Time of COVID-19: stability analysis of stocks, exchange rates, minerals and metals markets

Figures & data

Table 1. Descriptive statistics of returns.

	Stock indices				Exchange rates
	S&P 500	NASDAQ		Dow Jones	USD/EURO	USD/JPY		USD/CAD	USD/GBP			USD/CHF
Mean	0.007	0.001		0.0004	−0.00012	−8.16E-05		−8.22E-05	−8.23E-05			−0.00020
Maximum	0.093	0.09266		0.1081	0.02064	0.0315		0.02057	0.03761			0.0183
Minimum	−0.11	−0.1148		−0.1195	−0.0144	−0.0284		−0.0188	−0.0269			−0.0142
SD	0.01583	0.0170		0.01665	0.0039	0.0046		0.0043	0.0059			0.0040
Skew.	−1.1901	−0.8944		−1.1054	0.2082	0.7413		0.4167	0.2394			0.0985
Kurtosis	18.0577	12.6644		19.2358	5.3137	15.103		6.326	7.3689			5.0174
JB	5180.58**	2153.38**		5985.05**	121.82**	3277.11**		259.09**	425.77**			90.56**
	Minerals				Precious metals
	Oil		Gas	Coal	Gold	Silver	Platinum
Mean	0.0012		−0.0002	−0.0005	0.0005	0.0009	0.0006
Maximum	0.3196		0.1980	0.0547	0.0561	0.0890	0.0993
Minimum	−0.2822		−0.1098	−0.1223	−0.0511	−0.1235	−0.1361
SD	0.0434		0.0342	0.0129	0.0123	0.0237	0.0211
Skew.	0.2398		0.6828	−1.2668	−0.1097	−0.7962	−0.6891
Kurtosis	22.817		6.8696	18.2576	7.765	8.681	9.945
JB	8530.71**		366.938**	5212.862**	513.774**	786.145**	1132.20**

Note: JB = Jarque–Bera normality statistic, SD = standard deviation, Skew. = Skewness, * = rejection of null hypothesis at 10 percent, ** = at 5 percent, *** = at 1 percent.

Source: authors’ calculation.

Table 2. Unit root test with structural break.

Stock indices				Exchange rates
	S&P 500	NASDAQ	Dow Jones	USD/EURO	USD/JPY	USD/CAD	USD/GBP	USD/CHF
ADF statistic	−20.255**	−19.649**	−20.6757**	−22.028**	−27.331**	−24.92**	−21.796**	−21.944**
Break date	24/2/2020	21/2/2020	31/1/2020	19/3/2020	9/3/2020	18/3/2020	18/3/2020	19/3/2020
	Minerals			Precious metals
	Oil	Gas	Coal	Gold	Platinum	Silver
ADF statistic	−22.5805**	−23.085**	−22.2685**	−25.11**	−23.46**	−25.54**
Break date	30/4/2020	23/9/2020	29/1/2021	24/3/2020	24/3/2020	16/3/2020

Note: ** represents rejection of null hypothesis against critical value -5.72 at 1% level of significance.

Source: authors’ calculation.

Table 3. Markov switching model for stock indices.

Dependent variable	S&P 500		NASDAQ		Dow Jones
Frequency	Daily		Daily		Daily
AR(1) term	No		No		No
Stress period	LOW	HIGH	LOW	HIGH	LOW	HIGH
Constant	8.63e-06		0.00033 0.0044		−0.00013
Standard deviation	0.0015	0.0041			0.0019	0.0037
S&P 500			2.5802***	2.0121***	1.1706***	1.4673***
			(0.1996)	(0.0679)	(0.0305)	(0.0433)
NASDAQ	0.3280***	0.2402***			−0.2249***	−0.3979***
	(0.0091)	(0.0476)			(0.0271)	(0.0411)
Dow Jones	0.6243***	0.7258***	−2.004***	−0.9342***
	(0.0114)	(0.0440)	(0.1897)	(0.06640)
Transition probability
P11	0.9902		0.4770		0.9344
P22		0.924		0.9519		0.8722
Expected duration	101.87	13.15	1.912	20.78	15.26	7.82
Log likelihood	2645.4481		2109.6525		2434.6383
Number of observations	535		535		535

Note: *p < 0.10, ** p < 0.05, *** p < 0.01.

Source: authors’ calculation.

Table 4. Markov switching model for exchange rates.

Dependent variable	USD/EURO		USD/JPY		USD/CAD		USD/GBP		USD/CHF
Frequency	Daily		Daily		Daily		Daily		Daily
AR(1) term	No		No		No		No		No
Stress period	Low	High	Low	High	Low	High	Low	High	Low	High
Constant	0.00006 0.00192		0.00009		−0.0001				−0.0001
Standard deviation			0.0023	0.0040	0.0019	0.0035	0.0018	0.0055	0.0019
USD/EURO			−0.2133**	0.2440	−0.5445***	0.6606***	0.6442***	0.4785***	0.7649***	0.6984***
			(0.0717)	(0.1733)	(0.1278)	(0.0995)	(0.0905)	(0.1567)	(0.0452)	(0.0656)
USD/JPY	−0.05963*	0.04935			−0.5506***	−0.1246**	0.3705***	0.3274***	0.0647*	0.4807***
	(0.0321)	(0.0425)			(0.0492)	(0.0578)	(0.0710)	(0.0851)	(0.0336)	(0.0482)
USD/CAD	0.1723***	0.0817*	0.0385	−0.7925***			0.1462**	0.7037***	−0.0436	−0.0066
	(0.02891)	(0.0441)	(0.0402)	(0.0916)			(0.0630)	(0.0893)	(0.0349)	(0.5901)
USD/GBP	0.1202***	−0.0381	0.0323	0.4026***	0.2467***	0.1171***			0.0455	−0.0448
	(0.0206)	(0.0412)	(0.0303)	(0.0721)	(0.0516)	(0.0403)			(0.0284)	(0.0382)
USD/CHF	0.6325***	0.9905***	0.4927***	0.7825***	0.5889***	−0.2885***	−0.1534	−0.0726
	(0.0332)	(0.0621)	(0.0632)	(0.1663)	(0.1368)	(0.1022)	(0.0934)	(0.1567)
Transition probability
P11	0.9974		0.9105		0.1129		0.4949		0.9786
P22		0.9804		0.7096		0.6751		0.6588		0.9734
Expected duration	382.48	51.13	11.18	3.44	1.13	3.04	1.98	2.93	46.78	37.53
Log likelihood	2551.8681		2336.1463		2263.0833		2134.2037		2538.779
Number of observations	535		535		535		529		529

Note: * p < 0.10, ** p < 0.05, ***p < 0.01.

Source: authors’ calculation.

Table 5. Markov switching model for minerals.

Dependent variable	Oil		Coal		Gas
Frequency	Daily		Daily		Daily
AR(1) term	No		Yes		No
Stress period	Low	High	Low	High	Low	High
Constant	0.00096 0.0091		−0.0005		−0.0013
Standard deviation	0.0195	0.1078	0.0103 0.0423		0.0215	0.0508
Oil			0.0442***	−0.1148	0.2151***	0.0309
			(0.0108)	(0.3605)	(0.0396)	(0.0739)
Coal	0.2409***	2.4553*			0.2761**	−0.6616**
	(0.0697)	(1.2590)			(0.1141)	(0.3317)
Gas	0.7017**	0.4862	0.0071 (0.0138)
	(0.2829)	(0.3222)
Transition probability
P11	0.9890		0.9863		0.9432
P22		0.9572		0.6401		0.8680
Expected duration	91.28	11.70	78.82	2.78	17.61	7.58
Log likelihood	1180.8483		1597.3897		1083.9245
Number of observations	523		522		523

Note: *p < 0.10, ** p < 0.05, *** p < 0.01.

Source: authors’ calculation.

Table 6. Markov switching model for metals.

Dependent variable	Gold		Platinum		Silver
Frequency	Daily		Daily		Daily
AR(1) term	No		No		No
Stress period	Low	High	Low	High	Low	High
Constant	0.00023		0.001238		−0.00035
Standard deviation	0.0040	0.0101	0.01386 0.03736		0.0061	0.0199
Gold			−0.1470	0.5846	0.9888***	1.4982***
			(0.9060)	(0.4996)	(0.0387)	(0.1377)
Platinum	0.0058	0.2402***			0.1934***	0.5187***
	(0.0176)	(0.0476)			(0.0230)	(0.0755)
Silver	0.2446***	0.7258***	0.5276***	0.6606
	(0.01780)	(0.0440)	(0.0488)	(0.2473)
Transition probability
P11	0.8046		0.9872		0.9316
P22		0.6522		0.7287		0.8511
Expected duration	5.12	2.88	78.11	4.60	14.62	6.71
Log likelihood	1947.682		1498.694		1715.3408
Number of observations	542		542		542

Note: * p < 0.10, ** p < 0.05, *** p < 0.01.

Source: authors’ calculation.

Figure 1. Bartlett Periodogram white noise test results for selected series.

Source: authors’ calculation.

Figure A1. Scatter plot of model standardised residuals.

Note: *** indicates the rejection of null hypothesis that residuals extracted are white noise.

Table A1. Daily returns series name.

Stock indices	Exchange rates	Minerals	Precious metal
S&P 500 Futures	US Dollar Euro	Crude Oil WTI Futures	Gold Futures
NASDAQ Futures	US Dollar Japanese Yen	Natural Gas Futures	Silver Futures
Dow Jones Futures	US Dollar Canadian Dollar	Newcastle Coal Futures	Platinum Futures
	US Dollar British Pound
	US Dollar Swiss Franc

Source: https://www.investing.com/.