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Does the “ice-breaking” of South and North Korea affect the South Korean financial market?
Chaos, Solitons and Fractals 132 (2020) 109564
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Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos
Does the “ice-breaking” of South and North Korea affect the South Korean financial market? Wei Shao a, Jian Wang b,∗ a b
Department of Economics, Korea University, Seoul 02841, Republic of Korea Department of Mathematics, Korea University, Seoul 02841, Republic of Korea
a r t i c l e
i n f o
Article history: Received 11 June 2019 Revised 8 November 2019 Accepted 6 December 2019
Keywords: Multifractality Market efficiency Foreign exchange Kospi
a b s t r a c t In this paper, we use the multifractal detrended fluctuation analysis (MF-DFA) to study the difference in financial market of South Korea before and after South and North Korean leaders’ meeting on April 27, 2018. Hurst exponent, quality index, and multifractal spectrum are used to analyze the characteristics and stability of South Korean financial markets before and after the South and North Korean leaders’ meeting. We investigate the foreign exchange and stock markets in South Korea. The results show that multifractality is existed in all time intervals for both the markets, and the multifractal characteristics after the meeting are stronger, which indicates that both the markets before the meeting have a higher market efficiency, and decreased after the meeting. The meeting of South and North Korean leaders since April 27, 2018 is a possible interpretation for changes of efficiency in South Korean financial markets. To document the major source of multifractality, we shuffle and phase-randomize both the original series of two markets. The results show that both the long-range correlation and fat-tailed distribution contribute to multifractality for the time series before the meeting, and only fat-tailed distribution contributes to the multifractality of both times series after the meeting. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction In the research, we focus on whether the warming of relations between North and South Korea has an impact on the financial markets of South Korea. Many studies show that the external social crises and political conflicts can response to financial markets. The study in [1] showed that the latest financial crisis has truly affected complexity revealed in the volatility time series of the world major markets. In addition, the global financial crisis also resulted in the nonlinear dynamics of equity, currency and commodity markets [2]. Barro [3] proposed a model showing that the high observed stock premium has realistic risk aversion by extending Rietz’s model [4]. Rigobon and Sack [5] measured the influence of Iraq war on financial market, they found that the“war risk” factor accounted for a considerable portion of the variances of financial variables. Veronesi [6] believed that a higher degree of political instability result in a more volatile stock market. Berkman et al. [7] showed that disaster risk can affect the expected stock returns by using various samples of international political crises. In this paper, we examine whether the benefit of political event has an impact on financial markets. The political favourable event ∗
Corresponding author. E-mail address: [email protected] (J. Wang).
https://doi.org/10.1016/j.chaos.2019.109564 0960-0779/© 2019 Elsevier Ltd. All rights reserved.
we chosen was the meeting between South Korean leader Moon Jae-in and North Korean leader Kim Jong-un in Panmunjom on the Korean side on April 27, 2018. We need to point out that this is the first summit meeting between the top leaders of South and North Korea after the former President Roh moo Hyun crossed the 38th parallel of latitude 11 years ago. In the past 11 years, due to the continuous nuclear test of North Korea and the nuclear threat to South Korea, the relations between the two countries have been deteriorating. This summit meeting between the leaders of two countries is of historic significance. The two countries jointly signed the “Panmunjom declaration”, declaring that there will be no more war on the Korean Peninsula and stopping all hostilities. Some scholars have studied that the relationship between South and North Korea affects the financial markets of South Korea. Huh and Pyun [8] found that there is a negative correlation between the market’s concern about North Korean early nuclear threat and the South Korean stock market. Dibooglu and Cevik [9] used North Korean Threat Index to examine the effects of the threats on stock markets and foreign exchange markets in South Korea and Japan. The test results showed that there exists a causal relationship between the threat of North Korea and the stock returns and exchange rate returns in both countries. When studying the impact on the South Korean market of North Korean military attacks [10], Gerlach and Yook found that foreigners maintained
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their performance level before the attacks, while domestic individuals, who accounted for the vast majority of domestic trade, performed poorly. The South Korea’s stock market has a large scale and strong liquidity. Its annual turnover ranks 9th in the world and its total market value ranks 17th in 2011. Based on this, the sudden elimination of North Korea’s nuclear threat and the historic ice-breaking of bilateral relations are bound to have an impact on South Korea’s financial markets. In this paper, we will use the MF-DFA method to study the real historical data of stock and exchange rate, to confirm whether the ice-breaking in South and North Korea has played a role in the market efficiency of the financial market, and to explore the sources of multifractal characteristics of stock and foreign exchange market before and after the ice-breaking. The multifractal properties of empirical data have attracted wide attention due to a large range of properties related to scale invariance, which is one aspect in various scientific fields. This method has been tested in various financial time series, such as foreign exchange markets [11,12], stock markets [13–19], and bitcoin market [20–22]. More recently, high frequency multifractal characteristics of bitcoin was studied by Stavroyiannis et al. [23]. Moreover, Lahmiri and Bekiros [24] investigated the multifractal chaotic dynamics of Islamic and Green crypto-currency series in econophysics literature. Their findings indicated that the price, volatility and volume series of Islamic and green crypto-currencies embed high persistence compared to the conventional crypto-currencies. Also for Islamic financial markets, the authors estimated the Hurst exponents and found that the distributions are statistically different within Islamic and non-Islamic alternative markets [25]. The MF-DFA is one of the several techniques used to characterize the multifractal properties of financial time series. Many scholars used MF-DFA to analyze the impact of a shock on the financial market and did the comparative analysis before and after the event. Ning et al. [26] considered the Chinas foreign exchange reform as a shock to analyze the market efficiency of exchange rate market, they found the efficiency of both the onshore and offshore RMB/USD spot exchange rate changed, and they concluded that changes in intervention of the Peoples Bank of China since the reform is a possible explanation. Mensi et al. [27] assessed the role of the global financial crisis on market efficiency of Islamic stock markets by using an MF-DFA analysis. In addition, due to the effect of Shanghai Hong Kong stock connect program, the authors analyzed the Shanghai and Hong Kong stock markets before and after the connect program [28]. Besides, for more using MD-DFA to evaluate the impact of an emergency on the financial market, please refer to [29–31]. Thus, the MF-DFA is considered as a analysis method in our research. As a measure of testing the efficiency of financial markets, multifractality were widely studied in the past two decades. In addition to the financial market, multifractal analysis has also been applied for studying the fields of atmospheric Science, biomedical, and phase transitions. In related researches, the multifractal properties and cross-correlation behavior of air pollution index time series data were studied by using multifractal analysis method in [32]. Recently, MF-DFA was used to examine the time series of daily air temperature in [33]. By using multifractality, generalized Hurst exponents are calculated for distinguishing seizure and seizure-Free intervals of intracranial electroencephalogram (EEG) signals from epileptic patients [34]. The generalized Hurst exponents are also taken to classify the normal and abnormal EEG records in [35], and estimate differentiate EEG signals of healthy and epileptic patients in [36]. Li et al. [37] used the MF-DFA to analyze the human heart rate variability during exercise, which can provide useful information for athletes to choose the best sports time and accelerate the development of sports medicine.
Zhao et al. [38] focused on the phase transitions by analyzing the multifractality of the time series. The layout of the rest of this paper is as follows. In Section 2, we introduce the multifractal spectrum and MF-DFA. In Section 3, we provide a data description. We present empirical results in Section 4. In Section 5, some conclusions are delivered. 2. Principles and methodology 2.1. Multifractal singular spectrum method Multifractal describes the characteristics of different layers when the body of fractal geometry grows. Therefore, objects such as geometric body is divided into N with equal length r (r < 1). Assume that the growth probability of different growth interface areas is μi (r). If all the areas have the same growth probabilities, then it is monofractal, the growth probability is expressed by α . Otherwise, if different areas have different α , it is multifractal. The relationship between parameters is shown as
μi ( r ) ∝ r α ,
i = 1, 2, · · · , N.
(1)
Let the same α form a subset, and due to r < 1, the minimum α corresponds to the maximum probability subset. Let Nα (r) be the number of areas with same α , then by Telesca et al. [39],
Nα (r ) ∝ r − f (α )
( α → 0 ),
(2)
where α is the singularity exponent, f (α ) represents the fractal dimension of a subset which has same α , and f (α ) reflected the fractal dimension of whole. We call f (α ) the singular spectrum, and α − f (α ) is a basic group to describe the multifractal. 2.2. Multifractal detrended fluctuation analysis(MF-DFA) As an important method of multifractal analysis, Kantelhardt et al. [40] proposed the multifractal detrended fluctuation analysis (MF-DFA), which can effectively know whether the time series has multifractal properties. The general MF-DFA procedure can be conducted by five steps. The first four steps are the same as DFA, for more details, please refer to [12]. The last step is: Calculating the mean of 2Ns segments, obtaine the q order wave function Fq (s ) as
Fq (s ) =
2N 1 s [F (s, v )]q/2 2Ns
1q .
(3)
v=1
When q = 0, according to Lopida’s law,
2N 1 s Fq (s ) = exp ln[F 2 (s, v )] . 2Ns
(4)
v=1
Fq (s ) is a function of segment s and fractal order q. With the increase of s, the series are long-range power-law correlated, the generalized Hurst exponent h(q) is defined by Fq (s ) ∝ sh(q) , when q = 2, Fq (s ) is the standard DFA. When the original sequence is monofractal, the scales of variance F2 (s, v) in each segment s is constant, therefore, h(q) is a constant independent of q. The range of h(q) indicates the extent to which the series is multifractal. A higher h = h(qmin ) − h(qmax ) means stronger multifractal feature, in our study, a stronger multifractal feature represents a lower market efficiency. When h(2 ) = 0.5, the original time series is an independent process or short-range correlation, when 0.5 < h(2) ≤ 1, the sequence has the property of persistent. When h(2) < 0.5, the sequence is anti-persistent.
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2.3. Mass exponent and multifractal spectrum The singularity strength and probability distribution of multifractal system is usually described by the mass exponent spectrum τ (q) and the multifractality spectrum f(a). The h(q) obtained from MF-DFA is related to the mass index τ (q) by
τ (q ) = qh(q ) − 1.
(5)
The singularity strength α and the singularity spectrum f (α ) can be obtained via Legendre transform as
α = h(q ) + qh (q ),
(6)
f ( α ) = q [ α − h ( q )] + 1 .
(7)
α is the singularity strength which can be used to describe the singular degree of each segment in a complex system. The width of the fractal spectrum α represents the difference between the maximum probability and the minimum probability. The larger the α , the time series distribution is more uneven, the scale strength is larger. f (α ) is the singularity spectrum which is used to describe fractal dimension of the singularity strength α . According to Zunino et al. [41] and set α = αmax − αmin represents the multifractal degree, and a large α represents the data fluctuation is more intensely. 3. Data collection The experimental data source for ”Dollar-Won” exchange rate and Kospi index are downloaded from the websites ”https://www. investing.com/currencies/usd- krw- historical- data” and ”https://kr. investing.com/indices/kospi-historical-data”, respectively. We note that the meeting time of South and North Korean leaders is April 27, 2018. After weekends and holidays are excluded, the time series of exchange rate contain 616 observations from February 21, 2017 to April 26, 2019, the date of the April 27, 2018 is located in the middle of the observation period to ensure that the two sub-samples have the same 308 sample sizes before and after the meeting day. As well as the time series of Kospi index, we also locate the meeting day in the middle of the observation period which is selected from May 22, 2017 to April 9, 2019, after eliminating weekends and holidays, each sub-sample has 230 data. 4. Experiment results In this section, we perform empirical researches and compare Hurst exponent and multifractal properties before and after the meeting day. At first, we focus on exchange rate and then the Kospi index. All the calculations in this paper are computed by using Matlab R2018a on an Intel(R) Core(TM) i5-4430 CPU @ 3.00GHz processor. 4.1. Parameters selection for exchange rate Now we set the parameters which will be taken for the MF-DFA model. The parameters including segment scale s and fractal order q. In the second step of MF-DFA procedure, when fitting the polynomial, we need to select a value for order k. According to [42], when the smallest segment sizes contain 10 − 20 samples, k should be chosen between 1 and 3. After comparing the multifractal spectrum with different k values, we choose k = 2 in the MF-DFA model to prevent under-fitting or over-fitting of the polynomial trend. By Kantelhardt and Co-authors [40,42], the minimum segment size should be considerably larger than the polynomial order k, and the maximum segment size should be less than 1/9 of the sample size. Thus, we set the minimum segment scale smin = 5, the maximum segment scale smax = 24, then the segment sizes
Fig. 1. Candlestick chart of “Dollar-Won” exchange rate. For interpretation of the references to color in the figure, the reader is referred to the web version of the article.
in total is 20. Lashermes et al. [43] pointed out that the fractal orders q taken from −10 to 10 are sufficient in most cases. We take the total number of q by 51, from the interval between −10 and −10, that is, the interval is divided into 50 equal parts. Then these parameters are taken into the MF-DFA model for empirical research. 4.2. ”Dollar-Won” exchange rate before and after the meeting day As the exchange rate data chosen from Section 3, we draw the candlestick chart for the changing trend of “Dollar-Won” exchange rate. As shown in Fig. 1, the candlesticks are usually composed of many red and green bars, which are the first known style of chart analysis. They resemble a candlestick with a wick coming out the top and bottom. The body in the candlestick usually consists of an opening price and a closing price, the price excursions below or above the body are called the wicks. For a stock during the time interval represented, the wick contains the lowest and highest prices, as well as the body contains the opening and closing prices. The red body of a candlestick indicates the security has a higher closed price than it opened, the opening price at the bottom and the closing price at the top. The green body of a candlestick indicates the security has a lower closed price than it opened, the opening price at the top and the closing price at the bottom. Also, from the statistical features of the exchange rate in the figure before and after the meeting day, we can observed these significant changes at least two levels. One way, significant devaluation of “Won” occurred from the date at April 27, 2018. “DollarWon” exchange rate rose by approximately 8.53% over the next few months and continued to April 26, 2019. Second, within the three months before the meeting, both the exchange rate time series and tendency are stable. However, after the meeting, the time series shows an upward trend, which indicates that the exchange rate of the“Won” has fallen significantly since the meeting. 4.2.1. Multifractality analysis for exchange rate As MF-DFA can express multifractality, scale invariance and correlation of exchange rate time series, to measure the multifractality quantitatively, we apply MF-DFA to estimate properties for the time series of exchange rate before and after April 27, 2018. At first, we calculate the generalized Hurst exponent h(q), and then obtain the scaling exponent τ (q) and singularity spectrum f (α ) for two series. As shown in Fig. 2, we see that the generalized Hurst exponents for both time series are not fixed values, and h(q) decrease with the increase of q, which shows that both the time series before and after the meeting are not single fractal. In different periods, the curve fluctuation shows different states, which indicates that time series in two time periods have different multifractality. We note that in Fig. 2, when q = 2, the parameter h(2) calculated for both the time series are greater than 0.5 (see Table 1), which means the small fluctuations and large fluctuations have significant persistence. When q below 0, the value of h(q) decreases rapidly with
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Fig. 4. Multifractal spectrum of ”Dollar-Won” exchange rate.
Fig. 2. Hurst exponent of ”Dollar-Won” exchange rate. Table 1 Multifractality degrees of the series. Exchange rate
h(2) Hurst exponent H(q) Multifractality degree α
Kospi
Before
After
Before
After
0.5444 0.8897 1.1378
0.5901 1.1747 1.4023
0.7364 0.4899 0.6414
0.7061 1.0012 1.3116
the increasing of q, which shows that the wavelet fluctuations have significant persistence. On the other way, when q > 0, with the increasing of q, h(q) stays slightly, which means the minimum sustainability of large fluctuations, especially for the exchange rate time series after April 27, 2018. From the Hurst exponent curve, we define the degree of multifractality by equation
H (q ) = h(qmin ) − h(qmax ).
Fig. 5. Candlestick chart of Kospi index. For interpretation of the references to color in the figure, the reader is referred to the web version of the article.
(8)
We calculate H for each time series, the H before the meeting is 0.8897, while after the meeting, H reaches 1.1747, which indicates its multifractal characteristics of the time series after April 27, 2018 is stronger and the multifractality of the time series before meeting is more stable. The multifractality of both the time series also can be analyzed by the scaling exponent curve and multifractal spectrum. Now we calculate τ (q) by using Eq. (5), Fig. 3 shows the scaling exponent of each time series, and they are marked by circle and rhombus symbol respectively. Previous studies [44] have shown that curvature of quality index can be used to measure the multifractality. A time series who has a stronger multifractality, then the curvature of the scaling exponent curve is larger. A straighter line represents a higher linearity. From Fig. 3, we note that the curvature of
Fig. 6. Hurst exponent of Kospi index.
Fig. 7. Scaling exponent curve of Kospi index. Fig. 3. Scaling exponent curve of ”Dollar-Won” exchange rate.
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properties. From the figure, the α before and after the meeting are 1.1378 and 1.4023, respectively. It shows that the fluctuation range of the time series after the meeting is larger than that before the meeting, which implies that the time series before meeting is more stable, and the Korean foreign exchange rate has a lower market efficiency after the meeting. This is consistent with the Hurst index and scaling exponent show. 4.3. Kospi index before and after the meeting day
Fig. 8. Multifractal spectrum of Kospi index.
quality index after the meeting is higher than that before the meeting, which indicates that the time series after the meeting has stronger multifractal characteristics, and the multifractality of the time series before meeting is more stable, it is the same as what the Hurst exponent shows. At last, we calculate singularity strength α and singularity spectrum f (α ) by using Eq. (7). As shown in Fig. 4, the multifractality spectrums of the time series before and after the meeting are marked by circle and rhombus symbol, respectively. The width of the curve on the α axis represents the degree of the multifractal. A higher α indicates the time series has stronger multifractal
Now we focus the stock market. From the Kospi data selected from Section 3, we present a candlestick chart for the changing trend of Kospi index, as shown in Fig. 5. We observed that there exists a significant changes from the statistical features of Kospi index in the figure before and after the meeting. The Kospi index declining rapidly from April 27, 2018, and it is approximately dropped by 26.17% over the next few months and nearly continued to April 9, 2019. 4.3.1. Multifractality analysis for Kospi index As the same analysis of exchange rate time series, we calculate the generalized Hurst exponent h(q), scaling exponent τ (q), multifractal strength α , and multifractal spectrum f (α ) for both Kospi time series before and after the meeting. In Fig. 6, generalized Hurst exponents h(q) of both the time series are decreasing with q varying from 10 to 10, indicating that both the two series show multifractality, and in different time period, the curve fluctuation show different states, which shows that time series in two different periods have different multifractality.
Fig. 9. Hurst exponent of original, shuffled, and phase-randomized time series of (a) ”Dollar-Won” exchange rate before meeting, (b) ”Dollar-Won” exchange rate after meeting, (c) Kospi index before meeting, and (d) Kospi index after meeting. For interpretation of the references to color in the figure, the reader is referred to the web version of the article.
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When q = 2, we also present the Hurst exponents h(2) for two series in Table 1. We note that both Hurst exponents are larger than 0.5, implying that the correlation of both time series are positive persistent. Moreover, h(2) before the meeting is larger than that after the meeting, which indicates that the small fluctuations and large fluctuations have more significant persistence in this period. We note that when q < 0, the Hurst exponent h(q) represents the scaling properties of small fluctuations, and when q > 0, with the increasing of q, h(q) stays slightly, which means the minimum sustainability of large fluctuations. Then we calculate H(q) for each time series, the H(q) before and after the meeting are 0.4899 and 1.0012 (see Table 1), respectively. We find that with the increasing of q, the range of h(q) fluctuation of the time series after the meeting is larger, which indicates its multifractal characteristics is stronger, and the market efficiency of the Kospi time series before the meeting is higher. Now we analyzed the scaling exponent curve and multifractal spectrum of both the Kospi index time series before and after the meeting. We calculate τ (q), and the scaling exponents τ (q) plotted in Fig. 7 are nonlinearly along with the increasing of q, which shows further support of the multifractality in two time series. We note that the curvature of scaling exponent after the meeting is higher than that before the meeting, which indicates that the time series after the meeting has stronger multifractal characteristics, and the multifractality of the time series before meeting is more stable. In addition, we examine two time series using multifractal strength and spectrum, correlation curves between α and f (α ) are depicted in Fig. 8. The multifractal spectrums are not shown as
points, which implies the existence of multifractality in both series. We then compute the widths of multifractal spectrum α , and the α before and after the meeting are0.6414 and 1.3116 (see Table 1), respectively. We see that the fluctuation range of the time series after the meeting is larger than that before the meeting, suggesting that the multifractality of the time series is more stable before the meeting, and the stock market after the meeting has a weaker market efficiency. 4.4. The sources of multifractality The former studies [45] have documented that the causes of multifractality are long-range correlation and fat-tailed distribution. In this section, we discuss about the main source of multifractality for these discussed series. To measure the contribution of long-range correlations and fat-tailed distribution in a quantitative manner, we construct shuffled and phase-randomized time series of the original time series, respectively. Then we calculate the Hurst exponent h(q), scaling exponent τ (q) and α of original, shuffled, and phase-randomized time series for exchange rate and Kospi before and after the meeting, respectively. As shown in Figs. 9–11, all the time series are strongly multifractal, and h(2) (see Table 2) for all shuffled and phaserandomized time series are less than 0.5, indicating that except original series, all the series exist anti-persistent. As the calculated results shown in Table 2, we find that for exchange rate series before the meeting, a large part of the multifractality of the original series is removed after shuffling and phase randomizing. The result implies that long-range correlation and
Fig. 10. Scaling exponent of original, shuffled, and phase-randomized time series of (a) ”Dollar-Won” exchange rate before meeting, (b) ”Dollar-Won” exchange rate after meeting, (c) Kospi index before meeting, and (d) Kospi index after meeting. For interpretation of the references to color in the figure, the reader is referred to the web version of the article.
W. Shao and J. Wang / Chaos, Solitons and Fractals 132 (2020) 109564
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Fig. 11. Multifractal spectrum of original, shuffled, and phase-randomized time series of (a) ”Dollar-Won” exchange rate before meeting, (b) ”Dollar-Won” exchange rate after meeting, (c) Kospi index before meeting, and (d) Kospi index after meeting. For interpretation of the references to color in the figure, the reader is referred to the web version of the article. Table 2 Multifractality degrees of original, shuffled, and phase-randomized series for exchange rate and Kospi index. h(2)
α
Exchang rate (Before)
Original Shuffled Phase-randomized
0.5444 0.2693 0.2701
1.1378 0.4153 0.3712
Exchang rate (After)
Original Shuffled Phase-randomized
0.5901 0.2304 0.2297
1.4023 1.5424 1.0206
Kospi (Before)
Original Shuffled Phase-randomized
0.7364 0.2555 0.2732
0.6414 0.3369 0.3867
Kospi (After)
Original Shuffled Phase-randomized
0.7061 0.2218 0.1955
1.3116 1.3051 1.1404
fat-tailed distribution mainly contribute to multifractality. However, for the exchange rate series after the meeting, the multifractality of the original series is removed only after phase randomization, which shows the resource of multifractality is the fat-tailed distribution. The same phenomenon appears in the stock market, when we observe the multifractal spectrum widths of original, shuffled, and phase-randomized series of the Kospi series, we can reach the same conclusion.
after ”ice-breaking” time point of South and North Korea. We confirm that the warming of relations between North and South Korea has an impact on the financial markets of South Korea. The evident in the empirical research part show that all the time series have multifractal characteristics, however, the degrees of multifractionality for time series before and after meeting are different. By comparing the hurst exponent, quality index, and multifractal spectrum, the markets of foreign exchange rate and stock before the meeting has a higher market efficiency, which decreased after the meeting. The multifractality of the time series before meeting is more stable. We also checked the major source of multifractality by shuffling and phase-randomizing both the original series of two markets. The results show that both the long-range correlation and fat-tail distribution contribute to multifractality for the time series before the meeting, and only fat-tailed distribution contributes to the multifractality of both times series after the meeting. Despite this area is still needed to be further explored, there is reason to believe that the meeting of South and North Korean leaders is a possible interpretation for changes in efficiency of South Korean financial market. Therefore, the finding can help financial practitioners, investors and forecasters to make decisions or manage the portfolio, it can also provide theoretical support for them to arbitrage or avoid asset risk when they encounter social crises or external political events. Declaration of Competing Interest
5. Conclusions In this article, we examined the multifractal properties of South Korean financial market by comparing the time series before and
We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
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Contents lists available at ScienceDirect
Chaos, Solitons and Fractals Nonlinear Science, and Nonequilibrium and Complex Phenomena journal homepage: www.elsevier.com/locate/chaos
Does the “ice-breaking” of South and North Korea affect the South Korean financial market? Wei Shao a, Jian Wang b,∗ a b
Department of Economics, Korea University, Seoul 02841, Republic of Korea Department of Mathematics, Korea University, Seoul 02841, Republic of Korea
a r t i c l e
i n f o
Article history: Received 11 June 2019 Revised 8 November 2019 Accepted 6 December 2019
Keywords: Multifractality Market efficiency Foreign exchange Kospi
a b s t r a c t In this paper, we use the multifractal detrended fluctuation analysis (MF-DFA) to study the difference in financial market of South Korea before and after South and North Korean leaders’ meeting on April 27, 2018. Hurst exponent, quality index, and multifractal spectrum are used to analyze the characteristics and stability of South Korean financial markets before and after the South and North Korean leaders’ meeting. We investigate the foreign exchange and stock markets in South Korea. The results show that multifractality is existed in all time intervals for both the markets, and the multifractal characteristics after the meeting are stronger, which indicates that both the markets before the meeting have a higher market efficiency, and decreased after the meeting. The meeting of South and North Korean leaders since April 27, 2018 is a possible interpretation for changes of efficiency in South Korean financial markets. To document the major source of multifractality, we shuffle and phase-randomize both the original series of two markets. The results show that both the long-range correlation and fat-tailed distribution contribute to multifractality for the time series before the meeting, and only fat-tailed distribution contributes to the multifractality of both times series after the meeting. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction In the research, we focus on whether the warming of relations between North and South Korea has an impact on the financial markets of South Korea. Many studies show that the external social crises and political conflicts can response to financial markets. The study in [1] showed that the latest financial crisis has truly affected complexity revealed in the volatility time series of the world major markets. In addition, the global financial crisis also resulted in the nonlinear dynamics of equity, currency and commodity markets [2]. Barro [3] proposed a model showing that the high observed stock premium has realistic risk aversion by extending Rietz’s model [4]. Rigobon and Sack [5] measured the influence of Iraq war on financial market, they found that the“war risk” factor accounted for a considerable portion of the variances of financial variables. Veronesi [6] believed that a higher degree of political instability result in a more volatile stock market. Berkman et al. [7] showed that disaster risk can affect the expected stock returns by using various samples of international political crises. In this paper, we examine whether the benefit of political event has an impact on financial markets. The political favourable event ∗
Corresponding author. E-mail address: [email protected] (J. Wang).
https://doi.org/10.1016/j.chaos.2019.109564 0960-0779/© 2019 Elsevier Ltd. All rights reserved.
we chosen was the meeting between South Korean leader Moon Jae-in and North Korean leader Kim Jong-un in Panmunjom on the Korean side on April 27, 2018. We need to point out that this is the first summit meeting between the top leaders of South and North Korea after the former President Roh moo Hyun crossed the 38th parallel of latitude 11 years ago. In the past 11 years, due to the continuous nuclear test of North Korea and the nuclear threat to South Korea, the relations between the two countries have been deteriorating. This summit meeting between the leaders of two countries is of historic significance. The two countries jointly signed the “Panmunjom declaration”, declaring that there will be no more war on the Korean Peninsula and stopping all hostilities. Some scholars have studied that the relationship between South and North Korea affects the financial markets of South Korea. Huh and Pyun [8] found that there is a negative correlation between the market’s concern about North Korean early nuclear threat and the South Korean stock market. Dibooglu and Cevik [9] used North Korean Threat Index to examine the effects of the threats on stock markets and foreign exchange markets in South Korea and Japan. The test results showed that there exists a causal relationship between the threat of North Korea and the stock returns and exchange rate returns in both countries. When studying the impact on the South Korean market of North Korean military attacks [10], Gerlach and Yook found that foreigners maintained
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their performance level before the attacks, while domestic individuals, who accounted for the vast majority of domestic trade, performed poorly. The South Korea’s stock market has a large scale and strong liquidity. Its annual turnover ranks 9th in the world and its total market value ranks 17th in 2011. Based on this, the sudden elimination of North Korea’s nuclear threat and the historic ice-breaking of bilateral relations are bound to have an impact on South Korea’s financial markets. In this paper, we will use the MF-DFA method to study the real historical data of stock and exchange rate, to confirm whether the ice-breaking in South and North Korea has played a role in the market efficiency of the financial market, and to explore the sources of multifractal characteristics of stock and foreign exchange market before and after the ice-breaking. The multifractal properties of empirical data have attracted wide attention due to a large range of properties related to scale invariance, which is one aspect in various scientific fields. This method has been tested in various financial time series, such as foreign exchange markets [11,12], stock markets [13–19], and bitcoin market [20–22]. More recently, high frequency multifractal characteristics of bitcoin was studied by Stavroyiannis et al. [23]. Moreover, Lahmiri and Bekiros [24] investigated the multifractal chaotic dynamics of Islamic and Green crypto-currency series in econophysics literature. Their findings indicated that the price, volatility and volume series of Islamic and green crypto-currencies embed high persistence compared to the conventional crypto-currencies. Also for Islamic financial markets, the authors estimated the Hurst exponents and found that the distributions are statistically different within Islamic and non-Islamic alternative markets [25]. The MF-DFA is one of the several techniques used to characterize the multifractal properties of financial time series. Many scholars used MF-DFA to analyze the impact of a shock on the financial market and did the comparative analysis before and after the event. Ning et al. [26] considered the Chinas foreign exchange reform as a shock to analyze the market efficiency of exchange rate market, they found the efficiency of both the onshore and offshore RMB/USD spot exchange rate changed, and they concluded that changes in intervention of the Peoples Bank of China since the reform is a possible explanation. Mensi et al. [27] assessed the role of the global financial crisis on market efficiency of Islamic stock markets by using an MF-DFA analysis. In addition, due to the effect of Shanghai Hong Kong stock connect program, the authors analyzed the Shanghai and Hong Kong stock markets before and after the connect program [28]. Besides, for more using MD-DFA to evaluate the impact of an emergency on the financial market, please refer to [29–31]. Thus, the MF-DFA is considered as a analysis method in our research. As a measure of testing the efficiency of financial markets, multifractality were widely studied in the past two decades. In addition to the financial market, multifractal analysis has also been applied for studying the fields of atmospheric Science, biomedical, and phase transitions. In related researches, the multifractal properties and cross-correlation behavior of air pollution index time series data were studied by using multifractal analysis method in [32]. Recently, MF-DFA was used to examine the time series of daily air temperature in [33]. By using multifractality, generalized Hurst exponents are calculated for distinguishing seizure and seizure-Free intervals of intracranial electroencephalogram (EEG) signals from epileptic patients [34]. The generalized Hurst exponents are also taken to classify the normal and abnormal EEG records in [35], and estimate differentiate EEG signals of healthy and epileptic patients in [36]. Li et al. [37] used the MF-DFA to analyze the human heart rate variability during exercise, which can provide useful information for athletes to choose the best sports time and accelerate the development of sports medicine.
Zhao et al. [38] focused on the phase transitions by analyzing the multifractality of the time series. The layout of the rest of this paper is as follows. In Section 2, we introduce the multifractal spectrum and MF-DFA. In Section 3, we provide a data description. We present empirical results in Section 4. In Section 5, some conclusions are delivered. 2. Principles and methodology 2.1. Multifractal singular spectrum method Multifractal describes the characteristics of different layers when the body of fractal geometry grows. Therefore, objects such as geometric body is divided into N with equal length r (r < 1). Assume that the growth probability of different growth interface areas is μi (r). If all the areas have the same growth probabilities, then it is monofractal, the growth probability is expressed by α . Otherwise, if different areas have different α , it is multifractal. The relationship between parameters is shown as
μi ( r ) ∝ r α ,
i = 1, 2, · · · , N.
(1)
Let the same α form a subset, and due to r < 1, the minimum α corresponds to the maximum probability subset. Let Nα (r) be the number of areas with same α , then by Telesca et al. [39],
Nα (r ) ∝ r − f (α )
( α → 0 ),
(2)
where α is the singularity exponent, f (α ) represents the fractal dimension of a subset which has same α , and f (α ) reflected the fractal dimension of whole. We call f (α ) the singular spectrum, and α − f (α ) is a basic group to describe the multifractal. 2.2. Multifractal detrended fluctuation analysis(MF-DFA) As an important method of multifractal analysis, Kantelhardt et al. [40] proposed the multifractal detrended fluctuation analysis (MF-DFA), which can effectively know whether the time series has multifractal properties. The general MF-DFA procedure can be conducted by five steps. The first four steps are the same as DFA, for more details, please refer to [12]. The last step is: Calculating the mean of 2Ns segments, obtaine the q order wave function Fq (s ) as
Fq (s ) =
2N 1 s [F (s, v )]q/2 2Ns
1q .
(3)
v=1
When q = 0, according to Lopida’s law,
2N 1 s Fq (s ) = exp ln[F 2 (s, v )] . 2Ns
(4)
v=1
Fq (s ) is a function of segment s and fractal order q. With the increase of s, the series are long-range power-law correlated, the generalized Hurst exponent h(q) is defined by Fq (s ) ∝ sh(q) , when q = 2, Fq (s ) is the standard DFA. When the original sequence is monofractal, the scales of variance F2 (s, v) in each segment s is constant, therefore, h(q) is a constant independent of q. The range of h(q) indicates the extent to which the series is multifractal. A higher h = h(qmin ) − h(qmax ) means stronger multifractal feature, in our study, a stronger multifractal feature represents a lower market efficiency. When h(2 ) = 0.5, the original time series is an independent process or short-range correlation, when 0.5 < h(2) ≤ 1, the sequence has the property of persistent. When h(2) < 0.5, the sequence is anti-persistent.
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2.3. Mass exponent and multifractal spectrum The singularity strength and probability distribution of multifractal system is usually described by the mass exponent spectrum τ (q) and the multifractality spectrum f(a). The h(q) obtained from MF-DFA is related to the mass index τ (q) by
τ (q ) = qh(q ) − 1.
(5)
The singularity strength α and the singularity spectrum f (α ) can be obtained via Legendre transform as
α = h(q ) + qh (q ),
(6)
f ( α ) = q [ α − h ( q )] + 1 .
(7)
α is the singularity strength which can be used to describe the singular degree of each segment in a complex system. The width of the fractal spectrum α represents the difference between the maximum probability and the minimum probability. The larger the α , the time series distribution is more uneven, the scale strength is larger. f (α ) is the singularity spectrum which is used to describe fractal dimension of the singularity strength α . According to Zunino et al. [41] and set α = αmax − αmin represents the multifractal degree, and a large α represents the data fluctuation is more intensely. 3. Data collection The experimental data source for ”Dollar-Won” exchange rate and Kospi index are downloaded from the websites ”https://www. investing.com/currencies/usd- krw- historical- data” and ”https://kr. investing.com/indices/kospi-historical-data”, respectively. We note that the meeting time of South and North Korean leaders is April 27, 2018. After weekends and holidays are excluded, the time series of exchange rate contain 616 observations from February 21, 2017 to April 26, 2019, the date of the April 27, 2018 is located in the middle of the observation period to ensure that the two sub-samples have the same 308 sample sizes before and after the meeting day. As well as the time series of Kospi index, we also locate the meeting day in the middle of the observation period which is selected from May 22, 2017 to April 9, 2019, after eliminating weekends and holidays, each sub-sample has 230 data. 4. Experiment results In this section, we perform empirical researches and compare Hurst exponent and multifractal properties before and after the meeting day. At first, we focus on exchange rate and then the Kospi index. All the calculations in this paper are computed by using Matlab R2018a on an Intel(R) Core(TM) i5-4430 CPU @ 3.00GHz processor. 4.1. Parameters selection for exchange rate Now we set the parameters which will be taken for the MF-DFA model. The parameters including segment scale s and fractal order q. In the second step of MF-DFA procedure, when fitting the polynomial, we need to select a value for order k. According to [42], when the smallest segment sizes contain 10 − 20 samples, k should be chosen between 1 and 3. After comparing the multifractal spectrum with different k values, we choose k = 2 in the MF-DFA model to prevent under-fitting or over-fitting of the polynomial trend. By Kantelhardt and Co-authors [40,42], the minimum segment size should be considerably larger than the polynomial order k, and the maximum segment size should be less than 1/9 of the sample size. Thus, we set the minimum segment scale smin = 5, the maximum segment scale smax = 24, then the segment sizes
Fig. 1. Candlestick chart of “Dollar-Won” exchange rate. For interpretation of the references to color in the figure, the reader is referred to the web version of the article.
in total is 20. Lashermes et al. [43] pointed out that the fractal orders q taken from −10 to 10 are sufficient in most cases. We take the total number of q by 51, from the interval between −10 and −10, that is, the interval is divided into 50 equal parts. Then these parameters are taken into the MF-DFA model for empirical research. 4.2. ”Dollar-Won” exchange rate before and after the meeting day As the exchange rate data chosen from Section 3, we draw the candlestick chart for the changing trend of “Dollar-Won” exchange rate. As shown in Fig. 1, the candlesticks are usually composed of many red and green bars, which are the first known style of chart analysis. They resemble a candlestick with a wick coming out the top and bottom. The body in the candlestick usually consists of an opening price and a closing price, the price excursions below or above the body are called the wicks. For a stock during the time interval represented, the wick contains the lowest and highest prices, as well as the body contains the opening and closing prices. The red body of a candlestick indicates the security has a higher closed price than it opened, the opening price at the bottom and the closing price at the top. The green body of a candlestick indicates the security has a lower closed price than it opened, the opening price at the top and the closing price at the bottom. Also, from the statistical features of the exchange rate in the figure before and after the meeting day, we can observed these significant changes at least two levels. One way, significant devaluation of “Won” occurred from the date at April 27, 2018. “DollarWon” exchange rate rose by approximately 8.53% over the next few months and continued to April 26, 2019. Second, within the three months before the meeting, both the exchange rate time series and tendency are stable. However, after the meeting, the time series shows an upward trend, which indicates that the exchange rate of the“Won” has fallen significantly since the meeting. 4.2.1. Multifractality analysis for exchange rate As MF-DFA can express multifractality, scale invariance and correlation of exchange rate time series, to measure the multifractality quantitatively, we apply MF-DFA to estimate properties for the time series of exchange rate before and after April 27, 2018. At first, we calculate the generalized Hurst exponent h(q), and then obtain the scaling exponent τ (q) and singularity spectrum f (α ) for two series. As shown in Fig. 2, we see that the generalized Hurst exponents for both time series are not fixed values, and h(q) decrease with the increase of q, which shows that both the time series before and after the meeting are not single fractal. In different periods, the curve fluctuation shows different states, which indicates that time series in two time periods have different multifractality. We note that in Fig. 2, when q = 2, the parameter h(2) calculated for both the time series are greater than 0.5 (see Table 1), which means the small fluctuations and large fluctuations have significant persistence. When q below 0, the value of h(q) decreases rapidly with
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Fig. 4. Multifractal spectrum of ”Dollar-Won” exchange rate.
Fig. 2. Hurst exponent of ”Dollar-Won” exchange rate. Table 1 Multifractality degrees of the series. Exchange rate
h(2) Hurst exponent H(q) Multifractality degree α
Kospi
Before
After
Before
After
0.5444 0.8897 1.1378
0.5901 1.1747 1.4023
0.7364 0.4899 0.6414
0.7061 1.0012 1.3116
the increasing of q, which shows that the wavelet fluctuations have significant persistence. On the other way, when q > 0, with the increasing of q, h(q) stays slightly, which means the minimum sustainability of large fluctuations, especially for the exchange rate time series after April 27, 2018. From the Hurst exponent curve, we define the degree of multifractality by equation
H (q ) = h(qmin ) − h(qmax ).
Fig. 5. Candlestick chart of Kospi index. For interpretation of the references to color in the figure, the reader is referred to the web version of the article.
(8)
We calculate H for each time series, the H before the meeting is 0.8897, while after the meeting, H reaches 1.1747, which indicates its multifractal characteristics of the time series after April 27, 2018 is stronger and the multifractality of the time series before meeting is more stable. The multifractality of both the time series also can be analyzed by the scaling exponent curve and multifractal spectrum. Now we calculate τ (q) by using Eq. (5), Fig. 3 shows the scaling exponent of each time series, and they are marked by circle and rhombus symbol respectively. Previous studies [44] have shown that curvature of quality index can be used to measure the multifractality. A time series who has a stronger multifractality, then the curvature of the scaling exponent curve is larger. A straighter line represents a higher linearity. From Fig. 3, we note that the curvature of
Fig. 6. Hurst exponent of Kospi index.
Fig. 7. Scaling exponent curve of Kospi index. Fig. 3. Scaling exponent curve of ”Dollar-Won” exchange rate.
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properties. From the figure, the α before and after the meeting are 1.1378 and 1.4023, respectively. It shows that the fluctuation range of the time series after the meeting is larger than that before the meeting, which implies that the time series before meeting is more stable, and the Korean foreign exchange rate has a lower market efficiency after the meeting. This is consistent with the Hurst index and scaling exponent show. 4.3. Kospi index before and after the meeting day
Fig. 8. Multifractal spectrum of Kospi index.
quality index after the meeting is higher than that before the meeting, which indicates that the time series after the meeting has stronger multifractal characteristics, and the multifractality of the time series before meeting is more stable, it is the same as what the Hurst exponent shows. At last, we calculate singularity strength α and singularity spectrum f (α ) by using Eq. (7). As shown in Fig. 4, the multifractality spectrums of the time series before and after the meeting are marked by circle and rhombus symbol, respectively. The width of the curve on the α axis represents the degree of the multifractal. A higher α indicates the time series has stronger multifractal
Now we focus the stock market. From the Kospi data selected from Section 3, we present a candlestick chart for the changing trend of Kospi index, as shown in Fig. 5. We observed that there exists a significant changes from the statistical features of Kospi index in the figure before and after the meeting. The Kospi index declining rapidly from April 27, 2018, and it is approximately dropped by 26.17% over the next few months and nearly continued to April 9, 2019. 4.3.1. Multifractality analysis for Kospi index As the same analysis of exchange rate time series, we calculate the generalized Hurst exponent h(q), scaling exponent τ (q), multifractal strength α , and multifractal spectrum f (α ) for both Kospi time series before and after the meeting. In Fig. 6, generalized Hurst exponents h(q) of both the time series are decreasing with q varying from 10 to 10, indicating that both the two series show multifractality, and in different time period, the curve fluctuation show different states, which shows that time series in two different periods have different multifractality.
Fig. 9. Hurst exponent of original, shuffled, and phase-randomized time series of (a) ”Dollar-Won” exchange rate before meeting, (b) ”Dollar-Won” exchange rate after meeting, (c) Kospi index before meeting, and (d) Kospi index after meeting. For interpretation of the references to color in the figure, the reader is referred to the web version of the article.
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When q = 2, we also present the Hurst exponents h(2) for two series in Table 1. We note that both Hurst exponents are larger than 0.5, implying that the correlation of both time series are positive persistent. Moreover, h(2) before the meeting is larger than that after the meeting, which indicates that the small fluctuations and large fluctuations have more significant persistence in this period. We note that when q < 0, the Hurst exponent h(q) represents the scaling properties of small fluctuations, and when q > 0, with the increasing of q, h(q) stays slightly, which means the minimum sustainability of large fluctuations. Then we calculate H(q) for each time series, the H(q) before and after the meeting are 0.4899 and 1.0012 (see Table 1), respectively. We find that with the increasing of q, the range of h(q) fluctuation of the time series after the meeting is larger, which indicates its multifractal characteristics is stronger, and the market efficiency of the Kospi time series before the meeting is higher. Now we analyzed the scaling exponent curve and multifractal spectrum of both the Kospi index time series before and after the meeting. We calculate τ (q), and the scaling exponents τ (q) plotted in Fig. 7 are nonlinearly along with the increasing of q, which shows further support of the multifractality in two time series. We note that the curvature of scaling exponent after the meeting is higher than that before the meeting, which indicates that the time series after the meeting has stronger multifractal characteristics, and the multifractality of the time series before meeting is more stable. In addition, we examine two time series using multifractal strength and spectrum, correlation curves between α and f (α ) are depicted in Fig. 8. The multifractal spectrums are not shown as
points, which implies the existence of multifractality in both series. We then compute the widths of multifractal spectrum α , and the α before and after the meeting are0.6414 and 1.3116 (see Table 1), respectively. We see that the fluctuation range of the time series after the meeting is larger than that before the meeting, suggesting that the multifractality of the time series is more stable before the meeting, and the stock market after the meeting has a weaker market efficiency. 4.4. The sources of multifractality The former studies [45] have documented that the causes of multifractality are long-range correlation and fat-tailed distribution. In this section, we discuss about the main source of multifractality for these discussed series. To measure the contribution of long-range correlations and fat-tailed distribution in a quantitative manner, we construct shuffled and phase-randomized time series of the original time series, respectively. Then we calculate the Hurst exponent h(q), scaling exponent τ (q) and α of original, shuffled, and phase-randomized time series for exchange rate and Kospi before and after the meeting, respectively. As shown in Figs. 9–11, all the time series are strongly multifractal, and h(2) (see Table 2) for all shuffled and phaserandomized time series are less than 0.5, indicating that except original series, all the series exist anti-persistent. As the calculated results shown in Table 2, we find that for exchange rate series before the meeting, a large part of the multifractality of the original series is removed after shuffling and phase randomizing. The result implies that long-range correlation and
Fig. 10. Scaling exponent of original, shuffled, and phase-randomized time series of (a) ”Dollar-Won” exchange rate before meeting, (b) ”Dollar-Won” exchange rate after meeting, (c) Kospi index before meeting, and (d) Kospi index after meeting. For interpretation of the references to color in the figure, the reader is referred to the web version of the article.
W. Shao and J. Wang / Chaos, Solitons and Fractals 132 (2020) 109564
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Fig. 11. Multifractal spectrum of original, shuffled, and phase-randomized time series of (a) ”Dollar-Won” exchange rate before meeting, (b) ”Dollar-Won” exchange rate after meeting, (c) Kospi index before meeting, and (d) Kospi index after meeting. For interpretation of the references to color in the figure, the reader is referred to the web version of the article. Table 2 Multifractality degrees of original, shuffled, and phase-randomized series for exchange rate and Kospi index. h(2)
α
Exchang rate (Before)
Original Shuffled Phase-randomized
0.5444 0.2693 0.2701
1.1378 0.4153 0.3712
Exchang rate (After)
Original Shuffled Phase-randomized
0.5901 0.2304 0.2297
1.4023 1.5424 1.0206
Kospi (Before)
Original Shuffled Phase-randomized
0.7364 0.2555 0.2732
0.6414 0.3369 0.3867
Kospi (After)
Original Shuffled Phase-randomized
0.7061 0.2218 0.1955
1.3116 1.3051 1.1404
fat-tailed distribution mainly contribute to multifractality. However, for the exchange rate series after the meeting, the multifractality of the original series is removed only after phase randomization, which shows the resource of multifractality is the fat-tailed distribution. The same phenomenon appears in the stock market, when we observe the multifractal spectrum widths of original, shuffled, and phase-randomized series of the Kospi series, we can reach the same conclusion.
after ”ice-breaking” time point of South and North Korea. We confirm that the warming of relations between North and South Korea has an impact on the financial markets of South Korea. The evident in the empirical research part show that all the time series have multifractal characteristics, however, the degrees of multifractionality for time series before and after meeting are different. By comparing the hurst exponent, quality index, and multifractal spectrum, the markets of foreign exchange rate and stock before the meeting has a higher market efficiency, which decreased after the meeting. The multifractality of the time series before meeting is more stable. We also checked the major source of multifractality by shuffling and phase-randomizing both the original series of two markets. The results show that both the long-range correlation and fat-tail distribution contribute to multifractality for the time series before the meeting, and only fat-tailed distribution contributes to the multifractality of both times series after the meeting. Despite this area is still needed to be further explored, there is reason to believe that the meeting of South and North Korean leaders is a possible interpretation for changes in efficiency of South Korean financial market. Therefore, the finding can help financial practitioners, investors and forecasters to make decisions or manage the portfolio, it can also provide theoretical support for them to arbitrage or avoid asset risk when they encounter social crises or external political events. Declaration of Competing Interest
5. Conclusions In this article, we examined the multifractal properties of South Korean financial market by comparing the time series before and
We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
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