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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

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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