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Table 4 Granger causality tests under asymmetric VECM

From: Intrinsic bubbles and Granger causality in the Hong Kong residential property market

Period Bubble Null hypothesis Chi 2 Sig
1993–2019 Yes H0 : γp = 0and \( {\alpha}_{21}={\alpha}_{22}=\dots ={\alpha}_{2{k}_2} \) =0. 10.34355 0.4109
H0 : γd = 0 and \( {\beta}_{11}={\beta}_{12}=\dots ={\beta}_{1{k}_4}=0 \). 127.1764 0.0000a
  1. Notes. \( {H}_0:{\gamma}_p={\alpha}_{21}={\alpha}_{22}=\dots {\alpha}_{2{k}_2}=0 \) tests the joint null hypothesis of no causality from long-run deviation effect and lagged changes in the rental price index to changes in the property price index returns. Chi2 test is for joint test
  2. \( {H}_0:{\gamma}_d={\beta}_{11}={\beta}_{12}=\dots {\beta}_{1{k}_4}=0 \) tests the joint null hypothesis of no causality from long-run deviation effect and lagged changes in the property price index returns to changes in the rental price index returns. Chi2 test is for joint test. a indicates statistical significance at the 0.01 level