Volatility analysis of chili price at Bengkulu Province using ARIMA approach

Chili is an inflation-forming commodity (volatile food). Prediction of chili price time series data using the ARIMA model approach has good performance for predicting chili prices in the future. The second highest average per capita consumption of chili for a month is Bengkulu Province, below West Sumatra Province. This shows that the level of consumption and demand for chili is relatively high in Bengkulu Province. High demand has an impact on the price volatility of chili. The volatility analysis illustrates the standard deviation or diversity of chili prices that fluctuate over a certain period. Based on the description above, it is necessary to conduct research on the analysis of chili price volatility in Bengkulu Province. This research uses data sourced from the National Strategic Food Price Information Center. chili price volatility analysis using the ARIMA model with the help of R studio software. ARIMA models are suitable for time series data. The stages in this study were stationarity test, building the ARIMA model, selecting the best model, evaluating the model, identifying the ARCH effect and building the ARCH GARCH model, and calculating the volatility value. If there is no ARCH effect, there is no need to create an ARCH GARCH Model. the output of this research was the form of an international conference. The results of the data forecast using the ARIMA model (1,1,2) show prices that are relatively stable but have an upward trend. This shows that the level of volatility can be controlled and this is reinforced by the results that the model has no ARCH effect. The absence of an ARCH effect means that the data is still considered to have relatively the same diversity of variance and is in line with a relatively small volatility.


Introduction
Chili is an inflation-forming commodity (volatile food).Changes in chili commodity prices often have an impact on other food commodities compared to other commodity prices whose prices are regulated by the government (Administered Prices).Prices of non-oil and gas commodities can be used as the main indicator of inflation because they can respond quickly, especially to changes in increasing demand and economic changes specifically due to disasters [1].This occurs in agricultural commodities which are sensitive to macroeconomic changes and uncertainties [2].The contribution of rising chili prices to 1230 (2023) 012013 IOP Publishing doi:10.1088/1755-1315/1230/1/012013 2 inflation when partially calculated per commodity is often higher than other commodities in the same group.The increase in chili prices in certain periods is significant enough to affect the inflation rate.Chili prices often increase significantly, thus contributing to high inflation [3].Chili is one of 11 food commodities that contribute significantly to the formation of inflation, especially volatile food inflation.The government can implement a price control policy, including: Optimizing the buffer function owned by government agencies such as Bulog through market operations.Under certain conditions, it is hoped that the government can start initiating floor and ceiling price policies for farmers and consumers respectively, and improve the national chili distribution system through empowering producers and traders [4].
Prediction of chili price time series data using the ARIMA model approach has good performance for chili price forecasting.This prediction has good performance for data testing and training.This can be used as a basis for anticipating fluctuating market demand [5].Chili prices were also monitored by focusing on 10 cities, namely Medan, Bandar Lampung, Jakarta, Bandung, Semarang, Surabaya, Denpasar, Pontianak, Samarinda and Makassar.Research by [6] uses the ARIMA model to predict the possibility of chili price fluctuations so that they can analyze and predict chili prices for the following months.Based on the results of his research, the government can make efforts to anticipate price fluctuations and strive for a stable supply of chilies throughout the year.
In time series data, there are generally several data points that have different error variances than the others.This difference in error variance has an impact on the prediction level of the model.Heteroscedasticity test can be used to detect differences in error variances.Prediction of time series data using the ARIMA model approach has a drawback where the difference in error variance is not considered as a variant to be modeled.This causes unreadable information or data behaviour in the ARIMA model so that the level of prediction accuracy of the model becomes smaller.The approach using the ARCH GARCH model views heteroscedasticity as a variant to be modeled.This approach not only corrects the shortcomings of the ARIMA approach, but also calculates the variance of each error [7].Another study used the ARIMA ARCH GARCH method and the Single Moving Average conducted by [8] in the city of Semarang.The results of the study show that the ARIMA ARCH GARCH method is more suitable for data that has high volatility.The data that fits the ARIMA ARCH GARCH model is red chili data.ARIMA Single Moving Average is more suitable for data with low volatility, namely binocular, curly and green cayenne peppers.
Income, price changes in substitute commodities, and shifts in tastes lead to variations in consumption [9].Changes in these factors cause price volatility in the market.The market cannot automatically stabilize price changes that occur, therefore there is a need for government involvement to intervene in price changes [10].
The second highest average per capita consumption of chili for a month is Bengkulu Province, below West Sumatra Province.This shows that the level of consumption and demand for chili is relatively high in Bengkulu Province.High demand has an impact on the price volatility of chili.The volatility analysis illustrates the standard deviation or diversity of chili prices that fluctuate over a certain period.In fact, not all chili data contains volatility.The results of [11] for chili data in Central Java Province show that only prices at the consumer level contain volatile elements, while prices at the producer level do not have volatile elements.Price volatility at the consumer level in the future will be less, but it will last for a long time.
Based on the description above, it is necessary to conduct research on the analysis of chili price volatility in Bengkulu Province.Source: BPS (2022)

Method of collecting data
In this study, the data used is monthly time series data in the form of chili prices in Bengkulu Province from July 2017 to December 2022.The data used is secondary data sourced from the National Strategic Food Price Information Centre.

Analysis methods
Chili price volatility analysis using the ARIMA model with the help of R studio software.ARIMA models are suitable for time series data.The stages in this study were stationarity test, building the ARIMA model, selecting the best model, evaluate the model, identify the ARCH effect and building the ARCH GARCH model, and calculate the volatility value.If there is no ARCH effect, then there is no need to create an ARCH GARCH Model.

Stationarity test.
The first stage carried out in this research was checking the stationarity of the chili price time series data in Bengkulu Province.The stationarity test is one of the most basic and most important things to determine the behaviour of time series data [12].There are two behaviors of the time series data that are tested for stationarity, namely stationary on the mean and stationary on the variance of the data.If the data is not stationary on the variance, then a differencing process is needed on the data.If the data is not stationary on the mean, then transformation is needed on the data [13].
The test used to test the stationarity of the mean and the variance is the Augmented Dickey Fuller test [14].

2.2.2.
Building the ARIMA model.Data that is already stationary is used to make forecasting models.The model used is the ARIMA model.The stationary data determines the AR order (p) and MA order (q) of a tentative ARIMA (p.d.q) model.The order d is determined based on the stationarity of the data.The p, d, q orders were determined by observing the Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) patterns [15].The general form of the model with XT is the time data variable Netting,  is an AR operator with  () = 1− 1-⋯  ,  is the MA operator with  = 1− 1-⋯- , 0 =  (1− -⋯-⋯) and  is the residual value at the time .The formation of the ARIMA(p,d,q) model is divided into three groups, namely:

AR(p) models.
The AR(p) model is an ARIMA model with d = q = 0, so that equation (1) can be written 2.2.2.2 MA(q) models.The MA(q) model is an ARIMA model with p = d = 0, so that equation ( 1) can be written

Residual freedom (white noise)
The test used in this study to measure residual freedom is the L-Jung Box statistical test.This test examines the residual squared autocorrelation coefficients.The model has no residual freedom or is not feasible if the Q value is greater than the X2 value (α) with k-p-q degrees of freedom or if the p-value is less than the 5% significance level [16].

Identify the ARCH effect and building the ARCH GARCH model
The ARCH GARCH model is made if the mean model obtained contains the ARCH effect with the following stages.

Identify
The ARCH Effect.At this stage, the way to find out the Arch effect is to do the Lagrange Multiplier test (ARCH-LM test), where the null hypothesis (H0) has no ARCH error.If the p-value > α, it can be concluded that there is no Arch effect.if it does not contain ARCH errors, then there is no need to create the ARCH-GARCH model [17].

Building the ARCH GARCH model
The steps for determining the model begin with simulating several models of variance using the best ARIMA model, estimating model parameters, and selecting the best ARCH-GARCH model from several alternative models based on the size of the goodness of the model and the real coefficients.The criteria used as a measure of the goodness of the model are: If the AIC and SC values are smaller, then the model is better.Other requirements in the ARCH GARCH model that must be met are significant coefficients, coefficient values not greater than one (δ + α < 1), and coefficients not negative (k > 0, δ > 0, α > 0).

Calculate the volatility value
The best model will be used to estimate the volatility of chili prices in Bengkulu Province.Volatility is measured using the standard deviation value which is the square root of the estimated model variance.The greater the volatility value can be interpreted the more likely the price will rise and fall significantly.The formula used is as follows [18].
Information: PV = Price volatility n = Number of data i = time series to S = Price

Result and discussion
The first stage of the research is to ensure that the data is of the time series data type and then plots to see the trend of the time series data.This can be seen in Figure 1.Then a stationary test was carried out on chili price data for Bengkulu Province.The results of the stationary test using the Augmented Dickey-Fuller Test show p-value = 0.036.This explains that chili price data in Bengkulu Province is stationary at α = 5%.But if you use α = 1%, chili price data in Bengkulu Province is not stationary.When using the ACF graphical approach, it can be seen that the data still has a decreasing pattern at the beginning of the leg, so it can be assumed that the data is not stationary.Because the data is not stationary at α = 1%, the chili price data is differencing 1 time.Stationary test results using the Augmented Dickey-Fuller Test show that the data is stationary with a p-value = 0.01.On the ACF graph, the differencing chili price data also does not form a pattern at the beginning of the leg, so it can be concluded that the data is stationary.
Table 2. shows the ARIMA model with various AIC and BIC values.The ARIMA model with the lowest AIC and BIC values is the ARIMA model (1,1,2) with AIC = 1375.82and BIC = 1384.52.Forecasting results are ideal and feasible to use when MAPE is below 10% and MPE is negative [19].The ARIMA model (1,1,2) can be said to be not ideal because the MAPE figure is still above 10% even though the MPE value is negative.The ARIMA model is still chosen as the best model because it has the best criteria among the other models even though it is not ideal.The model feasibility test was carried out by conducting a normality test using the qqnorm chart or Q-Q plot and the residual freedom test or white noise using the Ljung-Box Test.In the Q-Q plot, the model residuals relatively form a straight line.This indicates that the residual model is normally distributed.The next step is to perform a residual freedom test using the Ljung-Box Test.The Ljung-Box Test on the residual yields a p-value = 0.7595 > α = 5%.This shows that accept H0 or random residuals and the white noise assumptions are met in the ARIMA model (1,1,2).The results of forecast data using the ARIMA model (1,1,2) show prices that are relatively stable with a volatility level of 0.532% but have an upward trend.This shows that the level of volatility is still controlled and this is reinforced by the result that the model has no ARCH effect.The absence of an ARCH effect indicates that the data have relatively the same variance.This is in line with the relatively small volatility.
However, the volatility of chili prices is high when compared to other commodities such as tomatoes and shallots which have lower volatility because they have less risk [20].The risk in question is price fluctuations caused by chili import policies.[21] explained that the chili reference price policy has not been effective in managing imports.This is evidenced by the still fluctuating chili prices, even though the chili price volatility was relatively smaller compared to the period before the implementation of the policy.With respect to export and import, fluctuations in chili prices do not only occur in Indonesia, but also in other countries such as India [22].The characteristics of demand and supply are easier to predict on data that has less volatility.This shows that the volatility of chili prices in Bengkulu Province is relatively predictable.One of the reasons for chili prices is predictable because chili is a seasonal commodity that is influenced by the weather, where production will be abundant during the dry season (on season) and production will decrease during the rainy season (off season) [9].
Price differences do not only occur between seasons, but also between regions due to the concentration of chili production in certain areas [23].Therefore, efforts to maintain chili price stability are closely related to efforts to provide curly chili throughout the year, not only in the dry season but also in the rainy season.

Conclusion
Chili is a commodity that is a component of inflation (volatile food).Prediction of chili price time series data using the ARIMA model approach has good performance for predicting chili prices in the future.Bengkulu Province ranks second highest with an average consumption of chilies per capita for a month, below West Sumatra Province.This shows that the level of consumption and demand for chili is relatively high in Bengkulu Province.High demand will have an impact on chili price volatility.The results of forecast data using the ARIMA model (1,1,2) show prices that are relatively stable but have an upward trend.This shows that the level of volatility is still managed and this is reinforced by the result that the model has no ARCH effect.The absence of an ARCH effect means that the data is still considered to have relatively the same diversity of variances and is in line with a relatively small volatility.
Based on the results of research that has been carried out with various limitations, the researchers provide in this study the ARIMA model can only be done for short-term forecasting so that the minimum accuracy value is only for several future periods.One other method that can be used for long-term forecasting is the Long Memory Model.

Figure 6 .
Figure 6.Q-Q plot for testing the normality of the residual model The next step is to identify Arch effect on the model by carrying out the Lagrange Multiplier test (ARCH-LM test), where the null hypothesis (H0) has no ARCH error.If the p-value > α, it can be concluded that there is no Arch effect.The test results show that the p-value = 0.9509728 > 5%.This shows that the ARIMA model (1,1,2) does not have an ARCH effect or an ARCH error, so it does not need to create the ARCH-GARCH model.It can be concluded that the best model is ARIMA (1,1,2) with the equation: log zt = -0.5580log zt-1 -0.4420 log zt-2 + 0.6674 log αt-1 (8)

Table 1 .
10 provinces with highest average per capita consumption of chili for a month .2.2.3 Mixed ARIMA models.The  (, ) model is an ARIMA model with a value of  = 0, by substituting equations (1) and (2), so that equation (3) can be written in the form  =  + 1− +  − , ~(0,  2 ) (4) 2.2.3.Selecting the best model.The best ARIMA model is the model that meets the criteria of residual random forecasting, parsimonious, the estimated parameters are significantly different from zero, the conditions of invertibility and stationarity are met, the process of iteration convergence, and the MSE is small.At this stage, the best ARIMA model will be selected based on the smallest Akaike Information Criteria (AIC) and Schwatrz Criterion (SC) values.
[13]4.Evaluate the model.Model evaluation is to test assumptions.If the model does not meet the assumptions, then return to the modelling stage to get a better model.The analysis steps are to analysis the residuals as follows.2.2.4.1 .Residual normality.The test used to measure normally distributed residuals is by plotting the residual data on a Q-Q plot.If the residuals form a straight line, it can be concluded that the model is normally distributed.The normality test can also use the Kolmogorov-Smirnov statistical test.The residuals are said to be normally distributed if the p-value is more than alpha (5%)[13].