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

Frontiers of Business Research in China

Table 3 Johansen and Juselius tests for co-integration relation, Jan. 1993–Feb. 2019

Time Series	Lags	Trace Statistics	H ₀	5%C.V	Max Statistics	Rank	5% C.V.
P _t D _t R _t I _t	10 (AIC, HQ, SBIC)	89.898	r = 0^b	47.856	64.999	R = 0^b	27.584
		24.898	r ≤ 1	29.797	17.020	r ≤ 1	21.132
		7.878	r ≤ 2	15.494	7.331	r ≤ 2	14.265
		0.547	r ≤ 3	3.841	0.547	r ≤ 3	3.841

Notes. 10 lags are used in all of the co-integration vectors based on the AIC. H₀ is the null hypothesis in which there exists at most r co-integration vectors in the system. The co-integration tests are done under the assumption of a trend in data and an intercept and trend in the co-integration eq. CV (5%) and CV (1%) are the critical values of the trace statistics and maximum eigenvalue statistics for cointegration tests. ^b indicates significance at the 5% level