Exploring the nexus between oil prices and sectoral stock prices: Nonlinear evidence from Kuwait stock exchange

Figures & data

Table 1. DF-GLS unit root test

Variable	Level	First difference
WTI	−1.58, [0]	−3.64^***, [18]
Brent	−1.82, [0]	−11.26^***, [13]
Banks	−0.95, [25]	−6.8^***, [23]
Basic materials	−0.8, [1]	−11.58^***, [3]
Consumer goods	−012, [12]	−15.13^***, [15]
Consumer services	0.19, [24]	−4.84^***, [23]
Financial services	−0.45, [1]	−24.54^***, [0]
Industrials	−0.24, [25]	−8.15^***, [24]
Oil & gas	−0.52, [0]	−3.59^***, [9]
Real estate	−0.46, [12]	−5.69^***, [23]
Technology	−2.03, [2]	−31.47^***, [0]
Telecommunications	−2.13, [0]	−18.08^***, [1]

Notes: The null hypothesis: has a unit root. The constant and trend terms are included in the test equations and the AIC is used to select the optimal lag order. Numbers in [ ] denote optimal lags. Critical values are: −3.48, −2.89, −2.57 at the 1, 5, and 10% levels respectively from Elliott et al. (1996, Table 1).

^*** Significance at the 1% level.

Table 2. Bounds test for nonlinear cointegration

	F-statistic	Conclusion	F-statistic	Conclusion
Dependent variable	Brent		WTI
Banks	4.42^*	Cointegration	3.44	No cointegration
Basic materials	1.75	No cointegration	0.73	No cointegration
Consumer goods	4.3^*	Cointegration	2.74	No cointegration
Consumer services	6.69^***	Cointegration	6.28^***	Cointegration
Financial services	1.25	No cointegration	0.66	No cointegration
Industrials	5.48^**	Cointegration	4.02^*	Cointegration
Oil & gas	1.78	No cointegration	0.88	No cointegration
Real estate	5.57^**	Cointegration	2.23	No cointegration
Technology	1.49	No cointegration	1.4	No cointegration
Telecommunications	2.53	No cointegration	2.53	No cointegration
	Critical values
Significance	I0 Bound	I1 Bound
10%	3.38	4.02
5%	3.88	4.61
1%	4.99	5.85

Notes: The bounds test includes a linear trend. The bounds test critical values are from Pesaran et al. (2001).

^* Significance at 10% level.

^** Significance at 5% level.

^*** Significance at 1% level.

Table 3. Nonlinear ARDL estimation results (Brent oil price)

Independent variable	Banks		Consumer goods		Consumer services		Industrials		Real estate
	Coefficient	p-value	Coefficient	Coefficient	p-value	Coefficient	Coefficient	p-value	Coefficient	p-value
Constant	0.001084^**	0.0172	0.000763	0.1529	0.001204^***	0.0029	0.000807^**	0.0457	0.000537	0.2841
S(−1)	−0.000328	0.1735	−0.000520	0.1609	−0.000147	0.3724	−0.000174	0.4862	−0.000156	0.6183
$O^{+}$(−1)	−0.000679	0.2916	−0.001636^**	0.0232	−0.001841^**	0.0014	−0.001708^***	0.0024	−0.002059^***	0.0018
$O^{-}$(−1)	−0.001329^**	0.0387	−0.002275^***	0.0021	−0.002300^***	0.0001	−0.002030^***	0.0004	−0.002564^***	0.0002
∆S(−1)	0.087346^***	0.0000	0.064437^***	0.0001	0.167916^***	0.0000	0.194531^***	0.0000	0.191117^***	0.0000
∆S(−2)	−0.035765^**	0.0253	0.018199	0.2561	0.020891	0.1976
∆S(−3)			0.033593^**	0.0357	0.027331^*	0.0875
∆$O^{+}$			0.000669	0.9622
∆$O^{+}$(−1)			0.024682^*	0.0785
∆$O^{+}$(−2)			−0.024426^*	0.0821
∆$O^{-}$									0.014534	0.2276
Diagnostics tests
ECMt−1	−0.000334^***		−0.000543^***		−0.000153^***		−0.000182^***		− 0.00011^***
Adjusted $R^2$	0.011805		0.010554		0.043663		0.044515		0.043347
LM(2)	1.626718		4.575769		0.392729		2.317746		4.660380
JB	2,636.45^***		1,186.49^***		1,447.81^***		1,408.27^***		1,640.86^***

^* Significance at 10% level.

^** Significance at 5% level.

^*** Significance at 1% level.

Table 4. Nonlinear ARDL estimation results (WTI oil price)

Independent variable	Consumer services		Industrials
	Coefficient	p-value	Coefficient	p-value
Constant	0.001905^***	0.0000	0.001425^***	0.0015
S(−1)	0.00	0.9743	0.00	0.8101
$O^{+}$(−1)	−0.001556^**	0.0140	−0.001271^**	0.0432
$O^{-}$(−1)	−0.001753^***	0.0037	−0.001458^**	0.0170
∆S(−1)	0.168873^***	0.0000	0.196715^***	0.0000
∆S(−2)	0.022584	0.1637
∆S(−3)	0.029544^*	0.0647
∆O^+			−0.021036^*	0.0531
∆$O^{-}$	0.012957	0.1731	0.006914	0.4946
∆$O^{+}$(−1)			−0.012177	0.2589
∆$O^{+}$(−2)			0.017932^*	0.0734
∆$O^{-}$(−1)	0.018250^*	0.0576	0.022330^**	0.0290
∆$O^{-}$(−2)	0.020447^**	0.0334
Diagnostics tests
ECMt−1	−0.000008^***		−0.000062^***
Adjusted $R^2$	0.041265		0.044091
LM(2)	0.185249		2.738665
JB	1478.47^***		1387.05^***

^* Significance at 10% level.

^** Significance at 5% level.

^*** Significance at 1% level.

Figure 1a. Brent oil price.

Figure 1b. WTI oil price.

Table 5. Long-run relations

Sector	Brent oil price		WTI oil price
	$O^{+}$	$O^{-}$	$O^{+}$	$O^{-}$
Banks	−2.072 (0.49)	−4.05 (0.302)
Consumer goods	−3.15 (0.308)	−4.38 (0.23)
Consumer services	−12.52 (0.44)	−15.64 (0.40)	−289.22 (0.97)	−325.83 (0.97)
Industrials	−9.8 (0.54)	−11.65 (0.51)	−20.38 (0.82)	−23.37 (0.82)
Real estate	−13.35 (0.65)	−16.63 (0.64)

Note: Numbers in () are p-values.

Table 6. Pairwise Granger causality tests

	$O_t^{+}$ does not Granger cause $S_t$		$S_t$ does not Granger cause $O_t^{+}$		$O_t^{-}$ does not Granger cause $S_t$		$S_t$ does not Granger cause $O_t^{-}$
	F-Statistic	Prob.	F-Statistic	Prob.	F-Statistic	Prob.	F-Statistic	Prob.
Brent oil price
Banks	3.64^**	0.03	5.72^***	0.00	3.53^**	0.03	1.59	0.20
Consumer goods	3.93^**	0.02	4.97^***	0.01	4.53^**	0.03	0.02	0.89
Consumer services	6.81^***	0.00	7.03^***	0.00	6.29^***	0.00	1.64	0.19
Industrials	3.45^**	0.03	6.04^***	0.00	3.26^**	0.04	0.21	0.81
Real Estate	2.58^*	0.08	2.39^*	0.09	2.57^*	0.08	1.37	0.25
WTI oil price
Consumer services	7.27^***	0.00	5.92^***	0.00	7.93^***	0.00	0.63	0.53
Industrials	3.58^**	0.03	3.87^**	0.02	4.75^***	0.01	0.37	0.69

Notes: S_t is sectoral stock market price. $O_t^{+}$ and $O_t^{-}$ are the partial sums of positive and negative changes in oil price.

Lags included in the test are 2.

^* Significance at 10% level.

^** Significance at 5% level.

^*** Significance at 1% level.

Elliott, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64, 813–836.10.2307/2171846

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Pesaran, M., Shin, Y., & Smith, R. (2001). Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics, 16, 289–326.10.1002/(ISSN)1099-1255

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