Linkages among commodity futures prices in the recent financial crisis: An application of cointegration tests with a structural break

Figures & data

Figure 1. Nikkei-TOCOM sub commodity indexes.

Figure 2. TG sub-commodity indexes.

Table 1. Descriptive statistics

	Mean	Standard error	Coefficient of variation	Minimum	Maximum
Nikkei-TOCOM Sub Index
Gold	170.5	56.5	0.33	89.2	279.9
Palladium	74.0	22.6	0.31	33.7	140.1
Platinum	214.2	74.4	0.35	89.7	426.3
Silver	203.5	87.0	0.43	87.0	442.0
TG Sub Index
Corn	112.8	31.1	0.28	64.0	229.3
Red bean	54.6	27.1	0.50	24.5	115.3
Soybean	131.8	28.6	0.22	88.4	239.4
Sugar	130.8	30.5	0.23	75.9	228.4

Table 2. Augmented Dickey–Fuller test

(a) Precious metal futures prices				(b) Agricultural futures prices
Commodity	Specification	Lag length	Test statistics	Commodity	Specification	Lag length	Test statistics
Precious metal futures price levels				Agricultural futures price levels
Gold	I	23	−2.32	Corn	I	1	−1.64
	II	23	−0.77		II	1	−1.50
	III	23	2.24		III	1	−0.24
Palladium	I	1	−1.74	Soybean	I	28	−2.35
	II	1	−1.28		II	28	−2.36
	III	1	0.31		III	2	0.31
Platinum	I	29	−2.47	Red bean	I	5	−2.16
	II	21	−2.10		II	1	−0.92
	III	21	1.18		III	1	−1.91
Silver	I	10	−2.03	Sugar	I	2	−1.73
	II	10	−0.58		II	2	−1.41
	III	10	1.62		III	2	0.87
First difference of precious metal futures prices				First difference of agricultural futures prices
Gold	I	22	−10.98**	Corn	I	1	−28.79**
	II	22	−10.99**		II	1	−28.80**
	III	22	−10.73**		III	1	−28.80**
Palladium	I	1	−31.12**	Soybean	I	1	−27.94**
	II	1	−31.10**		II	1	−27.95**
	III	1	−31.10**		III	1	−27.95**
Platinum	I	20	−9.91**	Red bean	I	4	−17.89**
	II	20	−9.86**		II	4	−17.90**
	III	20	−9.77**		III	4	−17.80**
Silver	I	9	−15.15**	Sugar	I	1	−29.67**
	II	9	−15.15**		II	1	−29.68**
	III	9	−15.05**		III	1	−29.66**

^** Null hypothesis can be rejected at the 1% significance level.

Notes: The auxiliary regression includes a constant and time trend (I), a constant (II) and none (III). Lag length is chosen according to the AIC with a maximum lag of 30.

Table 3. KPSS test

(a) Precious metal futures prices			(b) Agricultural futures prices
Commodity	Specification	Test statistics	Commodity	Specification	Test statistics
Precious metal futures price levels			Agricultural futures price levels
Gold	I	2.04**	Corn	I	2.40**
	II	22.21**		II	2.94**
Palladium	I	1.09**	Soybean	I	1.29**
	II	2.81**		II	2.06**
Platinum	I	3.13**	Red bean	I	2.48**
	II	15.76**		II	20.41**
Silver	I	2.86**	Sugar	I	1.94**
	II	19.41**		II	4.51**
First difference of precious metal futures prices			First difference of agricultural futures prices
Gold	I	0.0399	Corn	I	0.0762
	II	0.0398		II	0.1179
Palladium	I	0.099	Soybean	I	0.0541
	II	0.2538		II	0.0648
Platinum	I	0.0521	Red bean	I	0.0613
	II	0.1304		II	0.0898
Silver	I	0.0696	Sugar	I	0.0933
	II	0.0717		II	0.1003

^** Null hypothesis can be rejected at the 1% significance level.

Notes: The auxiliary regression includes a constant and time trend (I) and a constant (II).

Table 4. Zibot–Andrews test

(a) Precious metal futures prices				(b) Agricultural futures prices
Commodity	Specification	Test statistics	Break point	Commodity	Specification	Test statistics	Break point
Precious metal futures price levels				Agricultural futures price levels
Gold	I	−4.44	14 September 2005	Corn	I	−5.43**	25 August 2008
	II	−2.88	27 March 2007		II	−2.21	4 September 2007
	III	−4.42	14 September 2005		III	−4.73	28 August 2008
Palladium	I	−2.97	11 July 2008	Soybean	I	−4.44	27 August 2008
	II	−2.25	8 July 2009		II	−2.50	27 September 2007
	III	−4.76	11 July 2008		III	−4.24	27 August 2008
Platinum	I	−7.00**	11 July 2008	Red bean	I	−4.05	9 July 2009
	II	2.68	18 January 2007		II	−3.78	23 October 2008
	III	−6.53**	4 September 2008		III	−3.98	27 May 2008
Silver	I	−5.32*	22 July 2008	Sugar	I	−2.64	19 September 2006
	II	−2.70	7 April 2006		II	−2.12	30 June 2010
	III	−5.32*	4 August 2008		III	−3.06	27 August 2008
First difference of precious metal futures prices				First difference of agricultural futures prices
Gold	I	−11.14**	12 May 2006	Corn	I	−29.28**	25 June 2008
	II	−11.01**	2 August 2002		II	−29.05**	15 October 2008
	III	−11.20**	5 March 2008		III	−29.49**	3 July 2008
Palladium	I	−45.19**	3 March 2008	Soybean	I	−28.31**	22 February 2008
	II	−45.11**	29 September 2008		II	−28.22**	9 October 2008
	III	−45.33**	3 March 2008		III	−28.46**	3 July 2008
Platinum	I	−7.97**	1 December 2008	Red bean	I	−18.15**	14 November 2003
	II	−10.01**	26 September 2008		II	−18.09**	1 August 2005
	III	−10.49**	10 July 2008		III	−18.27**	14 November 2003
Silver	I	−15.43**	19 April 2006	Sugar	I	−30.16**	6 February 2006
	II	−15.35**	1 July 2010		II	−29.97**	30 April 2010
	III	−15.58**	14 July 2008		III	−30.17**	6 February 2006

^** Null hypothesis can be rejected at the 1% significance level.

Notes: The auxiliary regression includes a constant and time trend (I), a constant (II) and none (III). The lag length of each specification is set as chosen in the ADF unit root tests (Table 2).

Table 5. Cointegration tests

	Trace test			Maximal eigenvalue test
	I	II	III	I	II	III
(a) Precious metal futures prices
Lag = 1
r = 0	32.50	28.00	45.79	13.73	12.71	22.41
r ≦1	18.77	15.29	23.38	11.34	10.92	12.55
r ≦2	7.44	4.37	10.83	4.32	3.30	7.91
r ≦3	3.12	1.07	2.93	3.12	1.07	2.93
Lag = 2
r = 0	34.28	30.18	49.31	13.73	13.46	23.72
r ≦1	20.55	16.71	25.59	12.94	11.86	13.34
r ≦2	7.61	4.85	12.25	4.46	3.47	9.03
r ≦3	3.16	1.38	3.22	3.16	1.38	3.22
(b) Agricultural futures prices
Lag = 1
r = 0	39.88	34.17	60.09	25.44	25.20	45.82**
r ≦1	14.44	8.97	14.28	6.92	5.00	6.46
r ≦2	7.52	3.97	7.82	4.96	3.04	4.93
r ≦3	2.56	0.93	2.89	2.56	0.93	2.89
Lag = 2
r = 0	39.92	34.11	58.71	25.56	25.34	44.44**
r ≦ 1	14.35	8.76	14.27	6.89	5.08	6.78
r ≦ 2	7.46	3.68	7.50	4.91	2.85	4.79
r ≦ 3	2.55	0.83	2.71	2.55	0.83	2.71

^** Null hypothesis can be rejected at the 1% significance level.

Notes: I: The cointegrating equations have no intercepts and the level data have no deterministic trends.

II: The cointegrating equations have intercepts but the level data have no deterministic trends.

III: Both the cointegrating equations and the level data have linear trends.

Table 6. Cointegration tests with a structural break

	I	Break point	II	Break point
(a) Precious metal futures prices
Lag = 1
r = 0	53.98^**	14 July 2008	65.51^**	1 August 2008
r ≦ 1	21.62		31.86^*
r ≦ 2	9.56		13.27
r ≦ 3	1.84		1.73
Lag = 2
r = 0	52.07^**	14 July 2008	68.8^**	1 August 2008
r ≦ 1	23.40		34.74^**
r ≦ 2	10.29		14.39
r ≦ 3	2.08		1.98
(b) Agricultural futures prices
Lag = 1
r = 0	63.03^**	26 August 2008	69.41^**	26 August 2008
r ≦ 1	27.40^*		31.42^*
r ≦ 2	6.07		8.42
r ≦ 3	2.70		2.07
Lag = 2
r = 0	64.97^**	26 August 2008	71.44^**	26 August 2008
r ≦ 1	28.34^*		32.25^*
r ≦ 2	5.90		8.45
r ≦ 3	2.66		1.99

^* Null hypothesis can be rejected at the 5% significance level.

^** Null hypothesis can be rejected at the 1% significance level.

Notes: I: Equation 5 does not include a linear trend. II: Equation 5 includes a linear trend.

Table 7. VECM results: estimates of α

(a) Precious metal futures prices
Dependent variable	Δgold	Δpalladium	Δplatinum	Δsilver
Lag = 1
e1	−0.0005	0.0079	0.0160	0.0229
	(−0.12)	(1.00)	(1.77)	(3.13)
e2	−0.012	−0.0256	−0.0173	−0.0166
	(−5.04)	(−5.69)	(−3.40)	(−4.02)
Lag = 2
e1	−0.0009	0.0080	0.0156	0.0228
	(−0.20)	(0.95)	(1.63)	(2.93)
e2	−0.0120	−0.0238	−0.0174	−0.0165
	(−5.17)	(−5.72)	(−3.69)	(−4.32)
(b) Agricultural futures prices
Dependent variable	Δcorn	Δsoybean	Δredbean	Δsugar
Lag = 1
e1	−0.0205	−0.0020	−0.0135	−0.0217
	(−7.82)	(−0.82)	(-4.12)	(-8.96)
e2	0.0080	−0.0087	0.0107	0.0150
	(3.14)	(−3.65)	(3.36)	(6.64)
Lag = 2
e1	−0.0219	0.0052	−0.0111	−0.0207
	(−4.30)	(1.92)	(−5.53)	(−8.06)
e2	0.0088	−0.0082	0.0103	0.0160
	(3.46)	(−3.47)	(3.25)	(6.77)

Notes: Estimates of specification II for precious metals futures and those of specification I for agricultural futures prices are presented. The t-values are in parentheses.