Appendix: Simulation results

As specified in the simulation results section, there is weak evidence of consistency when the pa- rameters lie in the non-stationary regions. Indeed, the RMSE decreases very slowly as the sample size increases. Mostly in the strong cointegration case, the bias increases as the sample size increases. Inter- estingly, results are less impacted by non-stationarity in the weak cointegration case. This suggests that practitioners should devote a particular attention to the stationarity or non-stationarity of the data. In the latter case, they should use the estimator ofHualde (2014).

Table 7: Simulation results for 10000 replications of the strong cointegration model when ξ=0.1 and ρ=0

m= bn0.5c 256 512 1024

δ2 δ1 ˆθ Bias SD RMSE Bias SD RMSE Bias SD RMSE

0.6 0 δ2 0.024 0.027 0.166 0.032 0.016 0.131 0.032 0.009 0.101 δ1 0.169 0.045 0.271 0.197 0.027 0.257 0.234 0.017 0.267 ξ 0.002 0.003 0.055 0.001 0.001 0.036 0.001 0.001 0.027 β 0.039 0.013 0.122 0.043 0.010 0.110 0.050 0.008 0.103 0.8 0.2 δ2 0.007 0.029 0.170 0.004 0.018 0.133 0.001 0.011 0.105 δ1 0.185 0.042 0.277 0.217 0.028 0.273 0.259 0.017 0.290 ξ -0.007 0.005 0.071 -0.007 0.002 0.048 -0.006 0.001 0.034 β -0.002 0.037 0.193 0.005 0.029 0.169 0.010 0.022 0.148 0.9 0.4 δ2 -0.007 0.031 0.176 -0.007 0.021 0.144 -0.006 0.014 0.117 δ1 0.129 0.041 0.240 0.151 0.028 0.224 0.178 0.018 0.223 ξ -0.026 0.008 0.095 -0.024 0.004 0.069 -0.023 0.002 0.052 β -0.062 0.063 0.259 -0.070 0.051 0.236 -0.067 0.042 0.215 m= bn0.8c 0.6 0 δ2 -0.048 0.004 0.080 -0.052 0.002 0.071 -0.063 0.001 0.072 δ1 0.085 0.005 0.113 0.118 0.004 0.133 0.154 0.003 0.163 ξ 0.034 0.001 0.050 0.041 0.001 0.049 0.047 0.000 0.051 β 0.104 0.006 0.129 0.149 0.005 0.166 0.205 0.005 0.217 0.8 0.2 δ2 -0.051 0.005 0.087 -0.063 0.003 0.085 -0.083 0.002 0.096 δ1 0.092 0.006 0.122 0.133 0.005 0.151 0.180 0.005 0.192 ξ 0.041 0.002 0.060 0.056 0.001 0.065 0.070 0.001 0.074 β 0.104 0.015 0.160 0.183 0.013 0.216 0.287 0.012 0.308 0.9 0.4 δ2 -0.057 0.006 0.095 -0.066 0.005 0.095 -0.086 0.004 0.105 δ1 0.067 0.006 0.104 0.089 0.005 0.115 0.120 0.005 0.139 ξ 0.013 0.004 0.062 0.031 0.002 0.058 0.046 0.002 0.060 β 0.027 0.036 0.191 0.092 0.036 0.212 0.182 0.037 0.265 References

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Table 8: Simulation results for 10000 replications of the strong cointegration model when ξ=0.1 and ρ=0.4

m= bn0.5c 256 512 1024

δ2 δ1 ˆθ Bias SD RMSE Bias SD RMSE Bias SD RMSE

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Table 9: Simulation results for 10000 replications of the weak cointegration model when ξ=0.1 and ρ=0

m= bn0.5c 256 512 1024

δ2 δ1 ˆθ Bias SD RMSE Bias SD RMSE Bias SD RMSE

0.6 0.4 δ2 -0.017 0.034 0.185 -0.002 0.022 0.147 0.002 0.013 0.116 δ1 0.003 0.031 0.176 0.003 0.018 0.135 0.003 0.010 0.102 ξ 0.013 0.015 0.123 0.006 0.007 0.086 0.004 0.004 0.062 β 0.094 0.074 0.288 0.117 0.053 0.258 0.138 0.037 0.236 0.8 0.6 δ2 -0.022 0.033 0.184 -0.010 0.021 0.144 -0.008 0.013 0.113 δ1 0.010 0.031 0.176 0.008 0.020 0.141 0.006 0.012 0.109 ξ 0.020 0.021 0.146 0.013 0.011 0.107 0.012 0.006 0.079 β 0.139 0.184 0.451 0.157 0.137 0.402 0.166 0.098 0.354 0.9 0.8 δ2 -0.032 0.038 0.197 -0.025 0.027 0.165 -0.015 0.016 0.128 δ1 -0.000 0.029 0.171 -0.001 0.019 0.139 0.005 0.012 0.111 ξ 0.009 0.033 0.182 0.004 0.022 0.148 -0.003 0.012 0.109 β 0.107 0.388 0.632 0.083 0.271 0.527 0.064 0.196 0.447 m= bn0.8c 0.6 0.4 δ2 -0.052 0.004 0.085 -0.048 0.002 0.067 -0.047 0.001 0.059 δ1 -0.013 0.004 0.061 -0.007 0.002 0.044 -0.002 0.001 0.032 ξ 0.035 0.003 0.065 0.037 0.001 0.054 0.038 0.001 0.048 β 0.179 0.016 0.218 0.203 0.012 0.230 0.224 0.010 0.245 0.8 0.6 δ2 -0.061 0.004 0.090 -0.059 0.002 0.077 -0.062 0.001 0.073 δ1 -0.003 0.004 0.061 0.007 0.002 0.047 0.014 0.001 0.040 ξ 0.029 0.003 0.062 0.036 0.002 0.054 0.043 0.001 0.053 β 0.239 0.042 0.314 0.281 0.033 0.334 0.332 0.028 0.372 0.9 0.8 δ2 -0.046 0.006 0.090 -0.036 0.003 0.066 -0.031 0.002 0.053 δ1 -0.014 0.004 0.064 -0.005 0.002 0.049 0.002 0.001 0.038 ξ -0.014 0.005 0.069 -0.010 0.002 0.050 -0.005 0.001 0.038 β 0.058 0.093 0.311 0.072 0.078 0.288 0.091 0.073 0.286

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Table 10: Simulation results for 10000 replications of the weak cointegration model when ξ=0.1 and ρ=0.4

m= bn0.5c 256 512 1024

δ2 δ1 ˆθ Bias SD RMSE Bias SD RMSE Bias SD RMSE

0.6 0.4 δ2 -0.007 0.034 0.185 0.009 0.022 0.147 0.014 0.013 0.114 δ1 -0.003 0.032 0.179 -0.011 0.020 0.141 -0.011 0.011 0.107 ξ 0.030 0.011 0.111 0.022 0.005 0.076 0.019 0.002 0.053 β 0.413 0.091 0.511 0.434 0.064 0.502 0.455 0.043 0.500 0.8 0.6 δ2 -0.019 0.034 0.184 -0.008 0.022 0.149 -0.001 0.013 0.113 δ1 0.002 0.033 0.182 -0.000 0.021 0.145 -0.005 0.012 0.109 ξ 0.029 0.016 0.128 0.024 0.008 0.094 0.021 0.004 0.068 β 0.407 0.221 0.622 0.421 0.158 0.579 0.435 0.115 0.552 0.9 0.8 δ2 -0.037 0.039 0.200 -0.025 0.024 0.158 -0.015 0.017 0.131 δ1 -0.001 0.032 0.180 -0.007 0.021 0.143 -0.005 0.013 0.116 ξ 0.012 0.027 0.166 0.005 0.015 0.123 0.000 0.009 0.094 β 0.374 0.454 0.771 0.350 0.325 0.669 0.336 0.225 0.581 m= bn0.8c 0.6 0.4 δ2 -0.064 0.004 0.088 -0.057 0.002 0.071 -0.053 0.001 0.061 δ1 -0.007 0.003 0.056 -0.005 0.002 0.041 -0.004 0.001 0.031 ξ 0.065 0.002 0.081 0.064 0.001 0.073 0.061 0.001 0.067 β 0.502 0.017 0.518 0.525 0.012 0.536 0.544 0.010 0.552 0.8 0.6 δ2 -0.071 0.004 0.094 -0.065 0.002 0.079 -0.064 0.001 0.073 δ1 -0.004 0.004 0.059 0.003 0.002 0.045 0.007 0.001 0.038 ξ 0.059 0.003 0.079 0.064 0.001 0.074 0.068 0.001 0.074 β 0.523 0.047 0.567 0.569 0.036 0.599 0.623 0.030 0.646 0.9 0.8 δ2 -0.053 0.005 0.089 -0.042 0.003 0.068 -0.035 0.002 0.053 δ1 -0.015 0.004 0.066 -0.007 0.003 0.051 -0.003 0.002 0.039 ξ -0.001 0.004 0.061 0.002 0.002 0.046 0.006 0.001 0.036 β 0.339 0.104 0.468 0.342 0.088 0.452 0.365 0.081 0.462

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