Multifractal analysis of the impact of US–China trade friction on US and China soy futures markets

Journal Pre-proof Multifractal analysis of the impact of US–China trade friction on US and China soy futures markets Qiangbiao Ji, Xin Zhang, Yingming Zhu

PII: DOI: Reference:

S0378-4371(19)31810-2 https://doi.org/10.1016/j.physa.2019.123222 PHYSA 123222

To appear in:

Physica A

Received date : 5 February 2019 Revised date : 23 August 2019 Please cite this article as: Q. Ji, X. Zhang and Y. Zhu, Multifractal analysis of the impact of US–China trade friction on US and China soy futures markets, Physica A (2019), doi: https://doi.org/10.1016/j.physa.2019.123222. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2019 Published by Elsevier B.V.

*Highlights (for review)

Journal Pre-proof Multifractal Analysis of the Impact of US-China Trade Friction on US and China Soy Futures Markets Highlights:

of

p ro

Pr e-



al



urn



The cross-correlations coefficients decrease significantly during the trade friction, and different trends of cross-correlations are found. The singularity widths of all soy futures markets and the cross-correlations decrease during trade friction; whilst the generalized Hurst exponents of all series experience significant increases, especially for large fluctuations. The finite-size effect and the fat-tailed probability distributions can explain the major decrease in multifractality. Comparing the period before, soy futures markets became less correlated, less multifractal and more persistent during this trade friction. Comparing the period before, soy futures markets became less correlated, less multifractal and more persistent during this trade friction. The evidences suggest that as the tariff on soy was put into effect, investigators in two countries may take different hedging behaviors and be more risk averse

Jo



*Manuscript Click here to view linked References

Journal Pre-proof

Multifractal Analysis of the Impact of US-China Trade Friction on US and China Soy Futures Markets Qiangbiao Jia , Xin Zhangb,∗, Yingming Zhub a

of

College of Life Science, Guizhou University, 2708 Huaxi Street, Guiyang 550025, China School of Economics and Management, Nanjing University of Science and Technology, 200 Xiaolinwei Street, Xuanwu District, Nanjing 210094, China

p ro

b

Abstract

Pr e-

We investigate the impact of the 2018 US-China trade friction on the multifractality of soy futures markets. Using DMCA and MFDMA methods, we study the cross-correlation coefficient of soy futures markets, and analyze the multifractality and origins of multifractality before and during this trade friction. We find: (a) The cross-correlations coefficients decrease significantly during the trade friction, and different trends of cross-correlations are found. (b) The singularity widths of all soy futures markets and the cross-correlations decrease during trade friction; whilst the generalized Hurst exponents of all series experience significant increases, especially for large fluctuations. (c) The finite-size effect and the fat-tailed probability distributions can explain the major decrease in multifractality. Comparing the period before, soy futures markets became less correlated, less multifractal and more persistent during this trade friction. The evidences suggest that as the tariff on soy was put into effect, investigators in two countries may take different hedging behaviors and be more risk averse.

urn

al

Keywords: US-China trade friction, Multifractal detrended moving average analysis, soy futures markets

1. Introduction

∗

Jo

5

China and the United States were engaged in a trade friction in 2018, due to the dispute over tariffs on a variety of goods traded between the two sides1 . One of the most important tariffs is the 25% tariff imposed on soybeans imported from the US, which was issued by China on April 4st, 2018 and put into effect on July 6st, 2018. In 2017-2018, the United States was the world’s second largest soybean exporter, accounting for 37% of soybean exports; while China was the world’s largest soybean importer as well as the biggest buyer Corresponding author Email addresses: [email protected] (Qiangbiao Ji), [email protected] (Xin Zhang), [email protected] (Yingming Zhu) 1 https://en.wikipedia.org/wiki/China-United_States_trade_war_(2018–present) Preprint submitted to Physica A: Statistical Mechanics and its Applications

August 23, 2019

Journal Pre-proof

30

35

40

45

of

p ro

Pr e-

25

al

20

urn

15

Jo

10

of the US soybeans, occupying about 60% of total global imports2 . Thus, this trade friction exerted significant impact on soybean trade and related futures markets both in the US and China. To understand the risk and uncertainty brought by trade protectionism and frictions like US-China trade friction is of significance. During the past two decades, the fractality and multifractality of financial markets have drawn much attention. Financial markets are found to be complex dynamic systems, which can be featured by the degree of multifractality [1–4]. A variety of methods have been proposed to study the multifractality in financial time series, such as rescaled range analysis (R/S)� Wavelet transform module maxima (WTMM) method and multifractal detrended fluctuation analysis (MFDFA) [3, 5–10]. Also, based on the detrended fluctuation analysis, DCCA and MFDCCA methods were introduced to discuss fractal and multifractal features in cross-correlations between two financial time series [4, 11–15]. Another popular series of methods were developed on the basis of the detrended moving average (DMA) algorithm [16, 17], called multifractal detrending moving average analysis (MFDMA). Combining DCCA with DMA methods, He and Chen [18] as well as Jiang and Zhou [19] analyzed cross-correlations between two non-stationary time series using the detrending moving average cross-correlation analysis (DMCA). Compared with the MFDFA and MFDCCA methods that are based on the polynomial fitting, the MFDMA and DMCA methods adopt local moving average as the trend function for eliminating the intrinsic trend; thus the trends among each subinterval seem to be more continuous. From the (multi)fractal analysis methods above, mono-fractal or multifractal features in many financial markets, such as exchange rate, stock, gold and oil, are reported. [13, 20–23]. Multifractal characteristics are also detected in the agricultural futures markets, including those in China and the US [24–26]. Particularly, He and Chen studied the crosscorrelation between China’s and US agricultural futures markets using multifractal analysis [27]. They found a power-law cross-correlation and significant multifractal features in agricultural futures markets between China and the US, laying an empirical basis. Yet, how these markets react to extreme events remains uncovered. Literatures show that the multifractal behaviors of time series are influenced by extreme events, such as market crashes and financial crisis. A variety of investigations have been designed and performed, including those comparing the multifractal behaviors of crisis periods and calm periods. Using MF-DFA, Siokis compared the multifractal behaviors of DJIA returns between two crash periods (from August 1928 to January 1931 and August 1986 to December 1988 respectively) and “non-crisis” calm periods in 1964. The singularity width ∆α = 1.04 for the 1929 crash, ∆α = 0.97 for 1987, and ∆α = 0.19 for the calm period were obtained [28]. Different multifractal behaviors of the whole sample and of the time series around extreme events were also identified. Caraiani investigated three emerging European stock markets, Czech PX index from April 1994 to December 2010, Hungarian BUX index from June 1993 to December 2010, and the Polish WIG index between June 1993 and December 2010. The singularity width ∆α was found larger during the 2008 crisis than that during the whole sample period [29]. In addition, scholars also found significant variations 2

UN Comtrade Database https://comtrade.un.org

2

Journal Pre-proof

60

65

of

p ro

55

2. Methodology

Pr e-

50

in the multifractal behaviors before and after extreme events. Yalamova investigated the multifractal behaviors of seven stock market indices (DJIA, S&P500, AUS, TSX, NIKKEI, NASDAQ and FTSE) before and after the 1987 crash [30]. It was concluded that the most probable singularity exponent α0 decreased for DJIA, S&P500, TSX, NASDAQ and FTSE, increased for AUS, and remained stable for NIKKEI. Oh et al. analyzed the impact of the 1997 Asian crisis on the multifractality of four Asian foreign exchange rates [31]. They found that Korean and Thai foreign exchange markets experienced a significant increase in multifractality compared to that of Hong-Kong and Japan, and the multifractality showed stronger relation to the presence of high-values returns in the time series. The US-China trade friction in 2018 is unique and unexpected with profound effects. The import demand of soybeans for China is inelastic, and the tariff seems to have an profound impact on the prices of soy futures in both the US and China. This paper focuses on the impact of US-China trade friction on the multifractality of soy futures markets in the two countries. Using the MFDMA and DMCA methods [18], we first compared the crosscorrelations and multifractality of these soy futures markets before and during the trade friction, and then studied the origins of multifractality for the both periods.

We first introduce the DMCA method [18, 19]. The DMCA method can be described as follow: Step 1. Consider two time series x(i) and y(i), i = 1, 2, , N , where N is the length of the series. Construct the sequence of cumulative sums X(t) =

t ∑

x(i), Y (t) =

70

al

i=1

t ∑

∑ 1 ⌈(n−1)(1−θ)⌉ X(t − k), n (t) = n k=−⌊(n−1)θ⌋

∑ 1 ⌈(n−1)(1−θ)⌉ Y (t − k) n (t) = n k=−⌊(n−1)θ⌋

urn

Ye

(1)

(2)

where n is the window size, ⌊g⌋ is the largest integer smaller than g, ⌈g⌉ is the smallest integer larger than g, and θ is the position parameter with the value varying in the range [0, 1]. Hence, the moving average function considers ⌈(n − 1)(1 − θ)⌉ data points in the past and ⌊(n − 1)θ⌋ data points in the future. There are three special cases in this function. The first case θ = 0 refers to the backward moving average, where the moving average function ye(t) is calculated over all the past n − 1 data points of the signal. The second case θ = 0.5 corresponds to the centered moving average , where ye(t) contains half past and half future information in each window. The third case θ = 1 is called the forward moving average, where ye(t) considers the trend of n − 1 data points in the future. In this paper, we only consider the second case, the centered moving average, θ = 0.5. Step 3. Define the local trend function F (n) with the segment size n

Jo

80

t = 1, 2, ..., N

Step 2. Calculate the moving average function in a moving window, f X

75

y(i),

i=1

3

Journal Pre-proof

N −⌊((n−1)θ)⌋ ∑ 1 f (t))(Y (t) − Ye (t)) F (n) = (X(t) − X n n N − n + 1 t=n−⌊((n−1)θ)⌋ 2

(3)

Step 4. Calculate the qth order overall fluctuation function Fq (n) 1/q



of

N −⌊((n−1)θ)⌋ ∑ 1 F q (n) Fq (n) =  N − n + 1 t=n−⌊((n−1)θ)⌋

for q ̸= 0. When q = 0, we have



p ro



N −⌊((n−1)θ)⌋ ∑ 1 logF (n) F0 (n) = exp  N − n + 1 t=n−⌊((n−1)θ)⌋

(5)

The MFDMA method can be seen as a special case of this DMCA method when X(t) = Y (t). The local fluctuation function F (n) and qth order fluctuation function Fq (n) for MFDMA method are similar to the DMCA method. We can investigate the power-law relationship for different values of segment length n.

Pr e-

85

(4)

Fq (n) ∼ nh(q)

(6)

τ (q) = qh(q) − Df

(7)

According to the standard multifractal formalism, the multifractal scaling exponent τ (q) can be used to characterize the multifractal nature, which reads

where Df is the fractal dimension of the geometric support of the multifractal measure. For time series analysis, we have Df = 1. If the scaling exponent function τ (q) is a nonlinear function of q, the signal has multifractal nature. It is easy to obtain the singularity strength function α(q) and the multifractal spectrum f (α) via the Legendre transform.

al

90

3. Data

100

(8)

We use daily closing prices of No. 2 soybean futures and soy meal futures from China’s Dalian Commodity Exchange (DCE), and daily closing prices of soybean and soy meal futures from Chicago Board of Trade (CBOT). The daily price returns, rt is calculated as its logarithmic difference, rt = log(Pt ) − log(Pt−1 ). To study the impact of this trade friction on US and China’s markets, we divided each time series into two sub-periods with an equal length: (a) before trade friction (April 1st, 2017 to April 3rd, 2018), (b) during trade friction (April 4th, 2018 to April 1st, 2019, see Fig. 1). The descriptive statistics of all returns are shown in Table 1.

Jo

95

α(q) = dτ (q)/dq fxy (q) = qα − τ (q)

urn

{

4

Journal Pre-proof

Soybean Price:CBOT vs. DCE

1400

5000 CBOT DCE

tariff published

1200

tariff effected

800

07-02-2017

01-02-2018

Time

07-06-2018

3500 3000

12-31-2018

Soy meal Price:CBOT vs. DCE

500 450 400 350 300 250 01-03-2017

07-02-2017

Pr e-

CBOT(1$/ton)

04-04

p ro

600 01-03-2017

4000

of

1000

01-02-2018

04-04

4500

4500 CBOT DEC

4000 3500 3000 2500 2000

07-06-2018

12-31-2018

Time

al

Figure 1: The closing prices of soybean and soy meal futures in CBOT and DCE from January 3rd, 2017 to April 1st, 2019. The tariff on soy markets was published on April 4th, 2018 and put into effect on July 6th, 2018.

Table 1: The descriptive statistics of return series Mean(%)

S. D(%)

Soybean-CBOT Soybean-DCE Soymeal-CBOT Soymeal-DCE

0.00040 -0.00031 0.00086 0.00054

0.010 0.019 0.013 0.015

During

Mean(%)

Soybean-CBOT Soybean-DCE Soymeal-CBOT Soymeal-DCE

-0.00063 -0.00101 -0.00088 -0.00098

Min(%)

Max(%)

Skew

Kurt

J-B

ADF

-0.04445 -0.18653 -0.05407 -0.06188

0.02886 0.08222 0.04111 0.05824

-0.570 -4.000 0.022 0.164

5.989 47.006 5.377 8.416

101.484 19838.686 56.034 291.959

-14.268 -18.995 -13.534 -18.382

S. D(%)

Min(%)

Max(%)

Skew

Kurt

J-B

ADF

0.012 0.014 0.011 0.016

-0.04800 -0.06660 -0.03194 -0.08531

0.04517 0.04950 0.04568 0.05332

0.237 -0.288 0.517 -0.797

4.582 6.907 4.424 8.700

26.587 152.053 30.204 341.509

-16.534 -17.451 -16.135 -16.375

Jo

urn

Before

Note: “Max”, “Min”, “S. D”, “Skew”, and “Kurt” symbolize Maximum, Minimum, Std. Dev, Skewness and Kurtosis respectively. “J-B” denotes statistic tests for the null hypothesis of normality in sample returns distribution. “ADF” is the statistics of Augmented Dickey–Fuller test.

5

Journal Pre-proof

4. Empirical results

115

of

p ro

110

Pr e-

105

4.1. Cross-correlation coefficient China’s and US agricultural futures markets are geographically far but temporally correlated financial systems. He and Chen found there exits a power-law cross-correlation between China’s and US soy futures markets, and that the soy futures markets show strong cross-correlations and share much of their multifractal structure[27]. However, the crosscorrelations between two markets changed by the extreme affair. For example, Bashir et.al applied the detrended cross-correlation coefficient, ρDCCA , to investigate the dynamic linkages between stock price and exchange rate for the UK and four other EU countries before and after the Brexit referendum event[32]. They found positive and negative co-movements in UK and EU financial markets for these two periods, and most of the European financial markets tend to be negatively correlated in the long term. In the case of US-China trade friction, we introduce the cross-correlation coefficient based on DMCA [33], to investigate the cross-correlations shift before and during the trade friction period. Knowing such shift would enable investors to understand the impact of this political event on the co-movements of two markets. The cross-correlation coefficient is as follow: 2 (s) Fxy , ρDM A (s) ∈ [0, 1] ρDM A (s) = Fxx (s)Fyy (s)

130

135

140

al

urn

125

where Fxy (s), Fxx (s) and Fyy (s) are the local trend function F (n) in Eq. 3. The crosscorrelation ρDM A ranges from -1 to 1 and can be interpreted as a standard correlation coefficient. If −1 < ρDM A < 0 Fig. 2 shows the results of ρDM A for the periods before and during the trade friction. The critical values of ρDM A and the 95% confidence intervals from two identically distributed random series (i.i.d.) are also calculated for comparison [34]. The evidences in Fig. 2 there are obvious shifts in ρDM A for the two periods studied. First, compared with the period before, the cross-correlations between China’s and US soy futures markets become weak during the trade friction. The cross-correlations in soy meal futures markets are significantly positive before the trade friction for all time scales, with ρDM A values ranging from 0.7 to 0.84, while the cross-correlations becomes insignificant during the trade friction for all time scales, with ρDM A values ranging from 0.5 to 0.6. In soybean futures markets, ρDM A values before the trade friction are significant when s ≥ 50, and larger than that during the trade friction in long time scales (s ≥ 50). Second, there are two different trends of cross-correlations over varying time scales for the two periods. The cross-correlations increase with s in the early period, while the cross-correlations decrease with s in the later period. It seems that cross-correlations will not recover as long as the trade friction continues, which suggests that the impact of this trade friction is lasting, and these markets may share their multifractal structure no more. In fact, China’s tariff policy on imported soybeans will inevitably lead to a reduction in soybeans imported from US. However, the demand for soy (or protein) in China is rigid. There are abundant supply of soybeans in the US soy markets; while soybean supply in China’s market are in a tight state, which may result in a decline in the correlations of soybean futures markets between two countries. In general, the results of cross-correlations imply a possibly lasting and disruptive

Jo

120

(9)

6

Journal Pre-proof

Cross-correlations between US and China ( 0.85

DMA

)

0.8

0.75

of

0.7

0.65

0.55

0.5

p ro

0.6

Critical values Soybean-Before Soybean-During Soymeal-Before Soymeal-During

0.45

0.4 20

40

60

80

Pr e-

0

100

120

s

Figure 2: The cross-correlation coefficients ρDM A between US and China’s soy futures markets.

impact on the cross-correlations of soy futures markets. These evidences are beneficial to understand different behaviors between China’s and US soy futures markets.

155

160

Jo

150

urn

al

145

4.2. Multifractality before and during the trade friction Literatures conclude significant differences in the multifractal behavior before and during extreme events. This section attempts to observe the impact of this trade friction on soy futures markets by comparing the multifractality before and during the trade friction. First, the multifractal detrended moving average cross-correlation analysis (DMCA) is conducted on the return series of US and China’s soy futures markets in the both periods. Further, the multifractal detrended moving average analysis (MFDMA) is performed on each return series. Fig. 3 provides the plots of logF (q, s) versus logs when −10 ≤ q ≤ 10. Overall, the curves are liner for most values of q, suggesting power-law cross-correlations. Slops of logF (q, s) spectra are quite different between the two periods. To go further and confirm more details about this variation in multifractality between the two periods, we present multifractal spectra f (α) in Fig. 4 and generalized Hurst exponents h(q) in Fig. 5. Based on the multifractal spectra, the widths of these multifractal spectra (∆α) are calculated and given in Table. 2. Fig. 4 provides the singularity spectra of these series. Table 2 provides the singularity widths of the two periods (see 1-Bef and 2-Dur) and corresponding changes of the singularity widths (see NET(2-1)). As presented in Fig. 4, the cross-correlations between soy futures markets of the US and China become less multifractal during the trade friction (see left and right top of Fig. 4). The singularity width ∆α of cross-correlations in soybean futures 7

Journal Pre-proof

soybean:US-China, before

-3

soybean:US-China, during

-2.5

-3.5

soymeal:US-China, before

-2.5

soymeal:US-China, during

-2.5

-3 -3

-3

-3.5

-3.5

-4

-5

-6.5

-4.5

-5.5 2.5

3

3.5

4

4.5

2

2.5

3

3.5

4

4.5

2.5

3

-2.5

-4

-3

3.5

q=-10 q=-6 q=-2 q=0 q=2 q=6 q=10

-3.5

-4

-4.5

-6

-3

2.5

3

3.5

4

4.5

2.5

3

3.5

4

ln(s)

ln(s)

soybean:China, before

soybean:China, during

-2

-3.5

q=-10 q=-6 q=-2 q=0 q=2 q=6 q=10

-4.5

4.5

2

-2.5

-2.5

-3

-4 -3

q=-10 q=-6 q=-2 q=0 q=2 q=6 q=10

-5.5

-6

-6.5

-3.5

q=-10 q=-6 q=-2 q=0 q=2 q=6 q=10

-4

-4.5

-5

-7

-5.5 2

2.5

3

3.5

4

4.5

-4

-4.5

-5

2.5

3

3.5

4

2.5

ln(s)

3

3.5

ln(s)

4

4.5

4

4.5

2

-4.5

q=-10 q=-6 q=-2 q=0 q=2 q=6 q=10

-5

-5.5

-6

4.5

2

2.5

3

3.5

4

ln(s)

soymeal:China, before

soymeal:China, during

q=-10 q=-6 q=-2 q=0 q=2 q=6 q=10

-5.5

2

3.5

ln(s)

Pr e-

-5

ln(Fq (s))

ln(Fq (s))

ln(Fq (s))

-3.5 -4.5

3

soymeal:US, during

-4

-5.5 2

2.5

ln(s)

-4

-5

-5 2

2

-3.5

p ro

-5.5

ln(Fq (s))

ln(Fq (s))

ln(Fq (s))

q=-10 q=-6 q=-2 q=0 q=2 q=6 q=10

-5

4.5

soymeal:US, before

-3

-3.5

-4.5

4

ln(s)

soybean:US, during

-2

-3.5

ln(Fq (s))

-5 2

ln(s)

soybean:US, before

-3

-4.5

-5

ln(s)

q=-10 q=-6 q=-2 q=0 q=2 q=6 q=10

-4

of

2

q=-10 q=-6 q=-2 q=0 q=2 q=6 q=10

-4

ln(Fq (s))

-6

q=-10 q=-6 q=-2 q=0 q=2 q=6 q=10

-4

-4.5

2.5

3

3.5

-2

4.5

-2.5

-3

ln(Fq (s))

q=-10 q=-6 q=-2 q=0 q=2 q=6 q=10

-5

-5.5

ln(Fq (s))

ln(Fq (s))

ln(Fq (s))

-3.5 -4.5

q=-10 q=-6 q=-2 q=0 q=2 q=6 q=10

-3.5

-4

-4.5

-5 4

4.5

2

2.5

3

ln(s)

3.5

4

4.5

ln(s)

Figure 3: The plots of fluctuation functions log(Fq (s)) versus time scale log(s) between US and China’s soy futures markets, where q ranges from -10 to 10.

al

170

urn

165

markets shrinks from 0.802 (before the trade friction) to 0.553 (during the trade friction) with a net change of -0.249 (see Table 2). In soy meal futures markets, ∆α decreases from 0.513 to 0.435. Similar results can be found when comparing the singularity widths of each time series in the two periods. The singularity widths ∆α of US soybean and soy meal futures markets decrease with a net change of -0.198 and -0.247 respectively. In China’s soybean futures market, ∆α gets down from 1.297 (before the trade friction) to 0.621 (during trade friction) with a considerable net change of -0.676. Theses evidences show that soy futures markets in the US and China became less multifractal and more efficient. Table 2: Multifractal spectra widths ∆α and Generalized Hurst exponents (q = 2). ∆α

Cross

175

CHINA

Cross

2-Dur US

CHINA

Cross

NET(2-1) US

CHINA

0.695 0.617

1.297 0.723

0.553 0.435

0.497 0.369

0.621 0.673

-0.249 -0.078

-0.198 -0.247

-0.676 -0.050

Jo

Soybean 0.802 Soymeal 0.513

1-Bef US

Another novel finding is also obtained when checking the generalized Hurst exponents. Fig. 5 provides the generalized Hurst exponents for the two periods with q varying from -10 to 10. When q = 2, the Hurst exponents before the trade friction is less than 0.5 for all series before the trade friction, but larger than 0.5 for all series during the trade friction. In addition, h(q) values during the trade friction are larger than those before the trade friction at every q for all series. That is to say, an increment in returns during the trade friction will 8

of

Journal Pre-proof

f( )-

p ro

f( )-

1

1

0.9

0.8

0.8 0.7

0.6

f( )

f( )

0.6

0.4

0.5 0.4

0.2

Pr e-

0.3 0.2

0

0.1

Soybean:US-China,Before Soybean:US-China,During

-0.2 -0.2

0

0.2

0.4

0.6

0.8

f( )- :Soybean

1

1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

f( )- :Soymeal

1

0.8

0.8

0.6

f( )

0.6

0.4

al

f( )

Soymeal:US-China,Before Soymeal:US-China,During

0

0.2

0

0.2

0

0

urn

US-Before US-During China-Before China-During

-0.2 -0.2

0.2

0.4

0.6

0.8

1

0.4

-0.2 -0.2

1.2

US-Before US-During China-Before China-During

0

0.2

0.4

0.6

0.8

1

Jo

Figure 4: The singular spectrum of f (α) of cross-correlations in soy futures markets and each soy futures market; q ranges from -10 to 10.

9

Journal Pre-proof

of

p ro

Hurst exponent: Cross-correlations

0.9

Hurst exponent: Cross-correlations

0.8

Soymeal:US-China,Before war Soymeal:US-China,During war

Pr e-

Soybean:US-China,Before Soybean:US-China,During

0.8

0.7

0.7

0.6

0.6 0.5

H(q)

0.5

0.4

0.4

0.3 0.2

0.3

0.1

0.2

0 -0.1 -10

-8

-6

-4

-2

0

2

4

6

8

0.1 -10

10

-8

-6

-4

-2

Hurst exponent: Soybean

0.9

0.5 0.4 0.3 0.2 0.1 0 -0.1 -10

-8

-6

-4

-2

0

4

6

8

10

2

4

6

US-Before US-During CHINA-Before CHINA-During

0.9 0.8 0.7 0.6

H(q)

0.6

urn

0.7

2

Hurst exponent: Soymeal

1

US-Before US-During CHINA-Before CHINA-During

0.8

0

q

al

q

0.5 0.4 0.3 0.2 0.1

8

0 -10

10

Jo

190

H(q)

185

H(q)

180

cause a larger increment (for h(q) > 0.5, most likely when q < 2) or a smaller decrement (for h(q) < 0.5, most likely when q > 2) than that before. Further more, changes of the Hurst exponents in large fluctuations (q > 2) between the two periods are more prominent than those in small fluctuations (q < 2). The results indicate that the multifractality of soy futures markets in both US and China became more persistent for all fluctuations during the trade friction and the impact of this trade friction is stronger related with large fluctuations than small ones. The overall analysis of singularity spectra and the generalized Hurst exponents demonstrates significant differences in the multifractal behavior before and during the US-China trade friction. Compared to the previous period, all soy futures markets and the crosscorrelations experienced a significant decrease in multifractality during this trade friction. However, the generalized Hurst exponents for these markets increases, especially for large fluctuations (q > 2). These multifractal systems turn from anti-persistent to persistent in the whole investigated period.

q

-8

-6

-4

-2

0

2

4

6

8

10

q

Figure 5: Generalized Hurst exponents h(q) spectrum of cross-correlations in soy futures markets and each soy futures market, q ranges from -10 to 10.

10

Journal Pre-proof

of

200

p ro

195

4.3. Origins of multifractality and the impact of the trade friction The impact of extreme events can also be detected when analyzing origins of multifractality. The changes of multifractality in financial time series are usually attributed to long-range temporal correlations and the fat-tailed probability distributions of variations. However, considering the relatively short time range in the present analysis, the finite-size effect should be taken into account as well. The finite-size effect is caused by the linear long-term correlations in the volatility series and more likely to bring about a spurious multifractal strength (∆α) when the time length is short or the “scaling range” locates at small scales. In this case, non-linear temporal correlations, fat-tailed probability distributions and finite-size effect are considered as the components of the multifractality: ∆α = ∆αN L + ∆αF SE + ∆αP DF

215

Pr e-

al

210

where ∆α is the apparent multifractality from original time series; ∆αN L is the nonlinearity temporal component , ∆αF SE is the component of the finite-size effect� and ∆αP DF is the component of fat-tailed probability distribution. The method proposed by Zhou [35] is employed to qualify each component of the multifractal strength of the time series in the two periods: (a) Use an improved amplitude adjusted Fourier transform (IAAFT) algorithm [36] to generate surrogate data rLM , which has the same distribution and the linear long-term correlations as the original series, while any nonlinear correlations are eliminated. The singularity width in the surrogate data rLM is the finite-size effect component ∆αF SE . (b) Use the phase randomization algorithm [37] for generating the surrogate data rnorm with Gaussian distribution and same ranks as the original series to destroy the impact of fat-tailed distribution. Then detect the singularity width of rnorm and the finite-size effect component for rnorm , which are ∆αnorm and ∆αnorm,F SE respectively. (c) The components of non-linear temporal correlations and fat-tailed probability distributions are as follow: ∆αN L = ∆αnrom − ∆αnrom,F SE (11) and

urn

205

∆αP DF = ∆αorgin − ∆αF SE − ∆αN L

225

(12)

Fig. 6 provides the singularity spectra f (α). Table 3 lists the singularity widths ∆α in Fig. 6. For all series in Table 3, values of ∆αF SE are much larger than ∆αN L and ∆αP DF . This implies that the linear temporal correlation contributes most of the multifractality in these series and can explain the primary decrease in singularity width between the two periods in many cases. However, components of the nonlinear temporal correlation ∆αN L and the fat-tailed distribution ∆αP DF should not be ignored. For instance, ∆αN L of crosscorrelations in soy meal futures markets is 0.084 (before) and 0.039 (during) respectively and contributes most of the change in multifractality between the two periods. In US soybean futures market, ∆αP DF is 0.122 (before) and 0.079 (during) respectively and contributes a

Jo

220

(10)

11

Journal Pre-proof

230

considerable part of the change in multifractality. Specifically, in China’s soy meal futures market, values of ∆αP DF are 0.137 (before) and 0.088 (during) respectively and account for most of the change in multifractal strength. For US soybean futures market and China’s soy meal futures market, an impact on the fat-tailed probability distributions is detected. 1

Soybean cross-correlation:Before

1

Soybean cross-correlation:During

Soy meal cross-correlation:Before

1

0.8

0.6

0.6

0.8

0.8

of

0.8

Soy meal cross-correlation:During

1 0.9

0.9

0.7

0.7

0.4

f( )

f( )

f( )

f( )

0.6

0.4

0.6 0.5

0.5 0.4

-0.2 -0.2

0

0.2

0.4

0

0.6

0.8

-0.2 0.3

1

Soybean US:Before

1

Origin Norm FSE Norm FSE

0.3 0.2 0.1

0.4

0.5

0.6

0.7

0.8

0.9

1

0

Soybean US:During

1

0.8

0.6

0.6

0.8 0.7

f( )

f( )

f( )

0.6 0.5

0.4

0.4

0.4

0 -0.2

0

0.2

0.4

0

0.6

0.8

-0.2 0.3

1

Soybean China:Before

1

0.6

0.6

f( )

0.8

0.4

-0.2 -0.2

0

0.2

0.4

0.6

0.6

1

-0.2 0.3

1.2

0.8

0.9

1

0

0.4

0.5

0.6

0.7

0.1

0.3

0.4

0.5

0.6

0.8

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.2

0.3

0.4

0.5

0.8

0.9

0.9

0.5 0.4

Origin Norm FSE Norm FSE

0.3 0.2 0.1 0 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Soy meal cross-correlation:During

0.4

Origin Norm FSE Norm FSE

0

0.7

0.8

0.6

0.2

0.6

0.7

0.7

1

Origin Norm FSE Norm FSE

0.1

0.6

0.8

0.6

0

0.5

Soy meal US:During

1

0.9

0.4

0.4

0.9

0.6

-0.2 -0.1

1.1

0 0.3

0.9

0.8

0

1

0.8

0.8

0.2

0.9

0.7

Soy meal China:Before

1

Origin Norm FSE Norm FSE

0

0.8

0.7

0.4

0.2

Origin Norm FSE Norm FSE

0

0.5

Soybean China:During

1

0.8

0.2

-0.2 0.4

0.1

Origin Norm FSE Norm FSE

0

f( )

0.1

0.2

Origin Norm FSE Norm FSE

0.2

Pr e-

0.2

f( )

0.2

Origin Norm FSE Norm FSE

0.3

0.2

Soy meal US:Before

1

0.9 0.8

0.1

Origin Norm FSE Norm FSE

0.3

f( )

0

0.4

Origin Norm FSE Norm FSE

f( )

0.2

Origin Norm FSE Norm FSE

p ro

0.2

-0.2 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

al

Figure 6: Generalized Hurst exponents h( q) spectrum of origin, rLM (FSE), rnorm (Norm) and the finite-size effect component for rnorm (NormF SE ), q ranges from -10 to 10.

Table 3: Multifractality degrees of three kinds of series ∆αP DF

∆αF SE

During ∆αN L

∆αP DF

0.677 0.409 0.512 0.556 1.122 0.573

0.100 0.084 0.062 0.017 0.171 0.013

0.025 0.021 0.122 0.043 0.005 0.137

0.453 0.376 0.402 0.410 0.491 0.575

0.069 0.039 0.016 0.020 0.079 0.009

0.031 0.021 0.079 -0.049 0.050 0.088

Jo

CROSSsoybean CROSSsoymeal U Ssoybean U Ssoymeal Chinasoybean Chinasoymeal

Before ∆αN L

urn

∆αF SE

5. Conclusions

235

In this paper, we investigate the impact of the 2018 US-China trade friction on the multifractality of soy futures markets in the two countries. We first compare the crosscorrelations in soy futures markets between the US and China. Than we study and compare 12

Journal Pre-proof

255

260

265

of

p ro

Pr e-

250

al

245

urn

240

the multifractality before and during the trade friction. Moreover, we investigate and compare the origins of the multifractality in two periods, including finite-size effect, non-linear correlations and fat-tailed distributions. The results show that the cross-correlations coefficient decreases significantly during the trade friction and a possibly disruptive impact on cross-correlations is found. The soy futures markets in US and China once seen as a system became less temporally correlated. Comparing the period before trade friction, the singularity widths of all soy futures markets and the cross-correlations during trade friction decrease; whilst the Hurst exponents of all series experience a significant increases especially for large fluctuations. The soy futures markets became less multifractal and more persistent when the US-China trade friction broke out. Comparing the origins of multifractality in the two periods, the finite-size effect caused by the long-term linear correlation contributes most of the multifractality in these series and can explain the major changes in multifractality for cross-correlations in soybean futures market, US soy meal futures market and China’s soybean futures market. Decreases in the fat-tailed probability distributions are found in US soybean futures market and China’s soy meal futures market, which may also be attribute to the impact of this trade friction. The US-China trade friction has caused lots of tensions and fluctuations in commodity markets, exchange markets and stock markets. Soy futures market is one of the focal points in this trade friction. The demand for soybean and its derivatives in China has always been surging, with numerous industries involved. Meanwhile, agricultural products are one of the most important class of export products in US. As the tariff on soy was put into effect, investigators in two countries may take different hedging behaviors and be more cautious than ever before. For example, investigators and speculators in US are more likely to take short-selling, while in China speed up stock piling. Thus, the soy futures markets in two countries become less correlated, less multifractal, but more persistent. However, hedging behaviors cannot solve the contradiction between supply and demand. If the trade war continues, it may occur that China’s dependence on soy imported from US and the correlation between China’s and US soy futures markets will keep decreasing, and that China’s soy futures market may seek greater pricing power. Also, China’s tariff on soy may affect the exchange rate, stocks and futures related to agricultural commodity in both countries, or the ongoing trade negotiation. 6. Acknowledgments

This work was supported by the Major Program of National Social Science Foundation of China [15ZDA053], the Key Program of the National Social Science Foundation Project of China [14AZD021], Cultural Experts and Four batch Talents Independently Selected Topic Project [ZXGZ[2018]86], the Jiangsu Provice Natural Science Foundation of China [BK20171422].

Jo

270

References 275

[1] E. E. Peters, Fractal market analysis : applying chaos theory to investment and economics, Chaos Theory 34 (2) (1994) 343–345.

13

Journal Pre-proof

300

305

310

315

320

325

of

p ro

Pr e-

295

al

290

urn

285

Jo

280

[2] B. B. Mandelbrot, A multifractal walk down wall street, Scientific American 280 (2) (1999) 70–73. [3] J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, H. E. Stanley, Multifractal detrended fluctuation analysis of nonstationary time series, Physica A: Statistical Mechanics and its Applications 316 (1) (2002) 87–114. [4] B. Podobnik, H. E. Stanley, Detrended cross-correlation analysis: A new method for analyzing two nonstationary time series, Physical Review Letters 100 (2008) 084102. doi:10.1103/PhysRevLett. 100.084102. URL https://link.aps.org/doi/10.1103/PhysRevLett.100.084102 [5] H. E. Hurst, Long term storage capacities of reservoirs, Transactions of the American Society of Civil Engineers 116 (12) (1951) 776–808. [6] B. B. Mandelbrot, J. R. Wallis, Robustness of the rescaled range r/s in the measurement of noncyclic long run statistical dependence, Water Resources Research 5 (5) (1969) 967–988. [7] C. K. Peng, S. V. Buldyrev, S. Havlin, M. Simons, H. E. Stanley, A. L. Goldberger, Mosaic organization of dna nucleotides., Physical Review E Statistical Physics Plasmas Fluids & Related Interdisciplinary Topics 49 (2) (1994) 1685. [8] J. W. Kantelhardt, S. A. Zschiegner, E. Koscielny-Bunde, S. Havlin, A. Bunde, H. E. Stanley, Multifractal detrended fluctuation analysis of nonstationary time series, Physica A Statistical Mechanics & Its Applications 316 (1) (2012) 87–114. [9] M. Holschneider, On the wavelet transformation of fractal objects, Journal of Statistical Physics 50 (5-6) (1988) 963–993. [10] Z.-Q. Jiang, W.-J. Xie, W.-X. Zhou, D. Sornette, Multifractal analysis of financial markets, arXiv:1805.04750 [q-fin]. URL http://arxiv.org/abs/1805.04750 [11] W.-X. Zhou, Multifractal detrended cross-correlation analysis for two nonstationary signals, Physical Review E 77 (6) (2008) 066–211. [12] B. Podobnik, I. Grosse, D. Horvatić, S. Ilic, P. C. Ivanov, H. E. Stanley, Quantifying cross-correlations using local and global detrending approaches, The European Physical Journal B-Condensed Matter and Complex Systems 71 (2) (2009) 243–250. [13] M. Pal, P. M. Rao, P. Manimaran, Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series, Physica A: statistical mechanics and its applications 416 (2014) 452–460. [14] G. Cao, J. Cao, L. Xu, L. Y. He, Detrended cross-correlation analysis approach for assessing asymmetric multifractal detrended cross-correlations and their application to the chinese financial market, Physica A Statistical Mechanics & Its Applications 393 (1) (2014) 460–469. [15] Q. Wang, Y. Zhu, L. Yang, R. A. Mul, Coupling detrended fluctuation analysis of asian stock markets, Physica A: Statistical Mechanics and its Applications 471 (2017) 337–350. [16] E. Alessio, A. Carbone, G. Castelli, V. Frappietro, Second-order moving average and scaling of stochastic time series, The European Physical Journal B 27 (2) (2002) 197–200. [17] G. F. Gu, W. X. Zhou, Detrending moving average algorithm for multifractals, Physical Review E Statistical Nonlinear & Soft Matter Physics 82 (1 Pt 1) (2010) 011136. [18] L. Y. He, S. P. Chen, A new approach to quantify power-law cross-correlation and its application to commodity markets, Physica A Statistical Mechanics & Its Applications 390 (21–22) (2011) 3806–3814. [19] Z. Q. Jiang, W. X. Zhou, Multifractal detrending moving-average cross-correlation analysis, Physical Review E Statistical Nonlinear & Soft Matter Physics 84 (2) (2011) 016–106. [20] Y. Wang, Y. Wei, C. Wu, Cross-correlations between chinese a-share and b-share markets, Physica A: Statistical Mechanics and its Applications 389 (23) (2010) 5468–5478. [21] Y. Wang, L. Liu, Is WTI crude oil market becoming weakly efficient over time? : New evidence from multiscale analysis based on detrended fluctuation analysis, Energy Economics 32 (5) (2010) 987–992. [22] Y. Wang, C. Wu, Z. Pan, Multifractal detrending moving average analysis on the us dollar exchange rates, Physica A Statistical Mechanics & Its Applications 390 (20) (2011) 3512–3523. [23] G. Cao, Y. Han, Y. Chen, C.-X. Yang, Multifractal detrended cross-correlation between the chinese

14

Journal Pre-proof

340

[29] [30] [31]

345

[32] [33] 350

[34] [35] 355

[36] [37]

of

[28]

p ro

[27]

Pr e-

[26] 335

al

[25]

urn

[24]

Jo

330

domestic and international gold markets based on dcca and dmca methods, Modern Physics Letters B 28. doi:10.1142/S0217984914500900. M. Corazza, A. G. Malliaris, C. Nardelli, Searching for fractal structure in agricultural futures markets, Journal of Futures Markets 17 (4) (1997) 433–473. L. Y. He, S. P. Chen, Are developed and emerging agricultural futures markets multifractal? a comparative perspective, Physica A Statistical Mechanics & Its Applications 389 (18) (2010) 3828–3836. A. Chatrath, B. Adrangi, K. K. Dhanda, Are commodity prices chaotic?, Agricultural economics 27 (2) (2002) 123–137. L.-Y. He, S.-P. Chen, Multifractal detrended cross-correlation analysis of agricultural futures markets, Chaos, Solitons & Fractals 44 (6) (2011) 355–361. Siokis, M. Fotios, Multifractal analysis of stock exchange crashes, Physica A Statistical Mechanics & Its Applications 392 (5) (2013) 1164–1171. C. Petre, Evidence of multifractality from emerging european stock markets, Plos One 7 (7) (2012) e40693. R. Yalamova, Empirical testing of multifractality of financial time series based on wtmm, Fractalscomplex Geometry Patterns & Scaling in Nature & Society 17 (03) (2009) 323–332. G. Oh, C. Eom, S. Havlin, W. S. Jung, F. Wang, H. E. Stanley, S. Kim, A multifractal analysis of asian foreign exchange markets, European Physical Journal B 85 (6) (2012) 1–6. U. Bashir, G. F. Zebende, Y. Yu, M. Hussain, A. Ali, G. Abbas, Differential market reactions to pre and post Brexit referendum, Physica A: Statistical Mechanics and its Applications 515 (2019) 151–158. L. Kristoufek, Detrending moving-average cross-correlation coefficient: Measuring cross-correlations between non-stationary series, Physica A Statistical Mechanics & Its Applications 406 (10) (2014) 169–175. B. Podobnik, Z. Q. Jiang, W. X. Zhou, H. E. Stanley, Statistical tests for power-law cross-correlated processes, Physical Review E Statistical Nonlinear & Soft Matter Physics 84 (2) (2011) 066118. W. X. Zhou, Finite-size effect and the components of multifractality in financial volatility, Chaos Solitons & Fractals 45 (2) (2012) 147–155. T. Schreiber, A. Schmitz, Improved surrogate data for nonlinearity tests, Physical Review Letters 77 (4) (1996) 635. J. Theiler, S. Eubank, A. Longtin, B. Galdrikian, J. D. Farmer, Testing for nonlinearity in time series: the method of surrogate data, Physica D Nonlinear Phenomena 58 (92) (1992) 77–94.

15