Time-frequency analysis of financial stress and global commodities prices: Insights from wavelet-based approaches

Figures & data

Table 1. Descriptive statistics

Full sample	NFCI	STLF13	Oil	Gold	Silver	Cocoa
µ	−0.3582	0.0561	0.0003	−0.0002	−0.0006	−0.0006
σ	0.5955	1.1907	0.0404	0.0030	0.0148	0.0239
S	3.0740	3.5167	27.1929	−0.0191	0.6526	−40.8723
K	13.5356	20.0540	1085.91	7.1827	7.2057	1711.46
JB	11135	25,466	8797	1309	1451	219,000
P	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
Pre-GFC
µ	−0.4072	−0.0337	0.0003	−0.0002	−0.0005	−0.0006
Σ	0.4885	0.9828	0.0406	0.0029	0.0148	0.0241
S	3.3045	3.6110	27.2514	−0.0386	0.6645	−40.5275
K	17.0765	24.3657	1081.46	7.1702	7.3244	1680.5
JB	17724	37,280	85,462,722	1275	1500	20,700
P	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
GFC
µ	1.9714	1.5100	1.7211	2.9362	1.1166	3.3910
Σ	0.5766	0.1300	0.1256	0.0348	0.0435	0.0339
S	−0.2562	0.5700	0.8685	−0.6685	−0.6089	−1.0944
K	2.1469	1.7700	3.2492	2.3967	2.6367	3.2363
JB	1.5269	1.1700	4.7478	3.3172	2.4899	7.4726
P	0.4661	0.5600	0.0931	0.1904	0.2880	0.0238
Post-GFC
µ	−0.444	−0.202	0.001	0.000	0.000	0.000
σ	0.251	0.633	0.064	0.002	0.011	0.003
S	1.861	3.673	18.666	0.669	1.820	0.470
K	7.775	29.906	472.281	6.554	19.886	9.180
JB	1000	21,231	6,048,322	394	8144	1067
P	0.000	0.000	0.000	0.000	0.000	0.000

Notes: µ = mean; σ = standard deviation; S = skewness; K = kurtosis; JB = Jarque-Bera, P = JB probability; NFCI = Chicago Fed National Condition Index; STLF13 = Federal Reserve of Bank of St. Louis Fed Financial Stress.

Figure 1. Time series plot of commodity prices of cocoa, gold, oil and silver and St. Louis Fed Financial Stress (STLF13) and Chicago Fed National Condition Index (NFCI).

Figure 2. Wavelet coherence of NFCI and global commodities prices.

Figure 3. Wavelet coherence of STLF13 and global commodities prices. Panel A) Full sample, Panel B) Pre-GFC, Panel C) GFC, Panel D) Post-GFC.

Figure 4. Wavelet bivariate correlation matrix. Panel A: Full sample, Panel B: Pre-GFC, Panel C: GFC, Panel D: Post-GFC.

Notes: C1 = NFCI, C2 = STFL13, C3 = oil, C4 = gold, C5 = silver, and C6 = cocoa.

Figure 5. Multiple wavelet correlations between FSI and global commodities prices. Panel A: Full sample, Panel B: Pre-GFCPanel C: GFC, Panel D: Post-GFC.

Notes: U = upper bound; L = lower bound (95% confidence interval).

Figure 6. Multiple cross-correlations of wavelets.

Notes: The lag represents the localization which indicates the time lead/lag at which the strongest correlation values are localized.

Table A1. Wavelet multiple correlations

	Full Sample			Pre-GFC			GFC			Post-GFC
Scale	Lower	WMC	Upper	Lower	WMC	Upper	Lower	WMC	Upper	Lower	WMC	Upper
1	0.6341	0.6651	0.6941	0.6780	0.7104	0.7401	0.5389	0.8036	0.9239	0.4090	0.4955	0.5732
2	0.4075	0.4690	0.5263	0.5075	0.5704	0.6272	0.5489	0.8890	0.9766	0.3475	0.4758	0.5867
3	0.6371	0.6969	0.7484	0.6173	0.6893	0.7498	–	–	–	0.6951	0.7931	0.8622
4	0.8272	0.8699	0.9026	0.7937	0.8513	0.8938	–	–	–	0.8667	0.9277	0.9614
5	0.8858	0.9248	0.9508	0.8489	0.9069	0.9433	–	–	–	0.6496	0.8483	0.9385
6	0.9023	0.9471	0.9716	0.8518	0.9275	0.9652	–	–	–	0.9046	0.9775	0.9948
7	0.9449	0.9783	0.9916	0.9669	0.9892	0.9965	–	–	–	–	–	–

Table A2. Wavelet multiple cross-correlations

	Full Sample			Pre-GFC			GFC			Post-GFC
Scale	WMCC	Lags	Lead/lag variable	WMCC	Lags	Lead/lag variable	WMCC	Lags	Lead/lag variable	WMCC	Lags	Lead/lag variable
1	0.6651	0	NFCI	0.7104	0	NFCI	0.8036	0	STLF13	0.4955	0	STLF13
2	0.4763	−2	COCOA	0.5786	−2	COCOA	0.9964	5	SILVER	0.5545	−5	STLF13
3	0.6969	0	NFCI	0.6893	0	NFCI	–	–	–	0.7931	0	STLF13
4	0.9173	1	NFCI	0.8994	1	NFCI	–	–	–	0.9498	1	NFCI
5	0.9513	2	NFCI	0.9362	2	NFCI	–	–	–	0.8489	−1	STLF13
6	0.9670	4	NFCI	0.9501	4	NFCI	–	–	–	0.9894	−3	STLF13
7	0.9890	7	NFCI	0.9916	4	NFCI	–	–	–	–	–	–