The Wiley Finance Series : Handbook of News Analytics in Finance

Diagonal VECH

Mean equations: r 1 t¼r 1 t 1 þ 1 þ" 1 t; ð 12 : 5 Þ

r 2 t¼r 2 t 1 þ 2 þ" 2 t; ð 12 : 6 Þ

Variance equations: ^211 t¼! 11 þ 11 "^21 t 1 þ 11 ^211 t 1 þ 11 Nt; ð 12 : 7 Þ

^222 t¼! 22 þ 22 "^22 t 1 þ 22 ^222 t 1 þ 22 Nt; ð 12 : 8 Þ

Covariance equation: ^212 t¼! 12 þ 12 " 1 t 1 " 2 t 1 þ 12 ^212 t 1 þ 12 Nt; ð 12 : 9 Þ

Diagonal BEKK

Mean equations: r 1 t¼r 1 t 1 þ 1 þ" 1 t and r 2 t¼r 2 t 1 þ 2 þ" 2 t;

Variance equations: ^211 t¼! 11 þ 211 "^21 t 1 þ 211 ^211 t 1 þ 11 Nt; ð 12 : 10 Þ

^222 t¼! 22 þ 222 "^22 t 1 þ 222 ^222 t 1 þ 22 Nt; ð 12 : 11 Þ

Covariance equation: ^212 t¼! 12 þ 1122 " 1 t 1 " 2 t 1 þ 1122 ^212 t 1 þ 12 Nt; ð 12 : 12 Þ

in whichr 1 tandr 2 tare seasonally adjusted returns of the S&P/ASX 200 Index and the
SPI 200 Futures Index at thetth interval, and^21 tand^22 tare conditional variances of the
error process" 1 tand" 2 t, respectively.

12.B References

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