# Patent Keyword Analysis Using Time Series and Copula Models
## 1 Introduction  
The role of patent analysis is to analyze the patent documents related to a given technology using statistical methods or machine learning algorithms. Because the patent has abundant information on the completed research and development, many researchers have been carrying out technology analysis using the patent document data. In addition, since the patent system protects the inventor's right exclusively for their developed technology, many researchers have tried to file and register their developed technology to patent offices around the world [1]. In addition, they want to understand different types of relevant technology using on the results of patent analysis. So far, various patent analysis studies using statistical analysis and machine learning have been published. [PERSON] and [PERSON] (2013) used a social network analysis (SNA) method for analyzing Apple's patents to understand thetechnology innovation of Apple [2]. This research represented the technological relations between various sub technologies of Apple by using an SNA visualization. Also, [PERSON] and [PERSON] (2014) proposed a patent keyword network analysis method using network construction based on graph theory [3]. They applied their method to improve technology development efficiency in light emitting diode (LED) and wireless broadband fields. In addition, many patent analysis studies using visualization have been published in various fields [2; 4; 5; 6]. In addition to this network visualization technique, [PERSON] et al. (2017) performed patent analysis using statistical methods [7]. They considered penalized regression models based on ridge and least absolute shrinkage and selection operator (LASSO) regressions to get patent analysis results. [PERSON] et al. (2017) carried out a statistical inference to analyze patent keywords for technology forecasting [8]. This paper estimated the significance intervals of patent keywords, and provided the future trends of technological keywords. Recently, various research on patent analysis considering time has been in progress in diverse fields. If we analyze the patent data with time, we can understand more about the technological evolution. [PERSON] and [PERSON] (2014), [PERSON] et al. (2016), and [PERSON] et al. (2013) studied some meaningful approaches for patent analysis over time [9; 10; 11]. [PERSON] and [PERSON] (2017) proposed a time series model considering integer valued elements because the patent-keyword matrix has integer valued elements which use the frequency values of keywords in patents [12]. They used the integer valued generalized autoregressive conditional heteroskedasticity (GARCH) model with Poisson and negative binomial distributions for integer valued patent analysis.  
This study concentrated on the time factor in patent analysis, so it was limited to finding the technological relationships between the technological keywords. In this paper, we propose a patent analysis method that performs integer valued time series analysis and statistical relation analysis of technologies at the same time. We combined the integer valued GARCH with copula directional dependence to build the proposed patent analysis model [13]. To verify the performance of our research, we conducted experiments using the patent documents filed and registered by Apple. In addition, we will show the technological relationships of Apple's sub technologies over time. We organized this paper as follows. Section 2 introduces the research background of our study. We proposed a patent analysis model using copula directional dependence via integer-valued GARCH in Section 3. In Section 4, we illustrated the experimental results of this paper using Apple's patent keywords. Lastly, we provided our conclusions in Section 5.