## 3 Materials and Methods
### Autoregressive Conditional Heteroscedasticity (ARCH)  
Rice price volatility is calculated using the ARCH-GARCH method. Price changes with sharp fluctuations often occur, forcing market conditions to respond and impacting society, such as consumers. Volatility calculations are critical to see food price behavior,and policymakers can take intervention steps to maintain household food security for farmers. The analysis of price volatility is often in a homoscedastic state, thus several calculation stages are needed to obtain the ideal volatility. In the case of food commodity prices that have high volatility, the ARCH model is used. High volatility is characterized by fluctuations with high residual values in one period, followed by low residues. There is a strong correlation between the current residual value and the previous period. The ARCH model can only solve time series problems because the historical data of the prior period are needed to obtain residual difference values. The residual value that changes is not the result of a single independent variable function, but due to a large variety of previous residues.  
\[\sigma_{t}^{2}=\ \alpha_{0}+\alpha_{1}e_{t-1}^{2} \tag{3}\]  
\[\sigma_{t}^{2}=\ \alpha_{0}+\alpha_{1}e_{t-1}^{2}+\alpha_{1}e_{t-2}^{2}+\alpha_{1}e_{ t-3}^{2}+\ldots+\alpha_{p}e_{t-p}^{2} \tag{4}\]  
The ARCH model [54] can explain the variety of residual prices used as volatility values. The value commonly used is the logarithmic standard deviation. In the ARCH Equation (3), constant \(\alpha_{0}\) is part of the variety of residue \(\sigma_{t}^{2}\), which is calculated by adding up the residual difference squared from the past value \(e_{t-1}^{2}\), and the nature of heteroscedasticity is at that stage. This model is still simple, and Equation (4) is used in various residuals depending on the residual squared at several previous values (_lag p_).  
\[h_{t}=\ K+\delta_{1}h_{t-1}+\ldots+\delta_{p}h_{t-p}+\alpha_{1}e_{t-1}^{2}+ \ldots+\alpha_{p}e_{t-p}^{2} \tag{5}\]  
[PERSON] (1986) developed the ARCH model into the GARCH model by explaining that the value of various residues can depend on the previous period's deposition [53]. From Equation (5), we can see that GARCH calculates all changes in the length of the time series, so low volatility values can also be appropriately detected. However, the ARCH-GARCH model must be calculated in several stages, hence the resulting volatility value describes the fluctuation in the residual value accurately [61].  
Furthermore, we measured the effect of ARCH or heteroscedasticity on the Box-Jenkins model that was built. In this study, the ARCH-LM test was used to measure the heteroscedasticity effect before continuing the modeling process with GARCH. This process is vital in determining the time series model to be used. If it is found that the Box-Jenkins model is still homoscedastic, the estimation of price volatility will use the residual value of the model that has been selected. The ARCH-LM test stage estimates the equation using the ordinary least squares (OLS) method to obtain the residual and residual squared values. This is followed by making a regression of the residual with its lag value. Chi-square will be accepted, and the nature of the model can be seen. If the value is greater than the critical point (0.05), then H\({}_{0}\) is rejected, or the model has ARCH elements.