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Table 3 Diagnostic tests for the residuals of the VAR model (1995 to 2005) and VAR-BEKK model (2006 to 2015)

From: An analysis of price and volatility transmission in butter, palm oil and crude oil markets

  1995–2005 (monthly) VAR model
Statistic EU butter Oceania butter Crude palm oil Crude oil Brent
Ljung-Box test 7.77*** 4.69*** 14.36*** 8.67***
Ljung-Box test squared returns 10.55*** 6.53*** 15.76*** 16.76**
Engle test 7.87*** 11.46*** 13.84*** 16.27**
  Multivariate tests
Hosking test     146.29***
Hosking test squared returns     996.09***
Lagrange multiplier test     1107.5*
  2006–2015 (biweekly) VAR-BEKK model
Statistic EU butter Oceania butter Crude palm oil Crude oil Brent
Ljung-Box test 11.80*** 16.49** 8.29*** 5.80***
Ljung-Box test squared returns 5.49*** 13.95*** 10.51*** 10.03***
Engle test 5.03*** 12.34*** 10.20*** 9.54***
  Multivariate tests
Hosking test     171.93***
Hosking test squared returns     1039.2***
Lagrange multiplier test     1030.7***
  1. The symbols *, ** and *** denote acceptance of the null hypothesis at the 1, 5 and 10 % confidence level, respectively, for the residual diagnostic tests. The residual diagnostic tests were performed with 10 lags