## 2 Materials and Methods
### Methods  
In this study, we tested to see if a threshold existed between the frequency of news related to infectious diseases, specifically ASF and AI, and the retail prices of pork and chicken, respectively. In the threshold model, a sample was divided into two or more regimes based on the threshold level when external impacts existed [13]. We used infectious disease-related news frequency as a threshold variable. In addition, to estimate the effects of disease-related SNS, we used posting frequency as an exogenous variable. The threshold model used in the analysis is the TAR model, as introduced by [PERSON] and [PERSON] [14]. In the model used here, the threshold effect is added to an autoregressive model, AR(p), implying that it is mainly used for nonlinear time-series data [15]. The form of the TAR model with one threshold is as follows Equation (1):  
\[y_{t}=\left\{ \begin{array}{ll}c_{1}+\beta_{1}y_{t-1}+\beta_{2}y_{t-2}+\beta_{ 3}y_{t-3}+\cdots+\beta_{p}y_{t-p}+\varepsilon_{1t}\;if\;q_{t}<\gamma\\ c_{2}+b_{1}y_{t-1}+b_{2}y_{t-2}+b_{3}y_{t-3}+\cdots+b_{p}y_{t-p}+\varepsilon_{2t} \;if\;q_{t}\geq\gamma\end{array} \right. \tag{1}\]  
In the TAR model (\(y_{t}\)), \(q_{t}\) indicates the threshold time series variable and \(\gamma\) indicates the threshold value. The TAR model can be divided into two or more regimes based on \(\gamma\), as expressed by in Equation (2) through Equation (4) [16]:  
\[ \begin{split} x_{t}=\left[y_{t-1}\;y_{t-2}\;y_{t-3}\;\cdots\;y_{t -p}\right]\\ \theta=\left[\begin{array}{c}\beta\\ b\end{array}\right]\end{split}  \tag{2}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Year**} & \multirow{2}{*}{**Disease**} & \multirow{2}{*}{**No. of Cases**} & **No. of Disease-Related** & **No. of Disease-Related** \\  & & & **News Reports** & **SNS Posts** \\ \hline
2018 & & 14 & 1666 & 814 \\
2019 & Avian Influenza & 0 & 352 & 92 \\ \hline
2019 & African Swine Fever & 14 & 9586 & 16,111 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: List of Unstructured Data Used in this Study. Figure 2: Trends of retail chicken prices, Avian Influenza (AI)-related news and SNS frequencies in 2018 and 2019. The \(x\) axis indicates time and the \(y\) axis indicates retail chicken price and frequency. \[ \begin{split}& x_{t}(\gamma)=[x_{t}^{\prime}(q_{t}<\gamma)\ x_{t}^{ \prime}(q_{t}\ \geq\ \gamma)]^{\prime}\\ & l_{1}=\left\{\begin{array}{ll}1\ \ \text{if}\ \ q_{t}<\gamma\\ 0\ \ \text{if}\ \ q_{t}>\ \gamma\end{array},\ I_{2}=\left\{\begin{array}{ll}0\ \text{if}\ \ \ q_{t}<\gamma\\ 1\ \text{if}\ \ \ q_{t}\geq\ \gamma\end{array}\right.\\ & y_{t}=x_{t}(\gamma)^{\prime}\theta I_{1}+x_{t}(\gamma)^{\prime}\theta I_{2}+ \varepsilon_{t}\end{split}  \tag{3}\]  
The TAR model assumes that the error term (\(\varepsilon_{t}\)) is independent and identically distributed (IID) with a mean zero and constant variance. Under this assumption, it is possible to estimate the coefficient of the TAR model using a sequential conditional least square estimation via Equation (5). The threshold values can be estimated from the least square value that minimizes the variance of the residual, as shown in Equation (6). \[ \begin{split}&\hat{\theta}(\gamma)=\left(\sum\limits_{t=1}^{n}x_{t }(\gamma)x_{t}(\gamma)^{\prime}\right)^{-1}(\sum\limits_{t=1}^{n}x_{t}(\gamma )y_{t})\\ &\hat{\varepsilon}_{t}(\delta)=y_{t}-\hat{\theta}(\gamma)x_{t}( \gamma)\\ &\hat{\delta}_{n}^{2}(\gamma)=\frac{1}{n}\sum\limits_{t=1}^{n}( \gamma)^{2}\end{split}  \tag{5}\]  
\[ \begin{split}&\hat{\gamma}=argmin\ \hat{\delta}_{n}^{2}(\gamma)\\ &\hat{\gamma}\ \in\ \left[\underline{\gamma}\ \overline{\gamma}\right]\end{split}  \tag{6}\]  
Given that the TAR model should only be used when a threshold effect exists, it is necessary to test for a threshold effect. This can be done through an F-test of the sum of the squares for residuals (SSR) (\(\delta_{n}^{2}\)) both under the null hypothesis (\(\beta\) = b) and under an alternative hypothesis (\(\beta\) \(\
eq\) b), as shown in Equation (7). \[