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Table 8 Estimated result of GARCH (1,1) Model

From: The volatility of returns from commodity futures: evidence from India

Commodity futures→ Mentha oil Crude Oil Gold
Contract types → Next
Near
Far Near Next
Near
Far Near Next
Near
Far
Co-efficients↓
Mean
μ (constant) −4.30E − 05c −0.002299b 8.02E-05c 0.000215c -0.00044c 0.000251c 0.000436c −5.84E − 05b
Variance
 ω (constant) 5.01E − 06b 0.000315b 2.34E-06b 1.72E-06b 5.14E-05b 1.60E-06b 1.35E-06b 4.82E-06b
 α (arch effect) 0.099648b -0.003595b 0.032133b 0.030668b -0.00364b 0.071647b 0.084121b 0.217631b
 β (garch effect) 0.891336b 0.856938b 0.960178b 0.962725b 0.9111b 0.917732b 0.903237b 0.775297b
 α + β 0.990984 0.853343 0.992311 0.993393 0.90746 0.989379 0.987358 0.992928
 Log likelihood 5376.339 3241.84 5582.369 5772.936 4778.326 4315.175 3862.321 4295.068
 Akaike info. Criterion (AIC) −5.384801 −3.307962 −5.30673 −5.464648 −4.6343 −6.45236 −6.75537 −6.61537
 Schwarz info. Criterion (SIC) −5.370770 −3.293707 −5.29329 −5.451254 −4.62063 −6.43291 −6.73330 −6.59545
Residual Diagnostics for GARCH (1, 1):ARCH-LM (1) test for heteroskedasticity
 Obsa R-squared 1.204135 0.025106 0.264945 0.057879 0.003309 2.001935 0.12552 0.617633
 Prob. Chi-Square(1) 0.2725 0.8741 0.6067 0.8099 0.9541 0.1571 0.7231 0.4319
Wald Test
 F-statistic 1433.702 1191.443 1497.929 1524.253 2935.317 10.09822 9.188416 3.26E-34a
 Probability 0.000 0.000 0.000 0.000 0.000 0.0015 0.0025 1.000
  1. Note: For Wald test the null hypothesis is α + β = 1
  2. aSignificant at 1% level, b Significant at 5% level, c Significant at 10% level