Forecasting Crude Palm Oil Prices Using Support Vector Regression Radial Basis Kernel

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International Scientific Journal Intelligent Mathematics

Journal information ISSN (online): SOI: 1.1/IM DOI: 10.15863/IM Volume: 3 Rezzy Eko Caraka1,2*, Hasbi Yasin2, Issue: 1 Adi Waridi Basyiruddin2

Article information 1 Data Science Indonesia 2 Received: 2017-01-01 Department of Statistics, Faculty of Science and Accepted: 2017-01-01 Mathematics Published: 2017-01-01 Diponegoro University, Indonesia *E-mail: [email protected]

FORECASTING CRUDE PALM OIL PRICES USING SUPPORT VECTOR REGRESSION RADIAL BASIS KERNEL

Abstract: Palm is a plant that has potential economic value. The growing need for palm oil for cosmetics, pharmaceuticals, food, industry, biofuels or others made demand is increasing, causing increased demand for palm oil and higher selling prices. Therefore, we need a method to predict of crude palm oil prices. SVR is a deep learning technique that can provide good performance in forecasting. In this study, using a radial basis kernel and uses the data 80% testing and 20% training. Based on the forecast, the price of crude palm oil is increasing with good accuracy the value of MAPE of training 0.91% and testing 0.87% and also R2 of training 98.71% and testing 83.45%. Impacts that will arise with the price is the industry will become more frequent in producing palm oil that will impact both on the economy as a great profit margin. But if not addressed wisely in terms of the environment will suffer losses, therefore, the Government should issue a policy or regulation to anticipate them. Key words: Crude Palm Oil; Forecasting; SVR; Radial Basis; Kernel. Language: English Citation: Caraka, R.E., et al. (2017). Forecasting crude palm oil prices using support vector regression radial basis kernel. ISJ Intelligent Mathematics, Sweden, № 1(3), pp.1-10. Soi: http://s-o-i.org/1.1/im-2017-1 Doi: http://doi.org/ Pdf: http://int-math.com/arxiv/1im/2017/im-2017-1.pdf

1. Introduction But unlike all types of fat, saturated fat palm oil Indonesia is one of the countries producing palm contains a high percentage (The truth about fats: the oil. Palm oil producing regions in Indonesia spread on good, the bad, and the in-between). Part of palm oil the island of Sumatra, Java, Kalimantan, Sulawesi, and used is fruit. The fruit is processed to manufacture Papua. Economic impact in palm oil itself is quite crude oil and cooking, margarine, soaps, cosmetics, large, so for investors, predicts the price of palm oil is and products in the pharmaceutical field. While the very vital. According to data from the Ministry of rest, are used as ingredients for feed and compost after Agriculture of Indonesia, a total area of oil palm fermented. plantations in Indonesia currently reaches In the field of commodity crops, oil palm and approximately 8 million hectares; a doubling of the made the product of one of the most important in area in 2000 when about 4 million hectares of land in Indonesia. In 2014, Indonesia produced 33.5 million Indonesia is used for oil palm plantations. That number tons of palm oil, which generates $ 18.9 billion of is expected to increase to 13 million hectares in export revenue (Palm Oil Production by Country in 2020.Definition of palm oil or palm oil itself is a 1000 MT). Palm oil has become the most valuable vegetable oil obtained from mesocarp edible fruit of export behind coal and oil (Palm Oil). The rate of palm trees, generally of the species Elaeis guineensis, Indonesian palm oil is a relatively new phenomenon and a bit of a species Elaeis oleifera and Attalea maripa with a tremendous growth industry in the last 30 years (Reeves, 1979). According to a study at Harvard (From Palm Fruit to Product: Indonesia's Palm Oil University, the content in palm oil consists of fatty Industry). acids esterified with glycerol as well as all types of fat.

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The price movement of crude palm oil (CPO) has In the study, there is a statistical science that increased and strengthened. So also with the studies predict the value at the time came to be known production of palm oil in Indonesia only. Growth is by the time series forecasting or forecasting methods . evident in production and exports from Indonesia and Forecasting is a prediction of values of a variable based also the growth of oil palm plantation area. Driven by on the known values of the variable or variables related the global demand continues to rise and profits also ( Makridakis et al , 1992) . Introduced in 1970 by rose, oil palm cultivation has been significantly George E. P. Box and Gwilym M. Jenkins in his book improved by both small farmers and large employers Time Series Analysis : Forecasting and Control . The in Indonesia (with a negative impact on the rationale was the observation time series now (Yt) environment and decrease the amount of production of depends on one or several previous observations (Yt-k). other agricultural products, as farmers switch to the The purpose time series is to describe the specific cultivation of oil palm). mechanism, predicts a future value and optimize the Research on the application of the method of control system support vector regression (SVR) to the palm oil price predictions have been made (Buono, et al. 2016). They 2.3 Support Vector Regression (SVR) do research on the development of palm oil production Support Vector Regression (SVR) is the in Riau province in each period, to determine the application of Support Vector Machine for regression development of the production of the next few years. case. Support Vector Regression is also a method that In this study, researchers used two methods, the SVR can overcome the overfitting, so it will produce a good and Artificial Neural Network (ANN). The result of the performance. Suppose there are l training data,(퐱i, yi) N method SVR produce the best model compared with i = 1, … , l of the input data 퐱 = {퐱1, … , 퐱l} ⊆ ℜ and ANN. Based on the above, the author will conduct 퐲 = {y1, … , yl} ⊆ ℜ and l is the number of training research on forecasting crude palm oil (CPO) for some data. SVR obtained by the method of regression period in the future to facilitate the country and those function as follows: who need the investment in palm oil. f(퐱) = 퐰Tφ(퐱) + b (1)

2. Methods with: 2.1 Crude Palm Oil w = Vector weighting Crude palm oil is a commodity that is most always φ(퐱) = Function which maps 퐱 in a used by the public . So far Indonesia and Malaysia are dimension the largest supplier of crude palm oil in the world . The b = bias use of crude palm oil , among others for the food , In order to obtain good generalization for the cosmetics , pharmaceuticals , and biofuels industry . regression function, can be done by minimizing the Palm oil can be used to create basic oleochemicals and norm of퐰. Hence the need for the completion of the oleochemical derivatives . Some palm oil derivatives following optimization problem: 1 include fatty acids, fatty amines, fatty alcohol , fatty min { ‖퐰‖2} (2) esters , glycerol , ethylene methyl , and opoksi 2 compound. In the economic aspect, there are several with the provision of: T aspects that can influence the crude palm oil , among yi − 퐰 φ(퐱i) − b ≤ ε (3) T others 퐰 φ(퐱i) − yi + b ≤ ε, i = 1, 2, … , l 1 ) supply & demand 2 ) Price competition It is assumed that there is a function f(퐱) that can 3 ) weather approximate f(퐱) ± ε (feasible). All points (퐱i , yi) 4 ) import policy with precision ε. In the case of ineligibility (infeasible), 5 ) changes in tax policy and levies export / import where there are some points that may be out of range ∗ f(퐱) ± ε, so it can be added slack variablest, t to 2.2 Time Series Forecasting overcome the problem of inadequate limiting the optimization problem

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Fig 1. Margin Loss Function (Smola and Bernhard, 1998)

All the deviations greater than f(퐱) + ε the penalty (C − αi)ti = 0 (15) ∗ ∗ will be applied for C. Figure 1 shows this situation (C − αi )ti = 0 (16) graphically, just outside the points in affected areas that have contributed to large penalties. Further Thus obtained: T optimization of the above problems can be formulated b = yi − 퐰 φ(퐱i) − ε for 0 < αi < C (17) T ∗ as follows: b = yi − 퐰 φ(퐱i) + ε for 0 < αi < C (18) 1 min { ‖퐰‖2 + C ∑l (t + t∗)} (4) 2 i=1 i i with the provision of: 2.4 Kernel Radial Basis T Many data mining technique that was developed yi − 퐰 φ(퐱i) − b − ti ≤ ε, i = 1,2, … , l (5) 퐰Tφ(퐱 ) − y + b − t∗ ≤ ε, i = 1,2, … , l with the assumption of linearity, so that the resulting i i i algorithm is limited to cases linear. In general, the cases t , t∗ ≥ 0 i i in the real world is a case that is not linear so as to

overcome data not linear that often occurs in real cases, According Smola and Scholkopf (2003) optimal can be applied to the kernel function. With a kernel solution to the equation (4) with the boundary shown in function of the data in the input space is mapped to the equation (5) is at lagrange function as follows: 1 feature space with the higher dimensions through the L(w, b, t, t∗, α, α∗, η, η∗) = ‖퐰‖2 + C ∑l (t + t∗) − 2 i=1 i i map φ so: ∑l α (ε + t − y + 퐰Tφ(퐱 ) + b) − ∑l α∗(ε + ′ 1 ′ 2 i=1 i i i i i=1 i φ ∶ 퐱 → φ(퐱) KRBF(x, x ) = exp[− ‖x − x ‖ (19) ∗ T l ∗ ∗ 2 ti + yi − 퐰 φ(퐱i) − b) − ∑i=1(ηiti + ηi ti ) (6) 1 = exp [− 〈x − x′, x − x′〉] ∗ ∗ 2 Where C is defined by researchers and αi, αi , ηi, ηi 1 1 1 is lagrange multiplier. To obtain an optimal solution, = exp [− ‖x‖2 − ‖x′‖2] exp [− − 2〈x, x′〉] 2 2 2 then the partial derivatives of L with 퐰, b, t, andt∗. 1 1 ∗ ∗ C ∶= exp [− ‖x‖2 − ‖x′‖2] αi, αi , ηi, ηi ≥ 0 (7) 2 2 ∂L l ∗ = ∑i=1(αi − αi) = 0 (8) = C exp〈x, x′〉 ∂b ′ ′ ′ ∂L K (x, x ) ≔ K (x, x ) + K (x, x ) = 퐰 − ∑l (α − α∗)φ(퐱 ) = 0 (9) c a b ∂퐰 i=1 i i i ∂L = C − α − η = 0 (10) Implications with ψ so ∂t i i c i ( ) ∂L ∗ ∗ ψc x ≔ (ψa(x), ψb(x)) ∗ = C − αi − ηi = 0 (11) 〈 ( ) 〉 〈 ( ) ( ′)〉 〈 ( ) 〉 ∂ti ψc x , ψc(x′) ≔ ψa x , ψa x + ψb x , ψb(x′) 2.5 Loss Function From the partial derivatives are produced= According to Gunn (1998) loss function is a l ∗ function that shows the relationship between an errors ∑i=1(αi − αi )φ(퐱i), so that the regression function is explicitly formulated as follows: with how this error are subject to penalties. Differences l ∗ loss SVR function will produce different formulations. f(퐱) = ∑i=1(αi − αi )퐊(퐱i, 퐱) + b (12) ∗ There are two types of loss function used in this study, Where the difference between αi and αi produce beta value and b is bias. According Smola and the ε-insensitive and quadratic loss function. Here is a Scholkopf (2003) the optimal solution for bias (b) can mathematical formulation for the ε-insensitive loss be calculated using of the summit (Karush-Kuhn- function: Tucker) as follows: T o, for |f(퐱) − 퐲| < ε αi(ε + ti − yi + 퐰 φ(퐱i) + b) = 0 (13) L(퐲, f(퐱)) = { (20) ∗ ∗ T |f(퐱) − 퐲| − ε, otherwise αi (ε + ti + yi − 퐰 φ(퐱i) − b) = 0 (14)

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The solution provided is: (25) 1 l l ∗ ∗ or can be simplified into: max {− ∑i=1 ∑j=1(αi − αi )(αj − αj ) < 퐱i, 퐱j > 2 1 l l l l ∗ max {− ∑i=1 ∑j=1 βiβj < 퐱i, 퐱j > + ∑i=1 βiyi − + ∑i=1 αi(yi − ε) − αi (yi + ε)} (21) 2 1 l 2 or can be simplified into: ∑i=1 βi } (26) 1 2C max {− ∑l ∑l β β < 퐱 , 퐱 > − ∑l β y } (22) 2 i=1 j=1 i j i j i=1 i i with the provision of: with the provision of: l −C ≤ βi ≤ C, i = 1, … , l (23) ∑i=1 βi = 0 (27) l ∗ ∗ Where βi = αi − αi and βj = αj − αj ∑ βi = 0 i=1 2.6 Formulation Support Vector Regression in ∗ ∗ where βi = αi − αi and βj = αj − αj Quadratic Programming Standard While the quadratic loss function: L(퐲, f(퐱)) = (f(퐱) − 퐲)2 (24) According to Ancona (1999) to meet the standard Produce a solution: form quadratic programming so that it can be solved 1 max {− ∑l ∑l (α − α∗)(α − α∗) < 퐱 , 퐱 > with the quadratic programming solver commercial, 2 i=1 j=1 i i j j i j 1 equation (20) needs to be converted into: + ∑l (α − α∗)y − ∑l (α2 + α∗2)} i=1 i i i 2C i=1 i i

l l l l ∗ ∗ ∗ ∗ ∑ ∑(αi − αi )(αj − αj )퐱i. 퐱j = ∑(αi − αi )( ∑ αi퐱i. 퐱j − αj 퐱i. 퐱j) i=1 j=1 i=1 j=1 l l l l l l l l ∗ ∗ ∗ ∗ = ∑ αi ∑ αj 퐱i. 퐱j − ∑ αi ∑ αj 퐱i. 퐱j − ∑ αi ∑ αj퐱i. 퐱j + ∑ αi ∑ αj 퐱i. 퐱j i=1 j=1 i=1 j=1 i=1 j=1 i=1 j=1 l l l l l l ∗ ∗ ∗ = ∑ αI(∑ αj퐱i. 퐱j + ∑ αj (−퐱i. 퐱j)) + ∑ αi (∑ αj(−퐱i. 퐱j) + ∑ αj 퐱i. 퐱j) (28) i=1 J=1 j=1 i=1 j=1 j=1

The new vector 퐚 is defined by 2l ∗ ∗ ∗ 퐚 = (α1, α2, … , αl, α1, α2, … , αl ) and D is the matrix 2l × 2l defined as: 퐱 . 퐱 i = 1,2, … , l i j j = 1, 2, … , l

−퐱i. 퐱j−l i = 1, 2, … , l

퐃ij = j = l + 1, l + 2, … ,2l

−퐱i−l. 퐱j i = l + 1, l + 2, … ,2l

j = 1, 2, … , l { 퐱i−l. 퐱j−l i = l + 1, l + 2, … ,2 so : l l 2l 2l l 2l

∑ ai(∑ aj퐃ij + ∑ aj퐃ij) + ∑ ai(∑ aj퐃ij + ∑ aj퐃ij) i=1 j=1 j=l+1 i=l+1 j=1 j=l+1 l 2l 2l 2l

= ∑ ai ∑ aj퐃ij + ∑ ai ∑ aj퐃ij i=1 j=1 i=l+1 j=1

2l 2l

= ∑ ai ∑ aj퐃ij = 퐚. 퐃퐚 (29) i=1 j=1 l l l l l ∗ ∗ ∗ ∑(αi − αi )yi − ε ∑(αi + αi ) = ∑ αiyi + ∑ αi (−yi) + ∑ αi(−ε) i=1 i=1 i=1 i=1 i=1 푙 푙 푙 ∗ ∗ + ∑ 훼푖 (−휀) = ∑ 훼푖(푦푖 − 휀) + ∑ 훼푖 (−푦푖 − 휀) (30) 푖=1 푖=1 푖=1 Another vector c defined by size 2푙

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풄 = (푦1 − 휀, 푦2 − 휀, … , 푦푙 − 휀, −푦1 − 휀, −푦2 − 휀, … , −푦푙 − 휀) so: 푙 2푙 2푙

∑ 푎푖푐푖 + ∑ 푎푖푐푖 = ∑ 푎푖푐푖 = 풂. 풄 (31) 푖=1 푖=푙+1 푖=1

is the actual output data is all i, then the error can be Defined vector b with size 2푙 calculated by some calculations, the MSE, MAD, 풃 = (1,1, … ,1, −1, −1, … , −1) MAPE and MAE (Bowerman et al., 2005 in Santosa, Thus limiting linear be: 2007). The size of the error used in this study is the 푙 ∗ 2푙 ∑푖=1(훼푖 − 훼푖 ) = ∑푖=1 푎푖푏푖 = 풂. 풃 = 0 (32) value of MAPE (Mean Absolute Percentage Error), so the formula of MAPE can be expressed as follows ∑푛 퐴푃퐸 The new variables above, the standard form of the MAPE= 푖=1 Quadratic Programming can be written as: 푛 1 where : 푚푎푥 {− 풂푫풂 + 풂풄} (33) |푦푖−푦푖̂| 2 APE=(∑푛 ) 푥 100 With the provision of: 푖=1 푦푖 풂풃 = 0 As for determining the accuracy of prediction ퟎ ≤ 풂 ≤ 푪 models, this study used the calculation of the 2 coefficient of determination (R ).The coefficient of 2 2.7 How to search 휶 determination (R )aims to measure how far the ability According to Gunn (1998) how to find 훼 are as of the model in explaining the dependent variable. The follows: coefficient of determination is between zero and one (0 <² <1). R² small value meansthe ability of the 1 independent variables in explaining the variation of the 푚푖푛 { 풂푇푯풂 + 풄푇풂} (34) 2 dependent variable are very limited

Delimited: Sedangkan untuk menentukan akurasi dari model prediksi, pada penelitian ini digunakan perhitungan 풂. (1, … ,1, −1, … , −1) = 0 (35) koefisien determinasi (R2). Koefisien determinasi (R2) bertujuan mengukur seberapa jauh kemampuan model ∗ 푎푖, 푎푖 ≥ 0, 푖 = 1, … , 푙 dalam menerangkan variabel dependen. Nilai koefisien determinasi adalah antara nol sampai satu (0 < R2 < 1). Where: Nilai R2 yang kecil berarti kemampuan variabel- variabel independen dalam menjelaskan variasi 풙풙푇 −풙풙푇 휺 + 풚 휶 variabel dependen sangat terbatas. 푯 = [ ], 풄 = [ ] dan 풂 = [ ] 퐽퐾퐸 −풙풙푇 풙풙푇 휺 − 풚 휶∗ R2 = 1− 퐽퐾푇 푛 2 2 According Vanderbei (1998) 훼 can be calculated where: JKT =∑푖=1(푦푖 − (푦̅) ) 푛 2 by: JKE =∑푖=1(푦푖 − 푦̂푖)

푇 풂 풄 3. Results and Discussion [−(푯 + 푰) 푨 ] [ ] = [ ] (36) 푨 1 휆 푏 The data used in this research is secondary data, where 푨 = [1, … ,1, −1, … , −1] i.e. historical data are taken through the site (http://www.investing.com/commodities/crude-palm- oil-historical-data) The data crude oil palm prices of historical data from 01 January 2015 until September 5, 2.8. Accuracy of Discussion 2016 and then based on the formula of time series data In case there are several sizes regression error is modified to be a predictor variable (x) and the that is often used to assess a perfomansi prediction. If response variable (y) through PACF plot. For more details can be seen in Fig.2 푦̂푖 declared value of predictions for the data to-i and yi

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Start

Input data

Descriptive Statistics

Determination of Independent Variables through PACF plot

Dividing the data into Training and Testing

Determining the value of C, the value of epsilon and parameter values Kernel Radial Basis

Measuring the best model

Prediction

Finish

Fig 2. Flowchart

To view the characteristics of the data can be performed descriptive analysis are presented in Table 1.

Table 1. Descriptive Statistics

Mean StdDev Minimum Maximum 460,944 54,31 352,2 573,6

Based on Table 1. It can be seen that the minimum the analysis is viewed plot partial autocorrelation price of August 26, 2015 and a maximum value at 22 (PACF) based on Figure 2 can be seen that data out on April 2016 crude palm oil prices also have a diversity lag 1 so as input lag is Xt-1 of small to see stddev value of 54.31. The first step in

Partial Autocorrelation Function for Z (with 5% significance limits for the partial autocorrelations)

1.0 0.8

n 0.6

i t

a 0.4

e r

r 0.2

o c

o 0.0

t u

A -0.2

a i

t -0.4

r a

P -0.6 -0.8 -1.0

1 5 10 15 20 25 30 35 40 45 50 55 60 65 Lag

Fig 2. PACF

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To see the volatility of crude palm oil prices can be seen in the figure below

Time Series Plot of Volatility

l i

t 0

o V

-10

-20

1 44 88 132 176 220 264 308 352 396 Index

Fig 3 Volatility Crude palm oil prices

Based on Figure 3 above it can be seen that the advance using a grid search algorithm based Yasin and crude palm oil prices have a volatility that is not big Caraka (2016) the value of cost and epsilon taken if it enough. The next step is to do with support vector has a small error value regression modeling to estimate the parameters in

Table 2. Parameter Estimation

Cost Epsilon Error Dispersion 0,1 0,1000 68,17083 211,8879 1 0,1000 29,97035 62,0149 10 0,1000 28,9281 62,33006 100 0,1000 28,70373 60,60751 0,1 0,0100 63,07452 192,088 1 0,0100 29,51551 61,01827 10 0,0100 28,04148 58,58143 100 0,0100 27,83702 58,20656 0,1 0,0010 63,98349 196,3066 1 0,0010 29,39629 61,71205 10 0,0010 27,54666 58,0491 100 0,0010 28,06313 57,91202 0,1 0,0001 64,10834 196,5439 1 0,0001 29,3608 61,77654 10* 0,0001* 27,40893* 58,09817* 100 0,0001 28,0534 58,02616 *Best Parameter

Based on simulation results obtained with best With φ(퐱) this research is the radial basis kernel parameter value is 10 and the best cost epsilon 0.0001 according the equation (19). To see a comparison with the smallest error value 27.40893, The next step is between predictions and actual data on the training data to perform modeling based on the equation (1) based and test data can be viewed in Gambar.4 and Fig.5 on the simulation obtained value w is 13.57197 and bias From the picture we can see that the comparison (b) equal to 0.4954411 so that it can be written: between the target and the test data to each other, which f(퐱) = 퐰Tφ(퐱) + b means that the SVR modeling with radial basis kernel f(퐱) = 13,57197φ(퐱) + 0,4954411 data palm oil is successful

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Fig 4 Training SVR Radial Basis

Fig 5 Testing SVR Radial Basis

MAPE is an error quantity comparing actual data is so small that it can be concluded that the model-based with a data rate forecasting model estimation results radial SVR has good accuracy for forecasting as well SVR radial with percentage-based training data - as the R2 values of 98.71 and 83.45% for training % for testing used in this study is 80% - 20%. Gained 0.91% testing. to 0.87% for training and testing the value of the error

Table 3. Modeling Accuracy

Accuracy Data R2 MAPE(%) Training(80%) 0,9871738 0,9191906 Testing (20%) 0,8345659 0,8761705

The next step is to conduct SVR based forecasting model based on radial can be seen in Figure 6 that crude palm oil prices will always continue to rise

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564,5 563,6658 563,8863 564 563,5 563,127 563,9404 563 563,4544 563,8007 563,9744 562,5 561,8816 562 562,6273 561,5 561 560,5

560 560,8022 559,5 559 1 2 3 4 5 6 7 8 9 10

Fig 6 Forecasting

Based on Figure 6 can be seen that the crude palm and accuracy testing R2 amounted to 83.45% with oil prices will range in price of $ 560 that will arise with MAPE 87.61%. Based forecasting crude palm oil the impact of the price is the industry will become more prices will continue to rise. frequent in producing palm oil that will impact both on the economy as a great profit margin. But if not Acknowledgement. addressed wisely in terms of the environment will This paper was enriched significantly through suffer losses. Too much exploitation of land for oil helpful discussions with my co-authors Hasbi make forests and other land will be damaged. Pollution Yasin,S.Si,M.Si, providing guidance on the technical caused by the smoke result of clearing land by burning aspect of this paper, was essential to the difficult and waste disposal, are ways plantation poison living calibration of the data set and syntax, I am immensely things in the long term. To resolve these environmental grateful to Kadi Mey Ismail. Your insights and issues the government should make policies and comments are very much appreciated and I know the regulations more stringent environmental friendly true meaning of friendship. Thank you for supportive friends “Ekspedisi Nusantara Jaya chapter Riau Islands 4. Conclusion Province” the Coordinating Ministry for Maritime Based on the analysis concludes that the SVR with Affairs Republic of Indonesia for great experiences. radial basis kernel has excellent ability to forecast with accuracy training has R2 98.71% and MAPE 0.91%

References:

1. Abe, S. (2005) Support Vector Machine for Diponegoro.DOI:10.14710/medstat.9.1.1-13. pp Pattern Classification. Springer - Verlag. 01-13. London Limited. 4. Gunn, S. (1998). Support Vector Machines for 2. Box, G.E.P., G.M.Jenkins, And Classification and Regression. Technical Report, G.C.Reinsel.(1994). Time Series Analysis : ISIS. Forecasting and Control, third edition. Prentice 5. Hamel, L. (2009). Knowledge Discovery with Hall, New Jersey. Support Vector Machine. United State Of 3. Caraka, R.E., Yasin, H., Sugiyarto, W., Sugiarto America :A John Wiley &Sons, INC., and Ismail, K.E. (2016). Time Series Analysis Publication. Using Copula Gauss and AR(1)- 6. Mustakim., Buono (A)., dan Hermadi.i. (2015). N.GARCH(1,1). Vol.9 No.1; Jornal of Media Support Vector Regression Untuk Prediksi Statistika, Universitas Produktivitas Kelapa Sawit Di Provinsi Riau.

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