Nonparametric cointegration analysis

Table A.9: Johansen’s test results for the number (r) of cointegrating vectors: intercept and
time trend present, with cointegration restrictions on the trend parameters imposed

^p	r	test stat.	crit. 10%	val. 5%	conclusions:		test type	table^(*)
^p	r	test stat.	crit. 10%	val. 5%	10%	5%	test type	table^(*)
6	0	18.2	16.9	19.2	reject	accept	lambda-max	V
	1	6.7	10.6	23.5	accept	accept	’’	’’
	1	6.7	10.6	12.5	accept	accept	trace	’’
	0	24.9	23.0	25.4	reject	accept	’’	’’
	1	0.00	2.71	3.84	accept	accept	trend restr	. χ²(1)
					r=1	r=0
8	0	27.2	16.9	19.2	reject	reject	lambda-max	V
	1	7.9	10.6	23.5	accept	accept	’’	’’
	1	7.9	10.6	12.5	accept	accept	trace	’’
	0	35.1	23.0	25.4	reject	reject	’’	’’
	1	2.06	2.71	3.84	accept	accept	trend restr	. χ²(1)
					r=1	r=1

(*) Cf. Johansen (1994). Table V applies if cointegration restrictions have been imposed on the trend
parameters. The χ²(1) test tests for cointegration restriction on the trend parameters, i.e., the hypothesis that there
is a linear trend in the cointegration relation rather than in the error correction model itself.

Table A.10: Johansen’s LR test of the hypothesis that
the space of cointegrating vectors is spanned by the
column of a 2× 1 matrix H (linear trend present)

H^T:	test stat.	conclusions 10%		5%
(1,-0.40)	18.84	reject	reject
(1,-0.50)	16.32	reject	reject
(1,-0.60)	9.71	reject	reject
(1,-0.65)	3.86	reject	reject
(1,-0.70)	0.00	accept		accept
(1,-0.75)	3.78	reject	accept
(1,-0.80)	10.41	reject	reject
(1,-0.90)	17.65	reject	reject
(1,-1.00)	20.06	reject	reject

Additional references:

Newey,W.K. and K.D.West (1987), "A Simple Positive Definite Heteroskedasticity and

Autocorrelation Consistent Covariance Matrix", Econometrica 55, 703-708.

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