Volatility integration of crude oil, gold, and interest rates on the exchange rate: DCC GARCH and BEKK GARCH applications

Figures & data

Table 1. Variable description

Name	Description
Crude	Logarithmic value of Brent Crude Oil Spot Price
Gold	Logarithmic value of Gold Spot Price
Yield	Logarithmic 5-year bond yield (India)
USD/INR	USD/INR Currency Spot Price

Table 2. Correlation matrix

	5 Jan 2000 to 30 Dec 2022
	Crude	Gold	Yield	USD/INR
Crude	1.0000
Gold	0.0645	1.0000
Yield	0.0469	0.0106	1.0000
USD/INR	0.0079	−0.1165	0.0667	1.0000

Note: Correlation coefficients among Crude, Gold, Yield and USD/INR. * signifies correlation coefficient having significant p-value at 5%.

Table 3. Descriptive Statistics

	Jan 2000 to Dec 2022
	Crude	Gold	Yield	USD/INR
Mean	0.013	0.038	−0.015	0.011
Maximum	37.474	10.452	11.808	3.694
Minimum	−29.444	−9.730	−10.831	−3.550
Standard Deviation	2.851	1.133	0.887	0.425
Skewness	−0.322	−0.306	0.609	0.155
Kurtosis	24.312	9.303	29.980	11.236
Jarque-Bera	93748.480***	8269.625***	150414.500***	14006.210***
Observations	4949	4949	4949	4949
ARCH	328.142***	38.836***	110.872***	494.490***
Unit Root Tests
Augmented Dickey—Fuller	−19.995***	−16.436***	−17.055***	−19.402***
Phillips—Perron	−74.200***	−72.506***	−69.273***	−71.327***

Note: ***, **, * denotes the significance level at p-values of 1%, 5% and 10%, respectively. Unit Root Test is used considering constraint and trend having log return values of the timeseries variables. ARCH test signifies the autocorrelation of the heteroskedasticity in the data at 1 lag.

Table 4. Bivariate BEKK GARCH (1,1) estimation

	Crude (1) Yield (2)	Gold (1) Yield (2)	Crude (1) USD/INR (2)	Gold (1) USD/INR (2)	Yield (1) USD/INR (2)
Variance Equation:
X 11	0.346***	0.121***	0.323***	0.114***	0.098***
X 21	−0.005	0.007	0.002	0.002	0.001
X 22	0.099***	0.102***	−0.011***	−0.012***	0.012***
R 11	0.255***	0.188***	0.231***	0.185***	0.333***
R 12	−0.003	0.005	−0.001	−0.002	0.001
R 21	0.032	0.016	0.028	0.010	0.011
R 22	0.340***	0.362***	0.342***	0.356***	0.365***
P 11	0.965***	0.980***	0.966***	0.978***	0.944***
P 12	0.001	−0.001	0.000	−0.001	−0.001
P 21	−0.007	−0.005	−0.006	−0.005	−0.002
P 22	0.934***	0.930***	0.948***	0.945***	0.955***
Shape (t degrees)	3.917***	3.604***	5.093***	4.756***	3.273***
Model Diagnostics:
AIC	6.325	4.700	4.930	3.273	10.278
Log Likelihood	−15636.387	−11616.623	−12184.404	−8084.219	−1322.167

Note: AIC refers to Akaike Information Criterion. ***, **, * denotes the significance level at 1%, 5% and 10%, respectively.

Table 5. Bivariate DCC GARCH (1,1) estimation

	Crude (1) Yield (2)	Gold (1) Yield (2)	Crude (1) USD/INR (2)	Gold (1) USD/INR (2)	Yield (1) USD/INR (2)
Variance Equation:
X (1)	0.1227***	0.0187***	0.1032***	0.0156***	0.0097***
X (2)	0.0100***	0.0098***	0.0001**	0.0001**	0.0001**
R (1)	0.0908***	0.0564***	0.0787***	0.0492***	0.1464***
R (2)	0.1354***	0.1416***	0.1368***	0.1419***	0.1791***
P (1)	0.9112***	0.9431***	0.9114***	0.9418***	0.8628***
P (2)	0.8556***	0.8585***	0.8828***	0.8820***	0.8815***
DCC (A)	0.0130*	0.0047***	0.0035	0.0102***	0.0261***
DCC (B)	0.5318***	0.2248	0.6990***	0.9882***	0.9401***
Shape(t degrees)	3.9733***	3.6354	5.2902***	4.7945***	3.3878***
Model Diagnostics:
AIC	6.307	4.685	4.900	3.258	2.266
Log Likelihood	−15596.782	−11581.779	−12113.487	−8050.642	−5595.201

Note: AIC refers to Akaike Information Criterion. ***, **, * denotes the significance level at 1%, 5% and 10%, respectively.

Figure 1. Conditional correlation.

Table 6. Granger Causality Test

Alternate Hypothesis	5 Jan 2000 to 30 Dec 2022
	P-value
Crude oil price has forecasting ability (causal effect) for ER.	0.056*
Gold has forecasting ability (causal effect) for ER.	0.078*
Yield has forecasting ability (causal effect) for ER.	0.003***
ER has forecasting ability (causal effect) for crude oil.	0.067*
ER has forecasting ability (causal effect) for Gold.	0.068*
ER has forecasting ability (causal effect) for Yield.	0.015**
Crude oil price has forecasting ability (causal effect) for Yield.	0.012**
Yield has forecasting ability (causal effect) for Crude oil.	0.079*
Gold has forecasting ability (causal effect) on Yield.	0.086*
Yield has forecasting ability (causal effect) for Gold.	0.062*

Note: Crude, Gold, Yield, and USD/INR (exchange rate [ER]) are the timeseries variables for “Granger Causality Test”. (Y) and (X) represent the dependent variable and the independent variable of timeseries. *, **, and *** signify significant p-value at 10%, 5%, and 1%. For lag structure, lag length 1 is taken as suitable for the timeseries.

Table A1. Some important researches in literature

Authors	(Year)	Variables Studied	Country Studied	Period of the Study	Methodology Used	Key Findings
Akram, Q. F.	(2004)	Oil, Norwegian exchange rate	Norway	1998–2000 (quarterly)	Linear and Non-linear root mean square forecasts error (RMSE)	Inverse relationship between oil prices and the value of the Norwegian exchange rate.
Albuquerque, R., Loayza, N., & Servén, L.	(2005)	FDI impacted by factors like Taxes, Wage Rates, and Tariffs, etc.	Worldwide	1985–1999	equilibrium model	Globalisation measure complements with capital market liberalisation measures, thus worldwide sources of risk present due to increased market integration.
Arfaoui, M., & Ben Rejeb, A.	(2017)	oil, gold, US dollar and stock prices	Worldwide	1995–2015	simultaneous equations system	Negative linkages between oil and stock prices, but oil is positively affected by USD and gold. The US dollar is negatively impacted by the stock market and positively by gold and oil price.
Bahmani-Oskooee, M., & Mitra, R.	(2008)	exchange rate, trade data	USA and India	1962–2004	cointegration and error-correction modeling	Exchange rate volatility impacts 40% of industries in the short run.
Baur, D. G., & Lucey, B. M.	(2010)	gold, stock, bond	USA, UK, Germany	1995–2005	Asymmetric GARCH	Investors who invest in gold as a hedge after/during a major negative shock/event for more than 15 trading days lose money.
Kanjilal, K., & Ghosh, S.	(2017)	crude oil and gold	Worldwide	2009–2015	threshold vector error-correction model	Relationship between gold and oil price is non-linear and asymmetric.
Singhal, S., & Ghosh, S.	(2016)	oil and stock prices	India	2006–2015	VAR-DCC-GARCH	No volatility spillover from crude oil to the Indian stock market at the aggregate level; however, volatility spillover is seen from crude oil to auto, power and finance indices.
Berdiev, A. N., Kim, Y., & Chang, C. P.	(2012)	exchange rate, forex reserves	Worldwide	1974–2004	Multinomial logistic regression	Government ideology, political institutions and globalisation are important determinants for chosing exchange rate regime.
Capie, F., Mills, T. C., & Wood, G.	(2005)	gold and exchange rate	UK	1971–2004	TGARCH, EGARCH	A negative, typically inelastic, relationship exists between gold and these exchange rates. The strength of this relationship has shifted over time.
Chang, H. F., Huang, L. C., & Chin, M. C.	(2013)	oil, gold, and exchange rate	Taiwan	2007–2011	VAR model, Granger causality	The oil price, gold price and exchange rate remain largely independent from one another
Ciner, C., Gurdgiev, C., & Lucey, B. M.	(2013)	Stocks, Bonds, Gold, Oil and Exchange Rates	US, UK	1990–2010	quantile regression	Gold can be regarded as a safe haven against exchange rates in both countries, highlighting its monetary asset role
Du, X., Cindy, L. Y., & Hayes, D. J.	(2011)	Crude oil, corn and wheat prices	USA	1998–2009	Bayesian inference using Gibbs Sampling	Volatility spillover among crude oil, corn, and wheat markets after the fall of 2006
Muzaffar Asad, Mosab I. Tabash, Umaid A. Sheikh, Mesfer Mubarak Al- Muhanadi & Zahid Ahmad	(2021)	Gold-oil-exchange rate volatility, Bombay stock exchange	India	2003–2020	NARDL Model	Gold prices, oil prices, and currency values have an asymmetrical association with Bombay stock indexes as positive shocks to these variables have no impact on stock index.
Umaid A Sheikh, Muzaffar Asad, Zahid Ahmed, Umer Mukhtar	(2020)	oil prices, gold prices, exchange rate, and stock prices	Pakistan	2004–2018	ARDL Model	Mixed outcomes are observed between the variables.
Umaid A Sheikh, Muzaffar Asad, Aqeel Israr, Mosab I Tabash, Zahid Ahmed	(2020)	money supply, interest rates, consumer price index, terroristic disruptions, and Karachi stock exchange	Pakistan	2002–2015	ARDL model	All variables have significant impact on stock exchange.
Umair Saeed Bhutta, Aws AlHares, Yasir Shahab, Adeel Tariq	(2022)	real earnings management on investment inefficiency	Pakistan	2008–2018	Panel Data Analysis	Real earnings increase investment inefficiency
Suresh Kumar, Ankit Kumar, Gurcharan Singh	(2023)	crude oil, gold, exchange rate, and Indian stock market	India	1994–2019	NARDL model	crude oil has positive effect, exchange rate has negative effect, and Gold has no effect on stock market.