the size of the coefficient. Furthermore we cannot explain the duration of the effects from a VAR analysis. (Brooks, 2008) To obtain this knowledge we will perform an impulse response function after the VAR analysis. The impulse response function will be helpful to retrieve the responsiveness of the dependent variables in the model to shocks to each of the variables. (Brooks, 2008) We will execute an impulse response analysis after the VAR analysis and present the results after the VAR output (sub. 4.1 and 4.2). It should however be kept in mind that it is hard to interpret the results of the impulse response accurately. (Runkle, 1987) A difficulty with time series variables is that cointegration can be of influence on the output of the VAR analysis making the results spurious. Time series variables can often be as individual variable but when variables move together over time, the variables are cointegrating. Cointegrating variables indicate that the time series variables are related in the long run caused by a certain influence on the time series. A cointegrating relationship may be seen as a long term equilibrium phenomenon, because in the short run the variables can differ from each other but in the long run their association becomes clear. (Brooks, 2008) When the variables are cointegrated, the VAR model is not sufficient and a vector error correction model (VEC model), based on the VAR model, is needed correct for the cointegration. (Adkins and Carter Hill, 2011) The VEC model differs from the VAR in the sense that is adds error correction features. More details on the VEC model will be provided in appendix C. The significance level (α) throughout the whole analysis is set at 5%. 3.3.1 Model I The first model makes use of the three components of vehicle crime namely vehicle, combination and cargo theft over the period January 1996 – December 2011. We base our hypotheses on the results generated by the correlation tables presented in paragraph 3.2.1 although those might be spurious. Based on the significantly positive correlations of the variables with their lags, each component of vehicle crime is expected to show a positive and significant relation with itself in the VAR and impulse response analysis. Vehicle theft and combination theft have shown a significant and positive correlation indicating they influence each other in a positive way. We expect to see this impact in the
the size of the coefficient. Furthermore we cannot explain the duration of the effects from a VAR analysis. (Brooks, 2008) To obtain this knowledge we will perform an impulse response function after the VAR analysis. The impulse response function will be helpful to retrieve the responsiveness of the dependent variables in the model to shocks to each of the variables. (Brooks, 2008) We will execute an impulse response analysis after the VAR analysis and present the results after the VAR output (sub. 4.1 and 4.2). It should however be kept in mind that it is hard to interpret the results of the impulse response accurately. (Runkle, 1987) A difficulty with time series variables is that cointegration can be of influence on the output of the VAR analysis making the results spurious. Time series variables can often be as individual variable but when variables move together over time, the variables are cointegrating. Cointegrating variables indicate that the time series variables are related in the long run caused by a certain influence on the time series. A cointegrating relationship may be seen as a long term equilibrium phenomenon, because in the short run the variables can differ from each other but in the long run their association becomes clear. (Brooks, 2008) When the variables are cointegrated, the VAR model is not sufficient and a vector error correction model (VEC model), based on the VAR model, is needed correct for the cointegration. (Adkins and Carter Hill, 2011) The VEC model differs from the VAR in the sense that is adds error correction features. More details on the VEC model will be provided in appendix C. The significance level (α) throughout the whole analysis is set at 5%. 3.3.1 Model I The first model makes use of the three components of vehicle crime namely vehicle, combination and cargo theft over the period January 1996 – December 2011. We base our hypotheses on the results generated by the correlation tables presented in paragraph 3.2.1 although those might be spurious. Based on the significantly positive correlations of the variables with their lags, each component of vehicle crime is expected to show a positive and significant relation with itself in the VAR and impulse response analysis. Vehicle theft and combination theft have shown a significant and positive correlation indicating they influence each other in a positive way. We expect to see this impact in the