# Patent Keyword Analysis Using Time Series and Copula Models
## 4 Experimental Results
For the further analysis with the five transformed Apple time series keywords, we chose the best model based on the values of AIC for twenty transformed Apple keywords pairs in Table 2. Among 20 pairs of two main transformed Apple keywords in Table 2, the model shows that the 15 pairs had the smallest AIC values from the GCMR model with an ARMA(0,0) correlation error structure, and five pairs had the smallest AIC values from the GCMR model with an ARMA(0,1) correlation error structure. With the parameter estimates obtained from the best models chosen in Table 2, we computed \begin{table}
\begin{tabular}{c c c c c c} \hline
**INGARCH(1,1)** & \(\alpha_{0}\) & \(\alpha_{1}\) & \(\beta_{1}\) & **AIC** & **BIC** \\ \hline Device & 25.7 & 0.951 & 3.98E-10 & 2491.4 & 2495.7 \\ Data & 25.4 & 0.939 & 8.79E-11 & 1963.1 & 1967.4 \\ System & 12.2464 & 0.9327 & 0.0112 & 1665.6 & 1669.9 \\ User & 8.2126 & 0.9694 & 0.0005 & 1479.6 & 1484 \\ Media & 2.15 & 0.989 & 5.34E-10 & 1300.4 & 1304.7 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameter estimates for integer-valued GARCH (1,1) \begin{table}
\begin{tabular}{c c c c c} \hline
**AIC** & **ARMA(0,0)** & **ARMA(1,0)** & **ARMA(0,1)** & **ARMA(1,1)** \\ \hline (Device, Data) & \(-\)24.848 & \(-\)23.484 & \(-\)23.476 & \(-\)21.492 \\ (Data, Device) & \(-\)23.6 & \(-\)21.703 & \(-\)21.699 & \(-\)19.703 \\ (Device, System) & \(-\)15.411 & \(-\)14.322 & \(-\)14.121 & \(-\)12.332 \\ (System, Device) & \(-\)15.966 & \(-\)15.649 & \(-\)16.334 & \(-\)14.414 \\ (Device, user) & \(-\)26.51 & \(-\)26.271 & \(-\)26.145 & \(-\)24.272 \\ (User, Device) & \(-\)23.615 & \(-\)23.448 & \(-\)23.471 & \(-\)21.484 \\ (device, Media) & 1.395 & 3.071 & 3.135 & 4.6435 \\ (Media, Device) & 0.802 & \(-\)0.171 & \(-\)2.793 & \(-\)1.757 \\ (Data, System) & \(-\)28.602 & \(-\)27.202 & \(-\)26.941 & \(-\)25.838 \\ (System, Data) & \(-\)28.315 & \(-\)28.185 & \(-\)28.154 & \(-\)26.185 \\ (Data, User) & \(-\)43.011 & \(-\)41.428 & \(-\)41.367 & \(-\)39.435 \\ (User, Data) & \(-\)44.151 & \(-\)43.743 & \(-\)43.888 & \(-\)41.909 \\ (Data, Media) & 3.297 & 3.786 & 4.166 & 5.455 \\ (Media, Data) & 1.728 & 0.898 & \(-\)1.571 & \(-\)0.195 \\ (System, User) & \(-\)20.926 & \(-\)19.512 & \(-\)19.459 & \(-\)17.521 \\ (User, System) & \(-\)19.231 & \(-\)17.5 & \(-\)17.411 & \(-\)15.693 \\ (System, Media) & 4.494 & 5.98 & 5.922 & 7.904 \\ (Media, System) & 4.25 & 2.109 & \(-\)5.697 & \(-\)4.235 \\ (User, Media) & 1.947 & 3.817 & 3.842 & 5.498 \\ (Media, User) & 1.452 & 0.934 & \(-\)1.487 & \(-\)0.498 \\ \hline \end{tabular}
\end{table} 
Table 2: AIC comparison for GCMR models with a correlation error structure. Gaussian copula directional dependence with the beta logit model with the 20 pairs of five transformed Apple time series keywords. Figure 6 shows the overall picture of directional dependence of five transformed Apple keywords. In Figure 6, the directional dependence from Apple keyword 'Data' to Apple keyword 'Device' is greater than the directional dependence of Apple keyword 'Device' to Apple keyword 'Data'. The proportion of total variation of 'Device' that can be explained by the copula regression of 'Device' on 'Data' is higher than the proportion of total variation of 'Data' that can be explained by the copula regression of 'Data' on 'Device'. By following the higher directional dependencies starting from the transformed Apple keyword 'Data' in Figure 6, we can derive the directional relationship among five main keywords clockwise as follows: 'Data' to 'Device', 'Device' to 'System', 'System' to 'Media', and 'Media' to 'User'. This study focused on smart device technology among various technologies of Apple and carried out technology analysis. So in our experiment, we used five keywords (device, data, user, media, and system) representing the smart device technology of Apple. Figure 6 illustrates the technological dependencies between the five patent keywords using directionality and weight values.