DEPENDENCE ANALYSIS OF ETHANOL, SUGAR, OIL, BRL/USD EXCHANGE RATE AND BOVESPA: A VINE COPULA APPROACH

Resende, Anderson Gomes; Candido, Osvaldo

doi:10.1590/1413-8050/ea130174

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Artigos • Econ. Apl. 19 (3) • Jul-Sep 2015 • https://doi.org/10.1590/1413-8050/ea130174 copy

DEPENDENCE ANALYSIS OF ETHANOL, SUGAR, OIL, BRL/USD EXCHANGE RATE AND BOVESPA: A VINE COPULA APPROACH

Authorship SCIMAGO INSTITUTIONS RANKINGS

Abstract

The aim of this study is to assess the dependence relationship of the sugarcane sector (represented by Ethanol and Sugar), Oil, BRL/USD Exchange Rate and Brazilian stock market (represented by the BOVESPA – Bolsa de Valores de São Paulo – Index). Our methodology is based on paircopulas constructions, in which tree specification are compared: Regular Vine, more general, and two particular cases, Canonical vine (C-vine) and Drawable vine (D-vine). Primary results are shown to be aligned with the existing literature but they can change significantly when conditional dependence is taken into account.

Keywords:
Commodities; Biofuels; Multivariate dependence; Regular-vine Copulas

Variable	eth	sug	oil	brus	bov
Mean	0,00090	0,00112	0,00168	0,00018	0,00195
Median	0,00205	0,00110	0,00514	-0,00124	0,00531
Maximum	0,24164	0,13906	0,30305	0,10957	0,16842
Minimum	-0,28174	-0,20151	-0,26199	-0,14157	-0,22324
Standard deviation	0,04414	0,03963	0,05416	0,02309	0,04044
Kurtosis	4,93558	1,89175	3,71946	6,26386	3,19551
Asymmetry	-0,07771	0,00197	-0,19145	0,18459	-0,24927

	eth	sug	oil	brus	bov
Constant	0,000803	0,000517	0,002776	0,000518	0,002102
Constant	(0,6735)	(0,7853)	(0,1408)	(0,749)	(0,1467)
d-ARFIMA	-	-	-	0,134837**	-
d-ARFIMA	-	-	-	(0,0164)	-
AR(1)	0,266403***	0,377456***	-	-0,165821**	-
AR(1)	(0,000)	(0,000)	-	(0,0418)	-
AR(2)	0,100848**	0,131926***	-	-	-
AR(2)	(0,0111)	(0,0047)	-	-	-
AR(3)	-	0,025231	-	-	-
AR(3)	-	(0,5691)	-	-	-
AR(4)	-	-0,083522**	-	-	-
AR(4)	-	(0,0273)	-	-	-
ω	1,111257	1,242364**	1,817989***	0,220073**	0,594516*
ω	(0,3115)	(0,0107)	(0,0023)	(0,0347)	(0,0517)
α_i	0,216009**	0,314442***	0,088228***	0,219238***	0,082946***
α_i	(0,0425)	(0,000)	(0,0003)	(0,0015)	(0,0007)
β_i	0,765395***	0,618541***	0,840578***	0,7572***	0,87977***
β_i	(0,0000)	(0,0000)	(0,0000)	(0,0000)	(0,0000)
ν_i	-	-	9,519557***	5,653420***	10,821089**
ν_i	-	-	(0,0025)	(0,000)	0,0119
λ_i	-	-	-0,250815***	0, 336824***	-0,259935***
λ_i	-	-	(0,0001)	(0,0017)	(0,000)
Q(20)	19,9487	22,0921	17,6624	27,0131	22,0392
Q(20)	(0,3357)	(0,1402)	(0,6096)	(0,1043)	(0,3383)
Q²(20)	15,4504	16,2468	11,474	10,2231	11,68
Q²(20)	(0,6308)	(0,5753)	(0,8731)	(0,9243)	(0,8633)
AIC	-3,755697	-4,050045	-3,196026	-5,145204	-3,732258
KS	0,984228	0,942038	0,701932	0,983834	0,793718
BERK 0,636946	0,968043	0,605615	0,733342	0,458789

		Mixed Vine	R- Mixed VineIndep	R- R-Vine N, t	R-Vine N, t Indep.	Mixed Vine	C- Mixed VineIndep	C- Mixed . Vine	D- Mixed D-Vine Indep.
	# of parameters	13	10	15	11	14	10	14	11
Copula family	Independent-I			-	3	-	3	-	3
	BB8 rotated (90)- BB8_90	1	1	-	-	1	1	1	1
	Survival BB8 - SBB8			-	-	1	-	-	-
	Clayton - C	1	1	-	-	1	2	2	1
	Clayton rotated (270) - C_270			-	-	1	-	-	-
	Frank - F		1	-	-	1	-	1	-
	Gumbel - G	1		-	-	1	-	1	1
	Survival Gumbel - SG	1	1	-	-	-	-	-	-
	Joe - J	-		-	-	-	-	1	-
	Normal - N	1	1	5	3	2	2	1	1
	Student-t - t	2	2	5	4	2	2	3	3

		Mixed Vine	R- Mixed VineIndep	R- R-Vine N, t	R-Vine N, t Indep.	Mixed Vine	C- Mixed Vine Indep	C- Mixed . Vine	D- Mixed D-Vine Indep.
Vuong statistic Bench: Mixed R-Vine	Log-likelihood	370,39	367,42	377,60	374,57	370,71	366,44	383,68	379,73
	No correction	-	1,0272	-1,406	-1,010	-0,097	1,040	-2,443	-1,920
	No correction	-	(0,304)	(0,159)	(0,312)	(0,922)	(0,298)	(0,014)	(0,054)
	Akaike correction	-	-0,0169	-1,163	-1,248	0,307	0,247	-2,303	-2,208
	Akaike correction	-	(0,986)	(0,245)	(0,212)	(0,759)	(0,805)	(0,021)	(0,027)
	Schwarz correction	-	-2,3411	-0,620	-1,776	1,205	-1,518	-1,991	-2,850
	Schwarz correction	-	(0,019)	(0,535)	(0,075)	(0,228)	(0,128)	(0,046)	(0,004)
Vuong statistic Bench: Mixed D-Vine	No correction	2,4434	2,6746	0,7608	1,1093	2,4778	2,8829	-	1,1903
	No correction	(0,014)	(0,007)	(0.446)	(0,267)	(0,013)	(0,003)	-	(0,233)
	Akaike correction	2,3032	2,1496	0,8899	0,7357	2,4778	2,3430	-	0,3200
	Akaike correction	(0,021)	(0,031)	(0,373)	(0,461)	(0,013)	(0,019)	-	(0,748)
	Schwarz correction	1,9911	0,9809	1,1774	-0,0959	2,4778	1,1412	-	-1,6174
	Schwarz correction	(0,046)	(0.326)	(0,239)	(0,923)	(0,013)	(0,253)	-	(0,105)

Tree Pair-copula		Copula	T	Par. 1	Par. 2	XL	XU
1	bov, brus	t	-0,314	-0,474	10,834	-	-
	bov, brus	t		(0,030)	(5,535)	-	-
	oil, brus	N	-0,117	-0,182	-	-	-
	oil, brus	N		(0,034)	-	-	-
	sug, oil	G	0,100	1,112	-	-	0,135
	sug, oil	G	0,100	(0,029)	-	-	0,135
	eth, sug	t	0,341	0,511	10,163	0,083	0,083
	eth, sug	t	0,341	(0,027)	(3,800)	0,083	0,083
2	bov, oil\brus	C	0,088	0,193	-	0,028	-
	bov, oil\brus	C	0,088	(0,055)	-	0,028	-
	brus, sug\oil	t	-0,368	-0,546	9,602	-	-
	brus, sug\oil	t	-0,368	(0,026)	(4,320)	-	-
	oil, eth\sug	J	0,034	1,061	-	-	0,078
	oil, eth\sug	J	0,034	(0,027)	-	-	0,078
3	bov, sug\brus, oil	C	0,044	0,091	-	0,001	0,000
	bov, sug\brus, oil	C	0,044	(0,049)	-	0,001	0,000
	eth, brus\sug, oil	BB8_90	-0,311	-5,802	-0,447	-	-
	eth, brus\sug, oil	BB8_90	-0,311	(3,378)	(0,217)	-	-
4	bov, eth\brus.sug	F	-0,005	-0,048	-	-	-
4	bov, eth\brus.sug	F	-0,005	(0,245)	-	-	-

Tree	Pair-copula	Copula	τ	Par. 1	Par. 2	λ_L	λ_U
1	bov, brus	t	-0,314	-0,474	10,834	-	-
	bov, brus	t	-0,314	(0,030)	(5,401)	-	-
	oil, brus	N	-0,117	-0,182	-	-	-
	oil, brus	N	-0,117	(0,033)	-	-	-
	sug, oil	G	0,100	1,112	-	-	0,135
	sug, oil	G	0,100	(0,029)	-	-
	eth, sug	t	0,341	0,511	10,163	0,083	0,083
	eth, sug	t	0,341	(0,027)	(3,762)
2	bov, oil\brus	C	0,088	0,193	-	0,028	-
	bov, oil\brus	C	0,088	(0,055)	-		-
	brus, sug\oil	t	-0,368	-0,546	9,602	-	-
	brus, sug\oil	t	-0,368	(0,026)	(4,145)	-	-
	oil, eth\sug	I
	oil, eth\sug	I
3	bov, sug\brus, oil	I	-	-	-	-	-
	eth, brus\sug, oil	BB8_90	-0,311	-5,674	-0,457	-	-
	eth, brus\sug, oil	BB8_90	-0,311	(3,258)	(0,212)	-	-
4	bov, eth\brus.sug	I

Tree	Pair-copula	Copula	τ	Par. 1	Par. 2	λ_L	λ_U
1	eth, brus	BB 8_90	-0,421	-4,763	-0,671	-	-
	eth, brus	BB 8_90	-0,421	(1,209)	(0,078)	-	-
	sug, brus	t	-0,379	-0,561	10,817	-	-
	sug, brus	t	-0,379	(0,025)	(10,073)	-	-
	oil, bov	SG	0,131	1,151	- 0,174	-
	oil, bov	SG	0,131	(0,032)		-
	bov, brus	t	-0,314	-0,474	10,834		-
	bov, brus	t	-0,314	(0,030)	(5,358)		-
2	eth, sug\brus	N	0,189	0,293	-	-	-
	eth, sug\brus	N	0,189	(0,035)	-	-	-
	sug, bov\brus	C	0,047	0,098	-	0,001	-
	sug, bov\brus	C	0,047	(0,050)	-	0,001	-
	oil, brus\bov	F	-0,065	-0,587	-	-	-
	oil, brus\bov	F	-0,065	(0,242)	-	-	-
3	eth, bov\sug, brus	F	-0,013	-0,115	-	-	-
	eth, bov\sug, brus	F	-0,013	(0,242)	-	-	-
	sug, oil\bov, brus	G	0,039	1,040	-	-	0.001
	sug, oil\bov, brus	G	0,039	(0,022)	-	-	0.001
4	eth, oil\sug, bov, brus	F	-0,011	-0,098	-	-	-
4	eth, oil\sug, bov, brus	F	-0,011	(0,250)	-	-	-

Tree Pair-copula		Copula	τ	Par. 1	Par. 2	λ_L	λ_U
1	eth, brus	BB8_90	-0,421	-4,763	-0,671	-	-
	eth, brus	BB8_90	-0,421	(1,208)	(0,078)	-	-
	oil,brus	N	-0,117	-0,182
	oil,brus	N	-0,117	(0,037)
	sug,brus	t	-0,379	-0,561	10,817	-	-
	sug,brus	t	-0,379	(0,025)	(8,746)	-	-
	bov, brus	t	-0,314	-0,474	10,834	-	-
	bov, brus	t	-0,314	(0,029)	(6,796)	-	-
2	eth,sug\brus	N	0,189	0,293	-	-	-
	eth,sug\brus	N	0,189	(0,035)	-	-	-
	oil,sug\brus	G	0,042	1,044	-	-	0,06
	oil,sug\brus	G	0,042	(0,024)	-	-	0,06
	bov,sug\brus	C	0,047	0,098	-	-	-
	bov,sug\brus	C	0,047	(0,049)	-	-	-
3	eth,oil\sug,brus	F	-0,014	-0,122	-	-	-
	eth,oil\sug,brus	F	-0,014	(0,248)	-	-	-
	bov,oil\sug,brus	SBB8	0,098	1,335	0,893	-	-
	bov,oil\sug,brus	SBB8	0,098	(0,206)	(0,125)	-	-
4	eth, bov\oil,sug.brus	C _270	-0,010	-0,020	-	-	-
4	eth, bov\oil,sug.brus	C _270	-0,010	(0,039)	-	-	-

Tree Pair-copula		Copula	τ	Par. 1	Par. 2	λ_L	λ_U
1	eth, brus	BB8_90	-0,421	-4,763	-0,671	-	-
	eth, brus	BB8_90	-0,421	(1,208)	(0,078)	-	-
	oil, brus	N	-0,117	-0,182	-	-	-
	oil, brus	N	-0,117	(0,038)	-	-	-
	sug, brus	t	-0,379	-0,561	10,817	-	-
	sug, brus	t	-0,379	(0,025)	(7,132)	-	-
	bov, brus	t	-0,314	-0,474	10,834	-	-
	bov, brus	t	-0,314	(0,029)	(5,924)	-	-
2	eth, sug\brus	N	0,189	0,293	-	-	-
	eth, sug\brus	N		(0,035)		-	-
	oil, sug\brus	I	-	-	-	-	-
	bov, sug\brus	C	0,047	0,098	-	0,001	-
	bov, sug\brus	C		(0,048)	-	0,001	-
3	eth, oil\sug,brus	I	-	-	-	-	-
	bov, oil\sug,brus	C	0,087	0,190	-	0,026	-
	bov, oil\sug,brus	C	0,087	(0,055)	-	0,026	-
4	eth, bov\oil,sug.brus	I	-	-	-	-	-

Tree	Pair-copula	Copula	τ	Par. 1	Par. 2	λ_L	λ_U
1	eth, brus	BB8 90	-0,421	-4,763	-0,671	-	-
	eth, brus	BB8 90	-0,421	(1,209)	(0,078)	-	-
	sug,brus	t	-0,379	-0,561	10,817	-	-
	sug,brus	t	-0,379	(0,025)	(9,033)	-	-
	oil, bov	SG	0,131	1,151	-	0,174	-
	oil, bov			(0,032)
	bov, brus	t	-0,314	-0,474	10,834	-	-
	bov, brus	t		(0,030)	(5,352)	-	-
2	eth,sug\brus	N	0,189	0,293	-	-	-
	eth,sug\brus	N	0,189	(0,035)	-	-	-
	sug,bov\brus	C	0,047	0,098	-	0,001	-
	sug,bov\brus	C	0,047	(0,049)	-	0,001	-
	oil,brus\bov	F	-0,065	-0,587	-	-	-
	oil,brus\bov	F	-0,065	(0,243)	-	-	-
3	eth, bov\sug, brus	I
3	sug,oil\bov, brus	I
4	eth, oil\sug, bov, brus	I

Tree	Pair-copula	Copula	τ	Par. 1	Par. 2	λ_L	λ_U
1	eth, brus	t	-0,399	-0,586	3,943	0,008	0,008
	eth, brus	t	-0,399	(0,027)	(0,714)	0,008	0,008
	sug,brus	t	-0,379	-0,561	10,817	-	-
	sug,brus	t	-0,379	(0,025)	(4,375)	-	-
	oil,bov	t	0,139	0,217	8,626	0,033	0,033
	oil,bov	t	0,139	(0,040)	(3,597)	0,033	0,033
	bov, brus	t	-0,314	-0,474	10,834
	bov, brus	t	-0,314	(0,030)	(5,402)
2	eth, sug\brus	N	0,189	0,292
				(0,034)
	sug, bov\brus	N	0,043	0,068	-	-	-
				(0,039)
	oil, brus\bov	N	-0,060	-0,095	-	-	-
	oil, brus\bov			(0,039)
3	eth, bov\sug, brus	N	-0,002	-0,003	-	-	-
	eth, bov\sug, brus	N	-0,002	(0,039)	-	-	-
	sug, oil\bov, brus	t	0,047	0,073	19,714
	sug, oil\bov, brus	t	0,047	(0,041)	(13,971)
4	eth, oil\sug, bov, brus	N	0,003	0,004	-	-	-
4	eth, oil\sug, bov, brus	N	0,003	(0,039)	-	-	-

Tree	Pair-copula	Copula	τ	Par. 1	Par. 2	λ_L	λ_U
1	eth, brus	t	-0,399	-0,586	3,943	0,008	0,008
	eth, brus	t	-0,399	(0,027)	(0,714)	0,008	0,008
	sug, brus	t	-0,379	-0,561	10,817	-	-
	sug, brus	t	-0,379	(0,025)	(4,661)	-	-
	oil, bov	t	0,139	0,217	8,626	0,033	0,033
	oil, bov	t	0,139	(0,040)	(3,766)	0,033	0,033
	bov, brus	t	-0,314	-0,474	10,834
	bov, brus	t	-0,314	(0,030)	(5,418)
2	eth, sug\brus	N	0,189	0,292	-	-	-
	eth, sug\brus	N	0,189	(0,034)	-	-	-
	sug, bov\brus	N	0,043	0,068	-	-	-
	sug, bov\brus	N	0,043	(0,039)	-	-	-
	oil, brus\bov	N	-0,060	-0,095	'	'	'
	oil, brus\bov	N	-0,060	(0,039)	'	'	'
3	eth, bov\sug, brus	I
3	sug,oil\bov, brus	I
4	eth, oil\sug, bov, brus	I

Tree Pair-copula		Copula	τ	Par. 1	Par. 2	λ_L	λ_U
1	eth, brus	BB8_90	-0,421	-4,763	-0,671	-	-
	eth, brus	BB8_90	-0,421	(1,208)	(0,078)	-	-
	oil, brus	N	-0,117	-0,182	-	-	-
	oil, brus	N	-0,117	(0,038)	-	-	-
	sug, brus	t	-0,379	-0,561	10,817	-	-
	sug, brus	t	-0,379	(0,025)	(7,132)	-	-
	bov, brus	t	-0,314	-0,474	10,834
		t	-0,314	(0,029)	(5,924)
2	eth, sug\brus	N	0,189	0,293	-	-	-
	eth, sug\brus	N	0,189	(0,035)	-	-	-
	oil, sug\brus	I	-	-	-	-	-
	bov, sug\brus	C	0,047	0,098	-	0,001	-
	bov, sug\brus	C	0,047	(0,048)	-	0,001	-
3	eth, oil\sug, brus	I
	bov, oil\sug, brus	C	0,087	0,190		0,026
	bov, oil\sug, brus	C	0,087	(0,055)		0,026
4	eth, bov\oil, sug, brus

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[1] Note:(***), (**), (*) - significant at 1%, 5%, 10% respectively, p-value between brackets. w, a and are the GARCH(1,1) parameters. AIC (Akaike Information criterion). KS (Kolmogorov-Smirnov) and BERK (Berkowitz) are p-value for the uniform distributed test.