A Comparative Study of VaR Estimation for Structured Products

Table 6

The multivariate extension of the Diebold and Mariano [19] test for alternative notes during various periods.

RUD notes			SPO notes			DJQ notes
Explained variables	Constant	P-value	Explained variables	Constant	P-value	Explained variables	Constant	P-value
Panel A: The whole period
Based on AR(1)-GARCH(1,1)			Based on AR(1)-GARCH(1,1)			Based on AR(1)-GARCH(2,1)
Y1	0.001522	.9985	Z1	0.002467	.9445	W1	−0.002134	.9779
Y2	−0.001387	.9828	Z2	−0.003968	.9806	W2	−0.054672	.6081
Y3	−0.002345	.9988	Z3	0.004578	.9562	W3	−0.009875	.9198
						W4	−0.001236	.6804
Based on AR(1)- GARCH(1,4)			Based on AR(1)- GARCH(2,5)			Based on AR(1)-GARCH(2,5)
Y1	0.004587	.9865	Z1	0.001346	.9393	W1	0.007895	.8057
Y2	0.007895	.9828	Z2	0.008795	.9806	W2	0.008875	.6080
Y3	0.003547	.9972	Z3	0.006458	.9606	W3	0.001246	.6638
						W4	0.003746	.8244
Panel B: The low oil price period
Based on AR(1)-GARCH(1,1)			Based on AR(1)-GARCH(1,1)			Based on AR(1)-GARCH(2,1)
Y1	−0.011483	.4723	Z1	−0.036871	.4544	W1	−0.002246	.9776
Y2	−0.022464	.9824	Z2	−0.054692	.3373	W2	−0.007854	.6629
Y3	−0.044785	.9555	Z3	0.001458	.8565	W3	0.001365	.9462
						W4	0.004789	.9498
Based on AR(1)-GARCH(1,4)			Based on AR(1)-GARCH(2,5)			Based on AR(1)-GARCH(2,5)
Y1	−0.001456	.6626	Z1	−0.001648	.8451	W1	0.006591	.9162
Y2	0.008964	.9824	Z2	0.001935	.4916	W2	0.003169	.6629
Y3	−0.003659	.9745	Z3	0.008934	.4916	W3	0.007598	.7091
						W4	0.001564	.7206
Panel C: The high oil price period
Based on AR(1)-GARCH(1,1)			Based on AR(1)-GARCH(1,1)			Based on AR(1)-GARCH(2,1)
Y1	−0.004136	.7441	Z1	−0.002156	.8925	W1	−0.006647	.1296
Y2	−0.002159	.9668	Z2	0.001489	.9104	W2	−0.009917	.0219*
Y3	0.007845	.9871	Z3	−0.007156	.9825	W3	0.007814	.9757
						W4	−0.001398	.9188
Based on AR(1)-GARCH(1,4)			Based on AR(1)- GARCH(2,5)			Based on AR(1)-GARCH(2,5)
Y1	−0.009551	.7531	Z1	−0.002346	.8344	W1	0.001754	.1854
Y2	0.007415	.9668	Z2	−0.002805	.9104	W2	0.004879	.0219*
Y3	0.001365	.9656	Z3	−0.003224	.9099	W3	0.003456	.2122
						W4	0.003099	.2978

Note that Y1 and Y3 stand for the differences of the sum of squared errors (SSEs) of volatility in GARCH from AR(1)-ARCH(5) and AR(1)-EGARCH(1,1), respectively. Y2 denotes the differences of SSE of volatility in AR(1)-GARCH(1,1) from AR(1)-GARCH(1,4) as the benchmark is AR(1)-GARCH(1,1). Conversely, when the benchmark is AR(1)-GARCH(1,4),Y2 represents the differences of SSE of volatility in AR(1)-GARCH(1,4) from AR(1)-GARCH(1,1). Z1 and Z3 stand for the differences of SSE of volatility in AR(1)-GARCH from AR(1)-ARCH(5) and AR(1)-EGARCH(1,1), respectively. Z2 denotes the differences of SSE of volatility in AR(1)-GARCH(1,1) from GARCH(2,5) as the benchmark is GARCH(1,1). Conversely, when the benchmark is GARCH(2,5), Y2 represents the differences of SSE of volatility in AR(1)-GARCH(2,5) from AR(1)-GARCH(1,1).W1, W3, and W4 stand for the differences of the sum of SSE of volatility in AR(1)-GARCH from AR(1)-ARCH(5), AR(1)-EGARCH(2,1), and AR(1)-EGARCH(2,2), respectively. W2 denotes the differences of SSE of volatility in AR(1)-GARCH(2,1) from AR(1)-GARCH(2,5) as the benchmark is AR(1)-GARCH(2,1). Conversely, when the benchmark is AR(1)-GARCH(2,5), Y2 represents the differences of SSE of volatility in AR(1)-GARCH(2,5) from AR(1)-GARCH(2,1).The symbol ∗ denotes significance at 5 percent level.