We tested the price linkage, the law of one price (LOP) condition, and the causality of the price linkage between the U.S. and Japanese gold and silver futures markets with consideration of structural breaks in the price series. The LOP condition did not hold for both the gold and silver markets when structural breaks were not considered but it sustained in some periods when it was tested for the break periods. We found from the causality test that the price linkage between the U.S. and Japanese gold and silver futures markets were led by the U.S. market.gold futures market, silver futures market, cointegration, law of one price, causality test

Kentaka Aruga

Shunsuke Managi

English

Research Papers in Economics

     
 
 
  
  
Volume 31, Issue 2 
  
Tests on price linkage between the U.S. and Japanese gold and silver futures 
markets 
  
 
 
Kentaka Aruga  
Institute for Global Environmental Strategies 
Shunsuke Managi  
Tohoku University
Abstract 
We tested the price linkage, the law of one price (LOP) condition, and the causality of the price linkage between the 
U.S. and Japanese gold and silver futures markets with consideration of structural breaks in the price series. The LOP 
condition did not hold for both the gold and silver markets when structural breaks were not considered but it sustained 
in some periods when it was tested for the break periods. We found from the causality test that the price linkage 
between the U.S. and Japanese gold and silver futures markets were led by the U.S. market.
This research was funded by the Ministry of the Environment, Government of Japan. The results and conclusions of this paper do not 
necessarily represent the views of the funding agency. 
Citation: Kentaka Aruga and Shunsuke Managi, (2011) ''Tests on price linkage between the U.S. and Japanese gold and silver futures 
markets'', Economics Bulletin, Vol. 31 no.2 pp. 1038-1046. 
Submitted: Feb 28 2011.   Published: April 06, 2011. 
 
     1 
 
1.  Introduction 
Whether international linkage exists for the gold and silver futures markets is 
an important issue. This is because gold and silver have been historically considered as 
asset to hedge against economic uncertainty. International linkage among futures 
markets has been studied for agricultural commodities such as wheat (Goodwin, 1992) 
and soybean meal (Yang et al., 2000) but there are not many studies examining this for 
gold and silver futures markets. To fill this  gap  we  analyze the price relationship 
between the U.S. and Japanese gold and silver futures markets. The study identifies if 
the U.S. and Japanese gold and silver futures markets move together in the long-run, 
examines the law of one price (LOP) condition, and tests the causality of the long-run 
relationships. We use the 2001-2010  daily  data, which includes the global financial 
crisis of 2008. Hence, we test the price linkage when effects of structural breaks in the 
price series are considered as well.   
The results of the study will reveal whether international linkage exists for the 
gold and silver futures markets, the degree of the linkage, and the cause of the linkage. 
Therefore, the study will be useful when constructing effective global risk management 
strategies for investors and industries involved in the gold and silver markets. 
In the next section the methods used in the study are explained. The third 
section describes the data. Results are shown in the fourth section. Section five provides 
the conclusion of the study.   
 
 
2.  Methods 
The  long-run price linkage, the LOP condition,  and the causality of the 
long-run relationship between the U.S. and Japanese gold and silver futures prices are 
tested under the Johansen cointegration method (Johansen and Juselius, 1990). 
Cointegration requires all price series to be integrated of the same order so initially unit 
root tests are performed on all price series used in the study. We use the augmented 
Dickey-Fuller (1979), Phillips-Perron (1988), and Kwiatkowski-Phillips-Schmidt-Shin 
(1992) unit root tests for this purpose. If we find that the price series are integrated of 
the same order from the unit root tests, we perform the Johansen test between the U.S. 
and Japanese gold and silver futures prices. The Johansen test is performed using the 
following vector error correction model: 
      ∆Yt = ΠYt−1 + ∑ Γi∆Yt−i
q−1
i=1 + μ + εt                                   (1) 
where  Yt  is  the n × 1 vector (Y1t,Y2t,⋯,Ynt)′  of futures prices, q is the order of the 
vector autoregressive process, Π = −I + ∑ Πi
q
i=1   and  Γi = −∑ Πj
q
j=i+1   where   Π𝑖 2 
 
and   Π𝑗  are the 𝑛 × 𝑛  matrix of parameters, μ  is a constant, and εt  is a normally 
distributed n-dimensional white noise process. When cointegration relationship is found 
between the price series it is known that the Π  matrix in equation (1) can be 
decomposed as  Π = 𝗼𝗽′  (Johansen, 1991). 
The LOP condition and the causality of the long-run relationship are tested by 
imposing restrictions on the Π  matrix.  Thus it is necessary that a cointegration 
relationship holds between the U.S. and Japanese gold and silver futures prices. The 
LOP condition is tested under the following equation: 
      Pt
US = 𝑎 + 𝑏Pt
JP + et,                        (2) 
where  Pt
US  and  Pt
JP  are the prices of the U.S. and Japanese gold and silver futures 
contracts at time t,  𝑎  is a constant,  𝑏  is a coefficient, and  et  is the error term.
1  In this 
study we tested whether  𝑏 = 1  holds in equation (2), which is called the weak version 
of the LOP test (see Asche et al, 2004).
2  This test is performed by putting a restriction 
on the 𝗽  part  of the Π  matrix.  The causality test is performed by incorporating a 
restriction to the 𝗼  part of the Π  matrix. The hypothesis tested in the causality test is 
that the U.S. price leads  the gold or silver futures prices to reach the long-run 
relationship. 
The Bai-Perron test (Bai and Perron, 1998) is used to identify whether 
structural breaks exists in the price relationship between the U.S. and Japanese gold and 
silver futures prices. This test is useful for identifying multiple structural breaks in the 
price series when breaks are unknown. First the test performs the un-weighted and 
weighted maximum tests to find out whether at least one break exists in the price series. 
Once the existence of one break is confirmed by these double maximum tests,  the 
Bai-Perron test goes further to statistically identify the appropriate number of breaks by 
the  𝑠𝑢𝑝𝐹(𝑙 + 1|𝑙)  test. The 𝑠𝑢𝑝𝐹(𝑙 + 1|𝑙)  test tests the null hypothesis of having 𝑙 
breaks in the price series against the alternative hypothesis of having  𝑙 + 1  breaks. The 
price ratio between the U.S. and Japanese futures prices for gold and silver (Pt
US/Pt
JP) is 
used for the Bai-Perron test.
3   
After the breaks are determined by the Bai-Perron test the whole gold and 
silver price series are separated into break periods using the break dates identified by the 
Bai-Perron test. Then the same unit root tests, Johansen cointegration test, LOP test, and 
causality tests are tested for each break period to see if the price relationship between 
                                                   
1  The prices of Japanese gold and silver futures contracts are converted into U.S. dollars.   
2  In the strong version of the LOP it also requires  𝑎 = 0  to hold in equation (2) (see Asche et al., 2004). 
3  We followed Kristofersson and Anderson (2006) of using the price ratio to identify the structural breaks 
in the price relationship between the two price series. In the Bai-Perron test we set the maximum number 
of breaks to five and the trimming value to 0.15 (see Bai and Perron (1998) for details). 3 
 
the U.S. and Japanese gold and silver futures markets changed before and after the 
break dates.   
   
 
3.  Data 
For the U.S. gold and silver futures prices the daily continuous futures prices of 
Commodity Exchange Inc. (COMEX) gold and silver futures contracts are used in the 
study. The daily continuous price data for these COMEX futures prices are obtained 
from the EODData, LLC.
4  The Japanese gold and silver futures prices are taken from 
the Tokyo Commodity Exchange (TOCOM). The furthest contracts are the most active 
contracts at the TOCOM market so the daily continuous TOCOM gold and silver 
futures prices are created using the prices for the furthest contracts. January 2001 to 
June 2010 period is covered for the COMEX and TOCOM gold and silver futures 
prices. 
To match the minimum price units, all daily gold and silver futures prices are 
converted to U.S. dollars per gram. The TOCOM gold and silver prices are converted to 
U.S. dollars by using the daily currency rate between the U.S. dollars and Japanese yen. 
The daily currency rate is obtained from the OANDA Corporation.   
   
                                                   
4  The futures prices for the most active contracts were used for the continuous price data.   4 
 
 
   
Figure 1:  Plots of U.S. and Japanese gold and silver futures prices and their price 
differences 
 
  Figure 1 presents the plots of U.S. and Japanese gold and silver futures prices 
and the price difference between the U.S. and Japanese prices for gold and silver. In 
both the gold and silver futures markets the U.S. and Japanese prices seem to move 
together during the period used in this study so it is likely that the U.S. and Japanese 
prices will have a cointegration relationship in these markets.   
 
 
4.  Results 
Before performing the Johansen test we performed the unit root tests to check 
if all price series used in the study are integrated of the same order. The unit root tests 
conducted for the whole test period revealed that all price series are integrated of order 
one (see Table 1). Hence, we performed the Johansen test between the U.S. and 
Japanese futures prices for the gold and silver futures markets. 
 
 
0
5
10
15
20
25
30
35
40
45
Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10
U.S. Gold Japanese Gold
U
S
$
/
g
r
a
m
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10
U
S
$
/
g
r
a
m
Price difference for U.S. and Japanese Gold
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10
U.S. Silver Japanese Silver
U
S
$
/
g
r
a
m
-0.1
-0.05
0
0.05
0.1
0.15
Jan-01 Jan-02 Jan-03 Jan-04 Jan-05 Jan-06 Jan-07 Jan-08 Jan-09 Jan-10
U
S
$
/
g
r
a
m
Price difference for U.S. and Japanese Silver5 
 
Table 1: Unit root tests 
 
 
Table 2: Cointegration tests without breaks 
 
 
As seen from Table 2, for both the gold and silver futures markets, the U.S. and 
Japanese prices have a cointegration relationship and there is a long-run price linkage 
between the gold and silver futures markets of the two countries. However, for both the 
gold and silver markets, the LOP condition did not hold between the U.S. and Japanese 
futures prices. The causality test showed that in both the gold and silver futures markets 
it is the U.S. price that binds the U.S. and Japanese prices to move together in the 
long-run.   
 
Table 3: Bai-Perron tests 
 
 
Variable
ADF PP KPSS ADF PP KPSS
U.S. Gold -1.978 -2.121 1.025*  -11.454*  -46.632* 0.020
U.S. Silver -3.252 -3.367 0.324*  -11.197*  -48.093* 0.026
Japanese Gold -1.965 -2.312 0.996*  -13.096*  -52.365* 0.018
Japanese Silver -3.021 -3.253 0.327*  -15.931*  -50.583* 0.029
Log Level First difference of log level
Notes: * denotes significance at 1%. All the unit root tests for the level and first differences include constant and
trend. Lag orders for the ADF tests are determined by the AIC and the bandwidth for the PP and KPSS tests are
identified by Newey-West method (Newey and West, 1994).
Test variables H0: rank=r Trace test Max test
LR test statistic for
the law of one price
Variables
LR test statistic for
the causality test
r=0 104.80** 104.03** 22.75** U.S. 1.58
r<=1 0.77 0.77 Japanese 94.23**
r=0 247.25** 246.75** 20.02** U.S. 0.00
r<=1 0.50 0.50 Japanese 214.07**
Note: ** represents significance at 5% level. 
U.S. Gold vs
Japanese Gold
U.S. Silver vs
Japanese Silver
Gold Silver
Test Statistic Statistic
UDmax       153.17**        49.84**
WDmax       165.97**        55.73**
sup-F(2|1)       117.73**        12.99**
sup-F(3|2)         20.23**        11.46**
sup-F(4|3)         10.17          2.67
Note: ** denotes significance at 5% level.6 
 
  The Bai-Perron test revealed that three breaks exists in the January 2001 to 
June 2010 period covered in this study (see Table 3). Hence this whole period was split 
into four break periods using the break dates identified by the Bai-Perron tests. The 
details of the break dates for gold and silver markets are presented in Tables 4 and 5. 
The same above mentioned unit root tests, the Johansen test, the LOP test, and the 
causality test are performed on these break periods. Tables 4 and 5 show these results 
for the gold and silver futures markets.
5 
 
Table 4: Cointegration tests with breaks for the U.S. and Japanese gold futures markets   
 
 
Table 5: Cointegration tests with breaks for the U.S. and Japanese silver futures markets   
 
 
Tables 4 and 5 reveal that in both the gold and silver futures markets in every 
period the U.S. and Japanese markets have cointegration relationships. This implies that 
the price linkage between the two countries for the gold and silver futures markets was 
not affected by the breaks. However, the results in the tables suggest that the LOP 
condition  and the causality of the cointegration relationship are  affected by the 
structural breaks in the price series. Table 4 shows that the LOP condition holds for the 
gold market until August 2008 but this condition did not meet in the fourth period. The 
LOP condition also did not hold for the second and fourth period for the silver market 
                                                   
5  The results of the unit root tests suggested that in all break periods the price series used in the test 
periods are integrated of the same order. 
Period H0: rank=r Trace test Max test LOP Variables Causality test
r=0 23.96** 23.88** 2.88 U.S. 1.83
r<=1 0.08 0.08 Japan 15.70**
r=0 73.86** 73.42** 2.23 U.S. 1.94
r<=1 0.44 0.44 Japan 71.84**
r=0 39.77** 37.78** 0.35 U.S. 2.21
r<=1 2.00 2.00 Japan 35.23**
r=0 192.00** 191.39**     9.29** U.S. 0.06
r<=1 0.62 0.62 Japan 160.00**
Note: ** represents significance at 5% level. 
1
2
3
4
Dates
Jan. 4, 2001 - Jun. 3, 2002
Jun. 4, 2002 - Oct. 7, 2005
Oct. 11, 2005 - Aug. 14, 2008
Aug. 15, 2008 - Jun. 30, 2010
Period H0: rank=r Trace test Max test LOP Variables Causality test
r=0 20.13** 18.05** 0.96 U.S. 3.17
r<=1 2.09 2.09 Japan 9.57**
r=0 209.36** 207.62** 17.70** U.S. 0.62
r<=1 1.74 1.74 Japan 188.03**
r=0 41.74** 41.50** 0.36 U.S. 12.45**
r<=1 0.24 0.24 Japan 16.18**
r=0 123.87** 120.84** 13.20** U.S. 0.02
r<=1 3.03 3.03 Japan 99.18**
Note: ** represents significance at 5% level. 
1
Dates
Jan. 4, 2001 - Jul. 18, 2002
2
3
4
Jul. 19, 2002 - May 2, 2005
May 6, 2005 - Dec. 13, 2006
Dec. 14, 2006 - Jun. 30, 20107 
 
(see Table 5). For the silver market, Table 5 shows that the causality of the cointegration 
relationship between the U.S. and Japanese markets are also affected in the third period. 
These results imply that although the price relationship between the U.S. and Japanese 
gold and silver markets sustained even with the effects of structural breaks, the level of 
arbitrage and the cause of the price relationship between the U.S. and Japanese markets 
did have an influence from the breaks in the price series. 
   
 
5.  Conclusion 
This study tested the price linkage, the law of one price (LOP) condition, and 
the causality of the price linkage between the U.S. and Japanese gold and silver futures 
markets with consideration of structural breaks in the price series. We find price linkage 
do exist between the U.S. and Japanese gold and silver futures markets. This suggests 
that gold and silver futures markets are interdependent and price information can be 
shared between the two countries. The LOP condition did not hold for both the gold and 
silver markets when structural breaks were not considered but it sustained  in some 
periods when tested this condition for the break periods. This implies that for the whole 
test period arbitrage was not perfect between the U.S. and Japanese market but there 
were periods where arbitrage was very quick and price information were perfectly 
shared between the two countries. The causality test revealed that it is the U.S. price that 
leads the gold and silver futures markets to reach the long-run relationship but this price 
leadership was also affected for the silver market when tested for the break periods. 
 
 
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Distribution of the estimators for autoregressive time series with a unit root,

Estimating and testing linear models with multiple structural changes,

Is there a relationship between fisheries and farming? Interdependence of fisheries, animal production and aquaculture,

Maximum likelihood estimation and inference on cointegration: with applications to the demand for money,

Multivariate cointegration tests and the law of one price in international wheat markets,

Testing for unit roots in time series regression,

Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?,

Tests for market integration and the law of one price: The market for whitefish in France,

The law of one price: developed and developing country market integration,

Tests on price linkage between the U.S. and Japanese gold and silver futures markets

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Tests on price linkage between the U.S. and Japanese gold and silver futures markets

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