PREDICTION OF NATIONAL STRATEGIC COMMODITY PRICES BASED ON MULTIVARIATE NONPARAMETRIC TIME SERIES ANALYSIS

: Artificial Neural Network (ANN) or often referred to as artificial neural networks is a method inspired by the awareness of the complex learning system in the brain consisting of sets of neurons that are closely interconnected. While the Fourier series is a trigonometric polynomial function that has a very high degree of flexibility to overcome data that has a repeating pattern. In the time series data, both models can be used for nonparametric approaches that have many advantages, one of which is that they are more flexible and not tied to certain classical assumptions. In this study, a comparative study will be carried out between the ANN model and the Fourier series model to obtain forecasting results on national strategic food commodity prices simultaneously, with initial commodity prices referring to the website of Pusat Informasi Harga Pangan Strategis (PIHPS). The selection of the best model is selected based on the model that results in the smallest rate of prediction error in a commodity price prediction data by comparing the Mean Absolute Percentage Error (MAPE) values. The results of this test get the smallest MAPE value on the ANN model of 0.05974244, while the smallest MAPE value on the Fourier series model is 0.000325423. The results show that the Fourier series model is the best model for predicting the price of strategic commodities in Indonesia.

The price of these strategic commodities has a significant contribution in the formation of inflation rates, especially for inflation of volatile foods. According to Bank Indonesia (BI), volatile food inflation or volatile components is inflation that is predominantly influenced by shocks in the food group such as harvests, natural disturbances, or the developments of domestic food commodity prices as well as international food commodity prices [2]. In addition, currently the amount of inflation is also influenced by the impact of the Coronavirus Disease-2019 (Covid-19) pandemic in various related sectors. For example, inflation in November 2020, which was around 0.28%, was higher than in November 2019, which was 0.14%. BI considers this development was influenced by low core inflation amidst rising inflation in volatile foods and administered prices [3]. Therefore, it is necessary to predict the price of national strategic commodities to control inflation, especially inflation of volatile foods, at a low and stable level.
Simultaneous national strategic commodity prices can be predicted using nonparametric timerelated analysis. Time-guided analysis is a method of making observations over several periods taken over time sequentially with fixed time intervals [4]. Analysis using a nonparametric approach has many advantages, one of which is that it is more flexible and not tied to certain classical assumptions. Therefore, a nonparametric approach is used in this study, namely nonparametric regression with a Fourier series estimator simultaneously and forecasting using Artificial Neural Network (ANN). Fourier series estimators are generally used if the data pattern is not known and there is a tendency towards seasonal patterns [5]. While the ANN method can be used in various data pattern conditions by adjusting the use of the activation function during data processing. This is commonly referred to as architecture. An ANN model requires the right architecture if it wants to produce an optimal output. A deeper architecture will result in better forecasts [6].
The objectives to be achieved in this study are to get an overview of national strategic commodity prices; forming a Fourier series model; forming an ANN architecture; comparing the performance of the two models based on mean squared error (MSE) values; as well as helping related parties to predict the prices of national strategic commodities based on a comparison of 3 PREDICTION OF NATIONAL STRATEGIC COMMODITY PRICES selected methods.
Several studies related to the prediction of national strategic commodity prices have been carried out using several statistical methods. Anggraeni et al., [7] predict the price of one of the national strategic commodities, namely rice using a hybrid method between Artificial Neural Network (ANN) and Autoregressive Integrated Moving Average with Exogenous variables (ARIMAX).
Mardianto et al., [5] predicted the production of 11 strategic commodities in East Java with a nonparametric approach, namely the multi response Fourier series estimator. The conclusion from the study is that the multi response Fourier series estimator is suitable for predicting the production of strategic commodities in East Java.
Mardianto et al., [8] conducted price predictions of 10 national strategic commodities using a nonparametric approach, namely with kernel estimators and Fourier series simultaneously. The results of this study show that the Fourier series estimator is more suitable for making predictions by looking at the comparison of the values of the model's goodness criteria. This study predicts national strategic commodity prices by comparing two nonparametric approaches, namely the ANN method and the Fourier series estimator simultaneously. These results will be the basis for controlling volatile food inflation rates.

PRELIMINARIES
This study focuses on predicting national strategic commodity prices by comparing two nonparametric approaches, namely the Artificial Neural Network (ANN) method and the Fourier series estimator simultaneously.

A. National Strategic Commodities
National strategic commodities are commodities that have high economic value and making a significant contribution to the national According to the National PIHPS, there are 10 strategic economic commodities, including rice, shallots, garlic, red chilies, cayenne pepper, beef, purebred chicken meat, chicken eggs, granulated sugar, and cooking oil. The prices of these strategic commodities have a significant contribution to the formation of inflation rates, especially for volatile food inflation [1]. Therefore, this study uses prices data for 10 national strategic commodities obtained from the PIHPS website from the first week of January 2018 to the second wee k of January 2022 as the in sample and the third week of January 2022 to the forth week of February 2022 as the out sample.

B. Simultaneous Nonparametric Regression Using a Fourier Series Estimator
Fourier series is a trigonometric polynomial function that has a very high level of flexibility to deal with data that has repetitive patterns. The Fourier series estimator is usually used if after investigation the pattern of research data is unknown and there is a tendency to repeat the pattern [9].
Before moving on to the Fourier series estimator, it is necessary to test the correlation between variables. One of the correlation tests that can be applied is the Bartlett Sphericity Test.
The principle of the Bartlett Sphericity Test is that the variables X1, X2,…,Xp are said to be independent if the correlation matrix between variables forms an identity matrix. So that this test can be used as an independence test with the following hypothesis: 0 : = = There is a correlation 1 : ≠ = There is no correlation The results of the Bartlett Sphericity Test obtained must be significant (p-value <0.05) so that the factor analysis is appropriate [10]. Therefore, the decision that can be taken from this test is that H0 ditolak if p-value < α (0.05). This is because the Fourier series is a curve that shows the sine cosine function [11]. For example, with the observation data of ( , ) that follows the regression model as follows.
(1) Where = 1,2, … , show the number of observations. The regression function ̂( ) in equation (1) is unknown and will be estimated using a Fourier eries estimator approach, ̂( ) can be written as follow. (2) Where is the parameter of the j-th regression coefficient which has a scalar value.
Therefore, model (2) can change to: If equation (3) is written based on the Fourier series estimator approach, it becomes: If the estimation method used is Least Square which minimizes the number of squared errors, then ̂ is : where: Thus, the estimator of the Fourier series or ̂( ) is as follow The first study related with Fourier series estimators in nonparametric regression was carried out by Bilodeau [12]. Several subsequent studies on the Fourier series estimator in nonparametric regression were carried out by Biedermann et.al., [13], namely examining the optimal design to obtain oscillation parameters from nonparametric regression models with Fourier series. Dette et.al., [14] developed the study of Biedermann et.al., [13] using several constraints. Tjahjono et.al., [15] proposed a Fourier series estimator in the case of biresponse and applied it to predict electricity consumption. Mardianto et.al., [16] applied the Fourier series estimator to determine the prediction of rice production in in Indonesia Provinces.

C. Forecasting Using Artificial Neural Network (ANN)
Artificial Neural Network (ANN) is a method that is inspired by the awareness of the complex learning system in the brain which consists of closely related sets of neurons. ANN is the right tool The algorithm commonly used in ANN is the general delta rule, which calculates the derivative by applying a chain rule called backpropagation (BP) [17]. BP is an algorithm that consists of two steps. The first is to feedforward the input value and the second is to calculate the error and recalculate the previous layer. The layer in this step is one of the network architecture type. An example of an architecture that is often used is FFNN which consists of an input layer, a hidden layer connected to an output layer. According to Taylor, the equation to get the output of the FFNN architecture is as follows [18].
where is the weight of the k-th neuron in the hidden layer, wik is the weight of the i-th input to the k-th neuron in the hidden layer, ℎ ( ) and 0 ( ) are the activation functions of the hidden layer and the output layer. Another architecture is DLNN which uses two hidden layers to connect the input and output layers. Gallant, [21]). ; Smith, [22]). ANN is considered a nonlinear estimation tool based on data that has been successfully applied in various fields including ecological science (Trichakis et al., [23]), water science (Makaya and Hense, [24]; Manu and Arun Kumar, [25]), hydrological sciences (Grid and Uncuoglu, [26]; Nourani et al., [27]), etc.
One of the architectur of Neural Network model is as follow.

A. Data Exploration
In modeling using time series data, the component that must be considered is the data pattern.  Figure 2B shows the development of commodity prices consisting of beef, purebred chicken meat, and garlic. It can be seen that the beef prices have been increasing. The price of garlic, also have very obvious fluctuations. However, for the price of purebred chicken meat, the price of this commodity fluctuates slightly but tends to be stable. Figure 2C shows commodity prices consisting of red chilies, rice, and shallots. it can be seen that there is a clear fluctuation pattern for red chilies and shallots, while for rice prices tend to be stable without fluctuations.
In the time series analysis, it is also very important to know the linearity relationship of each commodity to the time period. Therefore, the linearity testing using the Terasvirta test of each commodity is carried out to determine the linear relationship of each commodity to the time period.
The Terasvirta test is tested on the price data of each commodity at lags 1, 2, and 3. Based on

B. Forecasting with Fourier Series Estimator
Simultaneous modeling with Fourier series estimators for ten commodities must fulfill the assumption that statistically all ten commodities have a correlation with each other. Therefore, a calculation of the correlation between commodity prices must be done and the result can be seen in Figure 3 which shows that not all variables relationships have a high correlation. Because of this, Bartlett Sphericity test must be done to determine the correlation between commodities.
Based on the results, the test statistical value of 903. 15     Predictions of national strategic commodity production were carried out simultaneously using a

C. Forecasting with Artificial Neural Network (ANN)
To get the best forecasting results using the ANN model, there are some modeling steps that need to be done. That step is presented in Figure 4 below. The input in this Artificial Neural Network (ANN) modeling is lag variables that will be predicted.
To determine the optimal number of neurons a trial and error test is carried out, in this case the number of neurons used is 1 to 10. This study use Tanh activation function in the hidden layer to connect input to the output. The Tanh function is chosen because the results of data testing using Terasvirta test show that several of the show some nonlinear pattern.
In this study, the lag used as an input variable is lag 1, 2 and 3, this is based on the output results  The next process is that the selection of the best ANN model based on the Mean Absolute Percentage Error (MAPE) on each ANN model. MAPE results from the modeling process based on the activation function that has been run according to its lag variable can be seen in Table 7. using lag 1 and 10 neurons can be expressed in equation (11) for the input layer to the hidden layer and equation (12) for the hidden layer to the output layer.  Based on analysis that has been done, it can be concluded that in this case ANN model with lag 1 and neuron 10 can be used as a method in predicting commodity prices in Indonesia with a very high level of accuracy.

D. Model Comparison
To find out the best model to be used for forecasting, a comparison of forecasting results out sample data with forecasting models using the Fourier method and the ANN method was carried out. In Table 8 Table 8 shows that the model using the Fourier method with a sine component is the best model for predictions on each strategic commodity in Indonesia compared to the model using the ANN method with lag 1 and neuron 10. The results of the study using the Fourier method produced good forecasting seen from the forecast chart with the Fourier method following the graph from the out sample data. The results of the study are presented in Figure 5. Based on the Figure 5, it can be seen that the prediction using Fourier method with a sine component fit perfectly with the out sample data. This is support the statement before this that the prediction using Fourier method with a sine component is the best model to predict the commodities prices simultaneously.

CONFLICT OF INTERESTS
The author(s) declare that there is no conflict of interests.