 2018: Low carbon cities Selection and peer-review under responsibility the scientific Selection peer-review responsibility of the scientific committee of the Applied Energy Symposium and Forum 2018: Low carbon cities and urbanand energy systems, under CUE2018. and urban energy systems, CUE2018. 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection and peer-review under responsibility of the scientific committee of the CUE2018-Applied Energy Symposium and Forum 2018: Low carbon cities and urban energy systems. 10.1016/j.egypro.2018.09.246

Xinghua Fan et al. / Energy Procedia 152 (2018) 787–792 Author name / Energy Procedia 00 (2018) 000–000

788 2

going from 5 to 18. With the introduction of China’s carbon trading system (CN ETS) in 2018, global emissions carbon pricing programs would cover nearly 30% of global emissions [1]. China’s pilot programs contribute to its national ETS by providing experience and momentum. In June 2013, China announced the establishing of seven carbon trading pilots in five cities (Beijing, Tianjin, Shanghai and Chongqing) and two provinces (Hubei and Guangdong). By June 2015, all the seven pilots had completed their first compliance period. In general, those pilots work under the cap-and-trade mechanism while each remains independent. Different market performances exist since each pilot has local characteristics corresponding with their respective economic development as well as energy-saving and emission reduction technologies [2]. As the experience accumulated in the pilot programs is quite valuable for CN ETS [3], it is important to make a close look at the detailed differences of the market efficiency of those four-year-old ETS pilots. The efficiency of the carbon market is particularly important for emission intensive firms, risk managers, policy makers as well as for investors in the emerging class of energy and carbon hedge funds [4]. The current literature on the effectiveness is mainly focused on the EU ETS. Seifert et al. [5] showed that the EU carbon market was fully effective and echoed by Tang et al. [6] pointing that EUA futures market is efficient within one month. However, more researchers found the weak efficiency of the carbon market [7-9]. Charles et al. [10] pointed out that the main European carbon markets are inefficient but the market efficiency is found to be improved over the period. As to the efficiency of Chinese market, studies on are rather sparse. Zhao et al. [11] showed that the market efficiency of ETS pilots is not satisfactory in spite of the fact that system designs of ETS have achieved preliminary result. In a later research [12], they found signs of restoring market efficiency in the carbon emission market of four representative cities. Wang et al. [13] showed that part of the pilots such as Shanghai and Beijing achieved the weak efficiency. Cheng et al. [14] designed the evaluation indexes and built a DEA evaluation model for the pilot carbon market operation efficiency. The method of Multifractal De-trended Fluctuation Analysis (MFDFA) [15], has been applied in many fields. Wang et al. [16] investigate the efficiency and multifractality of the COMEX gold market based on MFDFA. Syed Aun R. Rizvi et al. [17] used a comparative analysis of Islamic and developed countries’ stock markets by extending the understanding of their multi-fractal nature. Wang et al. [18] tested for the efficiency of WTI crude oil market through observing the dynamic of local Hurst exponents employing the method of rolling window based on MFDFA. These study show that, one can obtain the nonlinear characteristics in both small and large fluctuations by using MFDFA. While prior studies have shown that the carbon markets are not efficient, there are no studies on the degree of efficiency of the market. As there are several pilots in Chinese carbon market, it is necessary to know an inefficiency ranking in order to make further rules or regulations in those pilots. These motivate us to introduce a reverse indicator for market efficiency so that we can rank the inefficiency of the pilot markets. MFDFA is applied in this paper to analyze the market efficiency. This methodology not only enables us to know the extent of inefficiency, but also assists in identifying the efficiency ranking. 2. Method Multifractal de-trended fluctuation analysis is applied in this paper. The procedure of MFDFA consists of five steps. For a series of signals �W�V�� 䁙 �� � � we firstly integrate the signals and get the profile of cumulative sums

y  j    i 1  xi  x , x  j

1 N



N

i 1

x i  .

(1)

Next, we divide the profile into � 䁙 䁐� segments of equal size. Considering that the length of the series is generally not an integer multiple of the time scale �, to include all data, we repeat the entire procedure starting from the end of the series, obtaining � � segments. Then in the �th segment, we fit the integrated time series by using a discretized linear function ���h�a , and the local trend is defined as

Yv , s i   y i   yv , fit , v  1s  i  vs.

For each of the �

�

segments, we calculate the mean square deviation from the local trend

(2)



Xinghua Fan et al. / Energy Procedia 152 (2018) 787–792 Author name / Energy Procedia 00 (2018) 000–000

Fs2 v  

1 s 2  Yv,s v  1s  i . 2 i 1

(3)

Finally, we average over all segments to obtain the �th order fluctuation function

 1 Fq s     2Ns

2Ns

 F v  2 s

v 1

q 2

789 3

1q

 1   , q  0 and F0 s   exp   4Ns 

1q

 ln F v   , q  0.  v 1  2Ns



2 s



(4)

A power-law relation �� W�V � ��W�V between �� W�V and the size � with the scaling exponent or correlation exponent �W�V indicates that the original signal �W�V is long-range correlated. The exponent �W�V is usually known as the generalized Hurst exponent. When �W�V is constant for all �, the time series are mono-fractal. Otherwise, the series are multifractal. Specifically, when �W�V  쳌䁐�, the kinds of fluctuations related to � are persistent. An increase (decrease) is always followed by another increase (decrease). When �W�V 䀀 쳌䁐�, the kinds of fluctuations related to � are anti-persistent. An increase (decrease) is always followed by another decrease (increase). But if �W�V 䁙 쳌䁐�, the kinds of fluctuations related to � display random walk behavior. 3. Data and experimental 3.1. Data Seven pilot carbon markets in China are selected as the sample. Among the seven markets, Chongqing pilot is the latest initiated. We choose the daily trading data of carbon prices. The time period covers from the initiation date of Chongqing to Feb. 9, 2018. Transaction data come from the website (http://k. tanjiaoyi.com/). Table 1. Descriptive statistics of carbon prices. Activity refers to the percentage of number of transaction days to that of the total calendar trading days. ADF is statistic of Augmented Dickey–Fuller unit root tests based on the least AIC criterion. KS denotes the test statistic of the Kolmogorov-Smirnov test for normality. ’***’ indicates rejection at the 1% significance level. Activity Min

Max

Mean

Std

Skew Kurt

ADF

KS

Beijing

60.92 30.000 77.000 49.748 6.617 0.154 5.445 -0.824 0.157***

Chongqing

27.1

1.000 47.520 17.654 11.671 0.325 2.004 -0.759 0.158***

Guangdong

77.27

7.570 71.090 18.931 10.822 2.574 9.908 -2.969 0.260***

Hubei

97.76 10.070 28.690 19.794 4.515 -0.087 1.559 -0.935 0.161***

Shanghai

58.01

Shenzhen

51.29 19.840 76.790 40.253 9.417 0.428 3.722 -1.430 0.113***

Tianjin

37.18

4.200 48.000 24.093 12.408 0.028 1.770 -1.099 0.161*** 7.000 42.410 18.087 6.707 0.051 2.396 -1.941 0.160***

Table 1 shows wide differences in prices across the markets. For example, while carbon emission daily prices in Beijing range between ¥30 and ¥70, Hubei is characterized by a much lower variation of between ¥10.07 and ¥28.69. These large differences are also reflected by the mean values. Table 1 also reports the asymmetric characteristics of the distributions which is an indicator of market inefficiency. The ADF tests confirm that prices data are nonstationary at the 1% significance level. The KS statistic rejects the null hypothesis of Gaussian distribution at the 1% significance level, also evidenced by the nonzero skewness and high values of kurtosis. The two pilots of Chongqing and Tianjin have the lowest trading activity, implying they may be the most deficient. 3.2. Multifractal analysis The fractality of the series is derived from a log-log plot between the length scale and the order of fluctuation function. The scaling range is set to between 5 (about one week) and 250 (about one year). Fig. 1 shows the relationship between �� and � for Hubei and Chongqing markets when � ranges from -10 to 10 with a fixed step 2 ( Plots of other markets are similar to that of Hubei. For the length of the paper we omit them).

Xinghua Fan et al. / Energy Procedia 152 (2018) 787–792 Author name / Energy Procedia 00 (2018) 000–000

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We can see that a linear behavior changes (especially for Chongqing market) when � 䁙 � 䁙 �㔲. Followed by Wang et al. [16], we classify � 䀀 � as short-term component and �  � as long-term component of carbon prices. We note that � 䁙 �㔲 is corresponding to about one month which is consistent with the results in most financial market. Table 2 shows the generalized Hurst exponents. From the table we confirm that the returns are multi-fractal both in the short and long terms because the �W�V is dependent on �. At the same time, as �W�V is greater than one for most cases, the original return series is fractional Brownian motion (fBM). We also know that all kinds of fluctuations are persistent both in the short-term since �W�V  쳌䁐� . The persistent dynamics is typical of systems with positive feedback mechanisms, which are intrinsically unstable [16]. Thus, all kinds of fluctuations are unstable. This is unusual for general financial markets. The possible reason lies in the abnormal trading performance. The generalized Hurst exponents �W�V show a more moderate change when � varies for both the terms. This change in �W�V implies that the multi-fractality characteristic of the markets becomes weaker and that the market efficiency is relatively improving. When � 䁙 �, the Hurst exponent H  h ( 2) is around zero which is far from 0.5, indicating that Chinese carbon markets are not efficient, neither in the short-term nor in the long-term.

Fig. 1. The curve of Fq(s ) versus

s in log log

plot for Hubei and Chongqing pilots.

Table 2. Generalized Hurst exponents. Beijing Chongqing Guangdong Hubei Shanghai Shenzhen Tianjin Short Long Short Long Short Long Short Long Short Long Short Long Short Long term term term term term term term term term term term term term term -10 1.4673 1.3844 1.0296 1.9210 1.7374 1.3457 1.5506 1.5665 1.4466 1.4852 1.4913 1.5335 1.6185 2.2670 q

-8

1.4551 1.3599 1.0305 1.8928 1.7030 1.3337 1.5324 1.5440 1.4218 1.4628 1.4686 1.5079 1.5955 2.2378

-6

1.4351 1.3225 1.0319 1.8444 1.6430 1.3186 1.5024 1.5082 1.3830 1.4266 1.4320 1.4668 1.5514 2.1900

-4

1.3904 1.2625 1.0348 1.7446 1.5297 1.2994 1.4448 1.4402 1.3188 1.3621 1.3607 1.3929 1.4534 2.1001

-2

1.2530 1.1696 1.0434 1.4918 1.3467 1.2675 1.2941 1.2741 1.2025 1.2408 1.1891 1.2496 1.2830 1.8793

0

1.0923 1.0727 1.0592 1.1518 1.1482 1.1839 1.0551 1.0627 1.0477 1.0334 1.0536 1.1075 1.1345 1.3320

2

1.0237 1.0065 1.0259 1.0414 1.0454 1.0710 1.0231 1.0105 1.0040 0.9251 1.0325 1.0527 1.0315 1.0601

4

0.9950 0.9761 1.0220 1.0149 1.0201 1.0083 1.0201 1.0057 0.9994 0.9150 1.0262 1.0278 1.0119 1.0072

6

0.9770 0.9618 1.0197 1.0036 1.0060 0.9792 1.0182 1.0046 0.9946 0.9039 1.0226 1.0102 1.0046 0.9834

8

0.9616 0.9535 1.0181 0.9962 0.9955 0.9627 1.0165 1.0036 0.9905 0.8920 1.0203 0.9968 1.0010 0.9676

10 0.9472 0.9478 1.0170 0.9901 0.9876 0.9514 1.0149 1.0024 0.9873 0.8808 1.0185 0.9863 0.9993 0.9557

3.3. Inefficiency measure We define a measure of the degree of market inefficiency related to the generalized Hurst exponents as,

INE 

1  h 6  0.5  h6  0.5 . 2

(5)



Xinghua Fan et al. / Energy Procedia 152 (2018) 787–792 Author name / Energy Procedia 00 (2018) 000–000

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The choice of �W �V comes from Fig.1 where the slope does not change much for ���  �. For a market to be efficient, all kind of fluctuations should follow random walk behavior, i.e., all � are equal to 0.5. Thus, for an efficient market, the value of � 䁙 has to be close to 0. Otherwise, a large value of � 䁙 indicates a less efficient market. For a further understanding of the efficiency, we compute the value of � 䁙 in different time periods about two years. The first period is named 2014, covering from the initial trading day to the end of the year 2015. The period 2015 starts from the beginning of the year 2015 to the end of the next year. The last period 2017 is from Jan.1, 2017 to the last of the sample period. Fig. 2 shows the inefficiency values. For the short-term time scale, it is evident that all inefficiency values are greater than 0.5 indicating none of the markets is efficient. But the degree of inefficiency varies among the market as well as in different time periods. The efficiency is improved as time goes by except for Tianjin. As to the Fig.2 rank of inefficiency, both Chongqing and Shanghai rank first in efficiency once and Tianjin twice in the short time window. Shanghai pilot performs the worst in the 2017 period, Hubei pilot in the 2015 period and Guangdong pilot in 2014 and 2016 periods. However, for the whole time period, it is Chongqing pilot takes the first place and Hubei takes the last place. For the long-term, it is almost the reverse results. Tianjin pilot behaves the worst in three periods out of the four and the whole time range. Beijing and Hubei pilots perform the best, each in a half time. Taking the whole sample time period, on average, Beijing pilot performs the relatively best, followed in order by Hubei, Shanghai, Shenzhen, Guangdong, Chongqing and Tianjin.

Fig. 2 Inefficiency values in different time windows. Each window covers about two years.The label ‘whole’refers to the whole sample period.

3.4. Efficiency and market activity Market efficiency has been found to be strongly related to market factors such as market development stage [17] and liquidity [19]. Poor trading activity in Chinese carbon pilots has been a common characteristic in that their average daily transactions volume did not meet expectation [20]. This subsection analyzes the role of trading activity plays in improving the efficiency of Chinese markets. Table 3. Regression of inefficiency on market activity.‘**’ and ‘***’ represent significance level at 5% and 1%, respectively.

Short term Long term Activity 0.47 -0.537 5.198 ** 12.931 *** a-value 7.716 ** 14.900 *** �-value A number of measures on trading activity in financial markets have been proposed and studied [21]. We use the ratio of number of transaction days to that of the total calendar trading days as the indicator of market trading activity. Values of the trading activity are shown in Table 1. Let the inefficiency be the dependent variable. Table 3 confirms that market activity does have a role in the market efficiency but the role is different between the short-term and the long-term. The INE is positively correlated

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Xinghua Fan et al. / Energy Procedia 152 (2018) 787–792 Author name / Energy Procedia 00 (2018) 000–000

with the market activity for the short-term while negatively in the long-term. The power for the market activity in the long term is slightly stronger than that in the short term (-0.537 to 0.47). Thus, to improve market efficiency, more trading should be encouraged and traders are suggested to focus on price fluctuation at least for one month. 4. Conclusions We measure the degree of market efficiency of the carbon pilots in China by using MFDFA. All the pilot markets are multifractal both for time scales smaller than a month and for time scales larger than a month. Each pilot market is lack of efficiency as reflecting by the large value of the general Hurst exponent. Introducing the inefficiency value, we quantify the market efficiency of the pilot markets and then rank them in different time windows. Ranking orders are different between the short term and the long term. Finally we find that market inefficiency is positively correlated with the market activity for the short-term while negative in the long term. Although there is a sign of improvement in efficiency for some pilots, it is still a long way to see an efficient carbon market even for the European market, let alone for the Chinese market. Ranking of market efficiency provides important information for policy makers, helping them making policies for CN ETS. Acknowledgements Research is supported by the National Natural Science Foundation of China (Nos.71673116,71690242,71403105) and the Humanistic and Social Science Foundation from Ministry of Education of China (Grant 16YJAZH007). References [1] Pizer, WA., Zhang, X., China’s new national carbon market, Working Paper of Nicholas Institute for Environmental Policy Solutions. 1801(2018), 1-11. [2] Ren, C., Lo, A., Emission trading and carbon market performance in Shenzhen, China. Applied Energy, 193(2017) 414-425. 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