Common use of Empirical Results Clause in Contracts

Empirical Results. We start by presenting the unit root tests on the individual series. The tests are the ADF and KPSS tests. The equations needed for both tests contain an intercept and a linear time trend. In this and future applications of the ADF statistic, the lag length, pi, was chosen using three criteria: AIC, ▇▇▇▇▇▇▇▇ Information Criterion (SIC) and the t-ratio for the coefficient of the last lag. A general-to-specific procedure was implemented, starting with an equation for which a large enough lag length, pmax, was specified. In all applications, pmax was chosen to be 13. Following Erlat (2002), we initially sought agreement between, at least, two of the criteria. If there was no agreement, then the result of the criterion indicating the largest lag was chosen. For this choice of pi, autocorrelation in the residuals was tested using the Ljung-Box statistic and if significant autocorrelation was found, pi was increased until it was eliminated. For the KPSS statistic, the number of weights, , (see equation (3) above) was decided upon by using a procedure suggested in Mayadune et al. (1995). We took the residuals obtained from equation (2), calculated their autocorrelations and compared them with twice their standard errors, which were estimated as T-1/2. We chose to be equal to the degree of the last significant autocorrelation. The results of the ADF and KPSS tests are given in Table 1. We note that only for four series is the unit root null rejected in the case of the ADF tests; Italy, Norway, Sweden and the UK. The rejection for the first three is only at the 10% level while the rejection for the UK series is very strong, at 1%. On the other hand, the KPSS results indicate that the stationarity null is not rejected only for Japan, the Netherlands and the UK. The KPSS results appear to confirm the ADF results only for the UK series. They do, however, indicate stationarity for series not picked up by the ADF statistic. Given that the power of the ADF statistic is low, this may be viewed as a useful result. On the other hand, the fact that the KPSS statistic does not offer collaboration of the ADF results for Italy, Norway and Sweden is not that surprising in view of Caner and ▇▇▇▇▇▇ (2001) where they show that the KPSS statistic tends to reject the stationarity null more often than it should. Table 1 ADF and KPSS Test Results P ADF LB KPSS Austri a 2 -2.189 13.325 (0.960) 20 0.132* Belgium 1 -2.689 16.904 (0.853) 19 0.135* Denmark 1 -2.714 15.218 (0.914) 18 0.135* Finland 1 -2.876 23.830 (0.471) 16 0.141* France 1 -2.736 16.032 (0.887) 19 0.132* Germany 1 -2.579 15.495 (0.929) 20 0.123* Greece 1 -2.980 21.473 (0.611) 22 0.130* Italy 1 -3.282* 21.819 (0.590) 14 0.181** Japan 1 -2.541 17.874 (0.809) 16 0.089 Netherlands 2 -2.262 12.913 (0.968) 18 0.116 Norway 1 -3.196* 13.598 (0.955) 16 0.127* S. Arabia 1 -2.450 10.316 (0.996) 36 0.150** Spain 2 -2.507 16.024 (0.914) 25 0.187** Sweden 1 -3.217* 14.607 (0.950) 22 0.174** Switzerland 1 -2.491 15.728 (0.896) 19 0.120* UK 1 -4.302*** 27.812 (0.268) 10 0.088 USA 1 -2.856 11.263 (0.987) 27 0.153**

Empirical Results. We start by presenting the unit root tests on the individual series. The tests are the ADF and KPSS tests. The equations needed for both tests contain an intercept and a linear time trend. In this and future applications of the ADF statistic, the lag length, pi, was chosen using three criteria: AIC, ▇▇▇▇▇▇▇▇ Information Criterion (SIC) and the t-ratio for the coefficient of the last lag. A general-to-specific procedure was implemented, starting with an equation for which a large enough lag length, pmax, was specified. In all applications, pmax was chosen to be 13. Following Erlat (2002), we initially sought agreement between, at least, two of the criteria. If there was no agreement, then the result of the criterion indicating the largest lag was chosen. For this choice of pi, autocorrelation in the residuals was tested using the Ljung-Box statistic and if significant autocorrelation was found, pi was increased until it was eliminated. For the KPSS statistic, the number of weights, , (see equation (3) above) was decided upon by using a procedure suggested in Mayadune et al. (1995). We took the residuals obtained from equation (2), calculated their autocorrelations and compared them with twice their standard errors, which were estimated as T-1/2. We chose to be equal to the degree of the last significant autocorrelation. The results of the ADF and KPSS tests are given in Table 1. We note that only for four series is the unit root null rejected in the case of the ADF tests; Italy, Norway, Sweden and the UK. The rejection for the first three is only at the 10% level while the rejection for the UK series is very strong, at 1%. On the other hand, the KPSS results indicate that the stationarity null is not rejected only for Japan, the Netherlands and the UK. The KPSS results appear to confirm the ADF results only for the UK series. They do, however, indicate stationarity for series not picked up by the ADF statistic. Given that the power of the ADF statistic is low, this may be viewed as a useful result. On the other hand, the fact that the KPSS statistic does not offer collaboration of the ADF results for Italy, Norway and Sweden is not that surprising in view of Caner and ▇▇▇▇▇▇ (2001) where they show that the KPSS statistic tends to reject the stationarity null more often than it should. Table 1 ADF and KPSS Test Results P ADF LB KPSS Austri a Austria 2 -2.189 13.325 (0.960) 20 0.132* Belgium 1 -2.689 16.904 (0.853) 19 0.135* Denmark 1 -2.714 15.218 (0.914) 18 0.135* Finland 1 -2.876 23.830 (0.471) 16 0.141* France 1 -2.736 16.032 (0.887) 19 0.132* Germany 1 -2.579 15.495 (0.929) 20 0.123* Greece 1 -2.980 21.473 (0.611) 22 0.130* Italy 1 -3.282* 21.819 (0.590) 14 0.181** Japan 1 -2.541 17.874 (0.809) 16 0.089 Netherlands 2 -2.262 12.913 (0.968) 18 0.116 Norway 1 -3.196* 13.598 (0.955) 16 0.127* S. Arabia 1 -2.450 10.316 (0.996) 36 0.150** Spain 2 -2.507 16.024 (0.914) 25 0.187** Sweden 1 -3.217* 14.607 (0.950) 22 0.174** Switzerland 1 -2.491 15.728 (0.896) 19 0.120* UK 1 -4.302*** 27.812 (0.268) 10 0.088 USA 1 -2.856 11.263 (0.987) 27 0.153**