RDP 9606: The Information Content of Financial Aggregates in Australia Appendix B: Detailed Out-Of-Sample Results

Ellis W. Tallman and Naveen Chandra

November 1996

Table B1: Out-Of-Sample Forecasts of Output Growth
Forecast error statistics
Model Measure Step  
  1 2 3 4 5 6 7 8
2VM3 Ratio(a) 1.110 0.958 0.969 0.960 0.976 0.957 1.003 1.006
  Theil U(b) 0.965 0.815 0.856 0.738 0.731 0.683 0.649 0.687
3VM3 Ratio 1.057 1.007 1.045 1.010 0.987 0.896 0.957 0.964
  Theil U 1.130 1.021 1.020 0.846 0.763 0.601 0.579 0.628
4VM3 Ratio 1.165 1.019 1.069 1.036 1.081 1.008 0.984 0.928
  Theil U 1.345 1.119 1.201 0.993 0.831 0.645 0.593 0.662
5VM3 Ratio 1.143 1.242 1.254 1.167 0.780 1.003 1.549 1.034
  Theil U 1.751 1.699 1.823 1.322 0.978 1.229 1.286 0.980

Notes: (a) This ratio is the ratio of the root mean square error of the forecast of output growth in the model with the financial aggregate relative to the root mean square error of the forecast of output growth in the corresponding model without the financial aggregate.
(b) This is the Theil U statistic for the output growth forecast in the model with the financial aggregate under consideration.
Table B2: Out-Of-Sample Forecasts of Inflation
Forecast error statistics
Model Measure Step  
  1 2 3 4 5 6 7 8
2VM3 Ratio(a) 1.047 1.034 1.021 0.997 0.972 0.981 0.959 0.960
  Theil U(b) 1.157 1.245 1.235 1.297 1.290 1.424 1.351 1.346
3VM3 Ratio 1.063 1.086 1.094 1.077 1.042 1.043 1.015 1.009
  Theil U 1.180 1.307 1.280 1.317 1.281 1.396 1.353 1.341
4VM3 Ratio 1.154 1.216 1.233 1.260 1.222 1.183 1.109 1.088
  Theil U 1.342 1.405 1.357 1.468 1.472 1.587 1.498 1.461
5VM3 Ratio 1.249 1.385 1.271 1.273 1.257 1.261 1.255 1.222
  Theil U 2.059 1.902 1.571 1.840 1.764 1.922 1.875 1.724

Notes: (a) This ratio is the ratio of the root mean square error of the forecast of inflation in the model with the financial aggregate relative to the root mean square error of the forecast of inflation in the corresponding model without the financial aggregate.
(b) This is the Theil U statistic for the inflation forecast in the model with the aggregate under consideration.
Table B3: Out-Of-Sample Forecasts of Output Growth
Forecast error statistics
Model Measure Step  
  1 2 3 4 5 6 7 8
2VCU Ratio(a) 1.307 1.310 1.306 1.210 1.150 1.188 1.166 1.166
  Theil U(b) 1.136 1.115 1.154 0.929 0.862 0.848 0.755 0.796
3VCU Ratio 1.250 1.252 1.246 1.191 1.127 1.112 1.149 1.212
  Theil U 1.337 1.269 1.215 0.997 0.870 0.747 0.695 0.789
4VCU Ratio 1.200 1.213 1.106 1.063 1.124 1.137 1.106 1.162
  Theil U 1.385 1.332 1.242 1.019 0.864 0.727 0.667 0.829
5VCU Ratio 1.326 1.597 1.154 1.332 1.400 1.546 1.424 1.509
  Theil U 2.032 2.185 1.678 1.508 1.755 1.895 1.183 1.430
Notes: (a) This ratio is the ratio of the root mean square error of the forecast of output growth in the model with the financial aggregate relative to the root mean square error of the forecast of output growth in the corresponding model without the financial aggregate.
(b) This is the Theil U statistic for the output growth forecast in the model with the financial aggregate under consideration.
Table B4: Out-Of-Sample Forecasts of Inflation
Forecast error statistics
Model Measure Step  
  1 2 3 4 5 6 7 8
2VCU Ratio(a) 1.031 0.993 0.938 0.888 0.908 0.894 0.894 0.891
  Theil U(b) 1.139 1.196 1.134 1.156 1.207 1.297 1.259 1.249
3VCU Ratio 1.125 1.026 1.006 0.959 0.947 0.913 0.918 0.903
  Theil U 1.248 1.234 1.177 1.172 1.165 1.221 1.225 1.200
4VCU Ratio 1.224 1.024 1.014 1.009 0.971 0.925 0.935 0.912
  Theil U 1.423 1.184 1.116 1.174 1.170 1.240 1.263 1.225
5VCU Ratio 1.120 1.198 1.205 1.164 1.124 1.073 1.038 1.062
  Theil U 1.848 1.647 1.490 1.682 1.578 1.636 1.550 1.500

Notes: (a) This ratio is the ratio of the root mean square error of the forecast of inflation in the model with the financial aggregate relative to the root mean square error of the forecast of inflation in the corresponding model without the financial aggregate.
(b) This is the Theil U statistic for the inflation forecast in the model with the aggregate under consideration.
Table B5: Out-Of Sample Forecasts of Output Growth
Forecast error statistics
Model Measure Step  
  1 2 3 4 5 6 7 8
2VBM Ratio(a) 1.192 1.072 1.142 1.120 1.117 1.123 1.120 1.093
  Theil U(b) 1.037 0.912 1.009 0.860 0.836 0.801 0.725 0.746
3VBM Ratio 1.100 0.989 1.094 1.029 1.005 1.008 1.033 0.978
  Theil U 1.176 1.002 1.067 0.861 0.776 0.677 0.625 0.637
4VBM Ratio 1.320 1.017 1.060 0.953 1.116 1.088 1.036 1.089
  Theil U 1.524 1.118 1.191 0.913 0.858 0.696 0.624 0.777
5VBM Ratio 1.101 1.610 1.051 1.259 0.827 0.950 1.333 0.944
  Theil U 1.686 2.202 1.527 1.426 1.037 1.164 1.107 0.895

Notes: (a) This ratio is the ratio of the root mean square error of the forecast of output growth in the model with the financial aggregate relative to the root mean square error of the forecast of output growth in the corresponding model without the financial aggregate.
(b) This is the Theil U statistic for the output growth forecast in the model with the financial aggregate under consideration.
Table B6: Out-Of Sample Forecasts of Inflation
Forecast error statistics
Model Measure Step  
  1 2 3 4 5 6 7 8
2VBM Ratio(a) 1.035 0.997 0.969 0.946 0.894 0.868 0.878 0.890
  Theil U(b) 1.143 1.200 1.171 1.231 1.187 1.259 1.237 1.247
3VBM Ratio 1.040 1.040 1.044 1.040 0.968 0.924 0.921 0.919
  Theil U 1.154 1.252 1.222 1.271 1.191 1.236 1.228 1.221
4VBM Ratio 1.359 1.092 1.073 1.074 1.066 0.950 0.962 0.964
  Theil U 1.436 1.325 1.224 1.279 1.224 1.246 1.259 1.270
5VBM Ratio 1.410 1.865 1.175 1.043 1.623 1.238 1.152 2.113
  Theil U 2.325 2.563 1.452 1.507 2.277 1.887 1.721 2.983

Notes: (a) This ratio is the ratio of the root mean square error of the forecast of inflation in the model with the financial aggregate relative to the root mean square error of the forecast of inflation in the corresponding model without the financial aggregate.
(b) This is the Theil U statistic for the inflation forecast in the model with the aggregate under consideration.
Table B7: Out-Of Sample Forecasts of Output Growth
Forecast error statistics
Model Measure Step  
  1 2 3 4 5 6 7 8
2VCR Ratio(a) 1.169 1.178 1.158 1.135 1.154 1.098 1.044 1.053
  Theil U(b) 1.017 1.002 1.024 0.872 0.865 0.784 0.676 0.719
3VCR Ratio 1.016 1.004 1.096 1.103 1.224 1.212 1.166 1.141
  Theil U 1.087 1.018 1.069 0.923 0.946 0.814 0.706 0.743
4VCR Ratio 1.480 1.180 1.057 1.164 1.432 1.553 1.281 1.321
  Theil U 1.708 1.294 1.187 1.116 1.101 0.994 0.772 0.943
5VCR Ratio 1.398 1.594 0.986 1.284 0.998 1.037 1.450 1.839
  Theil U 2.142 2.181 1.433 1.453 1.251 1.271 1.204 1.743
Notes: (a) This ratio is the ratio of the root mean square error of the forecast of output growth in the model with the financial aggregate relative to the root mean square error of the forecast of output growth in the corresponding model without the financial aggregate.
(b) This is the Theil U statistic for the output growth forecast in the model with the financial aggregate under consideration.
Table B8: Out-Of Sample Forecasts of Inflation
Forecast error statistics
Model Measure Step  
  1 2 3 4 5 6 7 8
2VCR Ratio(a) 0.937 0.898 0.874 0.860 0.854 0.826 0.805 0.798
  Theil U(b) 1.035 1.081 1.057 1.118 1.134 1.199 1.133 1.118
3VCR Ratio 0.962 0.926 0.940 0.938 0.915 0.862 0.825 0.804
  Theil U 1.068 1.114 1.010 1.147 1.125 1.153 1.100 1.069
4VCR Ratio 1.052 0.977 1.052 0.957 0.961 0.866 0.854 0.846
  Theil U 1.223 1.130 1.157 1.114 1.157 1.161 1.153 1.136
5VCR Ratio 1.199 1.135 1.354 1.009 1.053 0.977 0.992 0.931
  Theil U 1.978 1.559 1.674 1.457 1.477 1.490 1.482 1.314

Notes: (a) This ratio is the ratio of the root mean square error of the forecast of inflation in the model with the financial aggregate relative to the root mean square error of the forecast of inflation in the corresponding model without the financial aggregate.
(b) This is the Theil U statistic for the inflation forecast in the model with the aggregate under consideration.