Table 5. Results of non-linear unit root...

Table 5.

Results of non-linear unit root tests

KSS model: $Δ y_{t} = θ y_{t - 1}^{3} + Σ_{i = 1}^{k} δ_{i} Δ y_{t - i} + ε_{t}$
Sollis model: $Δ y_{t} = θ_{1} y_{t - 1}^{3} + θ_{2} y_{t - 1}^{4} + Σ_{i = 1}^{k} δ_{i} Δ y_{t - i} + ε_{t}$
CG Model 1: y_t = α₀ + α₁T + α₂T² + α₃T³ + ε_t
CG Model 2: ${\hat{ε}}_{t} = θ_{1} {\hat{ε}}_{t - 1}^{3} + θ_{2} {\hat{ε}}_{t - 1}^{4} + Σ_{i = 1}^{k} δ_{i} Δ {\hat{ε}}_{t - i} + ε_{t}$
Kruse model: $y_{t} = θ_{1} y_{t - 1}^{3} + θ_{2} y_{t - 1}^{2} + Σ_{i = 1}^{k} δ_{i} Δ y_{t - i} + ε_{t}$
Countries	k	KSS	Sollis	CG	Kruse
Bulgaria	6	−2.294	2.704	3.586	7.047
Croatia	6	−2.064	2.617	1.468	7.112
CzechR	5	−2.085	2.807	3.529	6.963
Estonia	8	−2.643	3.634	4.577	7.184
Hungary	8	−1.033	0.628	6.914	2.639
Kazakhstan	8	−0.937	0.764	7.084	1.311
KyrgyzR	1	−0.637	0.359	0.419	0.717
Latvia	7	−3.159	5.197	6.949	11.16^*
Lithuania	6	−2.280	3.100	3.667	8.022
Poland	5	−2.789	3.994	4.340	8.309
Romania	3	−0.966	7.161^**	8.203	13.49^**
SlovakR	8	−3.304^*	5.490	6.742	15.56^**
Slovenia	7	−1.903	2.012	3.284	6.578

KSS model: $Δ y_{t} = θ y_{t - 1}^{3} + Σ_{i = 1}^{k} δ_{i} Δ y_{t - i} + ε_{t}$
Bulgaria	6	−2.294	2.704	3.586	7.047
Croatia	6	−2.064	2.617	1.468	7.112
CzechR	5	−2.085	2.807	3.529	6.963
Estonia	8	−2.643	3.634	4.577	7.184
Hungary	8	−1.033	0.628	6.914	2.639
Kazakhstan	8	−0.937	0.764	7.084	1.311
KyrgyzR	1	−0.637	0.359	0.419	0.717
Latvia	7	−3.159	5.197	6.949	11.16^*
Lithuania	6	−2.280	3.100	3.667	8.022
Poland	5	−2.789	3.994	4.340	8.309
Romania	3	−0.966	7.161^**	8.203	13.49^**
SlovakR	8	−3.304^*	5.490	6.742	15.56^**
Slovenia	7	−1.903	2.012	3.284	6.578

Notes: For the KSS test, if null hypotheses are θ = 0, there is unit root, while for Sollis, CG and for Kruse tests, if null hypotheses are θ₁ = θ₂ = 0, there is unit root; Model 2 is estimated, as in the Sollis (2009) test, using residual from Model 1 in the Cuestas and Garratt test; k indicates the optimal number of lags. All unit root tests include intercepts and trends; Table critical values of unit root tests are taken from KSS (2003), Sollis (2009), Cuestas and Garratt (2011) and Kruse (2011). The critical values of the KSS unit root test are −3.93, −3.40, −3.13 and 1%, 5% and 10%, respectively. Table critical values of the Sollis unit root test are 8.95, 6.59, 5.59; table critical values are 22.44, 17.27 and 14.97 for the CG unit root test, and 17.10, 12.82 and 11.10 for the Kruse unit root test for 1%, 5% and 10%, respectively;

**and

*imply rejection of the unit root at the 5% and 10% levels, respectively

[ViewLarge]

KSS model: $Δ y_{t} = θ y_{t - 1}^{3} + Σ_{i = 1}^{k} δ_{i} Δ y_{t - i} + ε_{t}$
Sollis model: $Δ y_{t} = θ_{1} y_{t - 1}^{3} + θ_{2} y_{t - 1}^{4} + Σ_{i = 1}^{k} δ_{i} Δ y_{t - i} + ε_{t}$
CG Model 1: y_t = α₀ + α₁T + α₂T² + α₃T³ + ε_t
CG Model 2: ${\hat{ε}}_{t} = θ_{1} {\hat{ε}}_{t - 1}^{3} + θ_{2} {\hat{ε}}_{t - 1}^{4} + Σ_{i = 1}^{k} δ_{i} Δ {\hat{ε}}_{t - i} + ε_{t}$
Kruse model: $y_{t} = θ_{1} y_{t - 1}^{3} + θ_{2} y_{t - 1}^{2} + Σ_{i = 1}^{k} δ_{i} Δ y_{t - i} + ε_{t}$
Countries	k	KSS	Sollis	CG	Kruse
Bulgaria	6	−2.294	2.704	3.586	7.047
Croatia	6	−2.064	2.617	1.468	7.112
CzechR	5	−2.085	2.807	3.529	6.963
Estonia	8	−2.643	3.634	4.577	7.184
Hungary	8	−1.033	0.628	6.914	2.639
Kazakhstan	8	−0.937	0.764	7.084	1.311
KyrgyzR	1	−0.637	0.359	0.419	0.717
Latvia	7	−3.159	5.197	6.949	11.16^*
Lithuania	6	−2.280	3.100	3.667	8.022
Poland	5	−2.789	3.994	4.340	8.309
Romania	3	−0.966	7.161^**	8.203	13.49^**
SlovakR	8	−3.304^*	5.490	6.742	15.56^**
Slovenia	7	−1.903	2.012	3.284	6.578