## 4 Results
### Rice Price Volatility  
The ARCH effect in the ARIMA model will determine the model for further analysis using ARCH-GARCH. Table 3 shows six models of rice prices at the provincial level, namely West Sumatra, Babel Islands, Central Java, Central Kalimantan, Central Sulawesi, and Maluku. The volatility values of the six models were processed using the ARCH-GARCH model. The best ARCH-GARCH model was selected based on the criteria. All significant coefficients in the variance equation have the most considerable log-likelihood value and the smallest AIC and SIC values. They have positive values for all coefficients in the variance equation. Based on the existing criteria, the ARCH-GARCH model was selected for rice price variables. The GARCH model is the best for the three food commodities studied. After selecting the best GARCH model, the next thing to do is to evaluate the model. Model evaluation can be done through the normality test by paying attention to the Jarque-Bera statistical value. The results of the Jarque-Bera statistical test can be seen in Table 3. The normality test results show that the Jarque-Bera value is statistically significant, which means that the model error is not normally distributed. All ARCH-GARCH models for each variable were tested for normality and show that all of their errors are not normally distributed, so the ARCH-GARCH model is still the best. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Provines**} & \multicolumn{2}{c}{**Unit Root Test**} & \multirow{2}{*}{**Stationarity**} & \multicolumn{2}{c}{**Best ARIMA**} & \multirow{2}{*}{**F-Statistic**} & \multirow{2}{*}{**Prob.**} \\ \cline{2-2} \cline{5-6}  & **T-Statistic** & & & & **MacKinnon** & \\ \hline North Sulawesi & \(-9.702044\) & \(-2.886074\) & First diff & ARIMA (1,1,0) & 0.006 & 0.939 \\ Central Sulawesi & \(-8.158243\) & \(-2.886074\) & First diff & ARIMA (3,1,4) & 18.34 & 0.000 \\ South Sulawesi & \(-9.996535\) & \(-2.886074\) & First diff & ARIMA (2,1,1) & 0.149 & 0.697 \\ Southeast Sulawesi & \(-10.432900\) & \(-2.886074\) & First diff & ARIMA (2,1,2) & 0.631 & 0.424 \\ Gorontalo & \(-8.534030\) & \(-2.886074\) & First diff & ARIMA (3,1,3) & 0.401 & 0.524 \\ West Sulawesi & \(-9.982056\) & \(-2.886074\) & First diff & ARIMA (3,1,3) & 1.784 & 0.181 \\ Maluku & \(-8.451828\) & \(-2.886074\) & First diff & ARIMA (3,1,3) & 6.415 & 0.013 \\ North Maluku & \(-8.817694\) & \(-2.886074\) & First diff & ARIMA (1,1,1) & 0.006 & 0.936 \\ West Papua & \(-8.901620\) & \(-2.886074\) & First diff & ARIMA (1,1,0) & 2.132 & 0.144 \\ Papua & \(-7.393257\) & \(-2.886074\) & First diff & ARIMA (2,1,2) & 2.182 & 0.140 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: \(Cont.\) \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Provinec** & **Model** & **Jarque–Bera** & **Probability** \\ \hline West Sumatra & GARCH & 176.3329 & 0.000 \\ Babel Islands & EGARCH & 389.0305 & 0.000 \\ Central Java & GARCH & 60.5604 & 0.000 \\ Central Kalimantan & GARCH & 197.0539 & 0.000 \\ Central Sulawesi & GARCH & 276.5688 & 0.000 \\ Maluku & EGARCH & 423.9725 & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: GARCH model. The last part is to evaluate the model using the normality test. The value seen is Jarque-Bera. If the test results are significant, the model error is not normally distributed. The model is again tested if it still has an ARCH effect by using the ARCH-LM test. The probability score is greater than the 5% confidence level (\(\alpha\)). If there is still an ARCH effect, the model must be revised until it obtains a result that is free from the ARCH effect. Rice price volatility in this section uses the square of the logarithmic standard deviation of provincial monthly food price. Values below the average of 0.03 are rice prices with little volatility. So, it can be seen that rice has exceptionally high price volatility in several periods (Figure 3). The period with high volatility over the longest time refers to the value above the standard deviation from August to September 2017.