IRJFE by Abdul Aziz Karia and Imbarine Bujang

International Research Journal of Finance and Economics ISSN 1450-2887 Issue 64 (2011) © EuroJournals Publishing, Inc. 2011 http://www.eurojournals.com/finance.htm

Progress Accuracy of CPO Price Prediction: Evidence from ARMA Family and Artificial Neural Network Approach

Abdul Aziz Karia Faculty of Business Management, Universiti Teknologi MARA, Sabah Malaysia

Imbarine Bujang Faculty of Business Management, Universiti Teknologi MARA, Sabah, Malaysia E-mail: imbar074@sabah.uitm.edu.my Tel: +6088325154

Abstract

Oil palm can be considered as one major contributor of developing countries by not only bringing the capital investment but also technology, foreign workers, and management knowledge. On the other hand, some thinkers assume that oil palm can become future direction of the world economy. Therefore the race of oil palm industry has become increasing competitive. However, price of oil palm keeps fluctuating over time. Due to the instability price of oil palm, there is risk and uncertainties that would be faced by tree-corps farmers if they depend too much on this agriculture product. Indeed, oil palms are more volatile compare to other commodities like cocoa, soybean and rubber at the international market. Tree-corps farmers, shareholder, traders, government and producer should consider the uncertainty and high risk in palm oil business world. Therefore, we develop CPO price prediction by using ARMA family and artificial neural network (ANN) using data stretching from 3rd January 2006 to 30th December 2010. Besides, there is also a problem in determining the forecasting techniques. Every forecasting technique has its pros and cons. Such as ARIMA which is not compatible to be implemented in the nonlinear time series data. Whereas ANN, generates more forecasted error in linear time series data. If worst come to worst, there is difficulty in determining the linearity of time series data in order to implement Box-Jenkins and ANN. Therefore, it leads to the risk of unreliable and forecasting error. In this research paper, we forecasted the daily, weekly and monthly basis of the CPO price. Moreover, we selected power of forecasting technique based from the lower root mean squared (RMSE), and mean square error (MSE)

Keywords: Box-Jenkins (BJ); ANN; RMSE; MSE; Crude Palm Oil; NAR. JEL Classification Codes: C18 and C45

1. Introduction Oil Palm also known as Elaeis guineensis was brought to South East Asia from Africa in the 20

th century. According to Singh (1976), oil palm was first introduced in Malaysia in 1911 and became the commercial plantation commerce in year 1917. The various usage of oil palm such as lubricant, cooking, soap product, biofuel, food, and non-food material increased the demand of oil palm domestically and internationally. Oil palm is the only fruit that can produce palm oil and kernel palm

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oils. Palm oil is sometimes confused with kernel oil which has totally different compositions. According to Roberts (2010), nowadays, oil palm can be considered as vitally important to the world. This is because oil palm is a cheap and efficient biofuel which can be considered a future direction of world economy. This advantage makes oil palm an important agriculture product that mounts the world population. In addition, it is a vegetable oil and not animal or dairy product, and therefore does not contain cholesterol.

Oil palm not only helps generate the Gross Domestic Product (GDP) of Malaysia, but it is also creates million of job opportunities to the rural and urban area. Furthermore, oil palm also triggers the increase in population in the plantation area. Oil palm has been deliberated as a major backer of developing country in economic growth by carrying in capital investment, technology, foreign workers, and management knowledge which significantly contributes to economic growth. In Malaysia, Oil palm has played an important role by not only contributing to national income, but significantly contributes to yield and employment in the rural area. Oil palm can be considered a future direction of world economy.

However, the race of Oil palm industry has become increasingly competitive nowadays because of the increase of the Oil palm productions from other countries such as Indonesia and Nigeria. Therefore, unstable indices for CPO prices are relatively high suggesting significant price fluctuations. Due to price instability of CPO, there are risks and uncertainties that would be faced by tree-corps farmers if they depend too much on this agricultural production.

Besides, high price oil palm influences more capital to be invested and many recruitment of labour in order to increase production of oil palm. It is true that thinkers and researchers claim that oil palm contributes to gross domestic product, employment, and yield to developing countries, but it is also creates serious unemployment and harm a country’s GDP if the price of oil palm goes down and the firms average cost increases. The unstable price of oil palm is becoming a threat for, not only countries like Malaysia, but also other developing countries which are heavily involved in oil palm plantations. If the price of oil palm goes down badly, it not only affects the oil palm producer but also fringe industries such as transportation, infant industry and many other industries.

Moreover, to show the power of forecasting techniques in order to forecast CPO prices, we are comparing the BJ and ANN approaches based on the lowest errors generated from both of the models. This is because there are quite a number of researchers who claim certain approaches are better than other approaches. Therefore, the purpose of this research is to evaluate the forecasting performance using BJ and ANN.

Generally, the ANN forecasting techniques is more accurate compared to the ARMA family in the narrow dispersion and high frequency data. Whereas, for the ARMA family compared to ANN forecasting techniques, it is more accurate to forecast in the wider dispersion and low frequency of the time series. It is clear that Oil palm is an important agricultural commodity and hence it is vital to forecast its price, this prediction is important which can become a guideline for the policymakers to make a better decision and development for their own countries. Moreover, forecasting on CPO provide advices for organization in their future planning.

2. Literature Review 2.1. Crude palm oil overview and challenges

As discussed earlier in this study, CPO is a vitally important agricultural commodity. It can be considered as an impulse for generating the economy of developing countries. This is proven by millions of job opportunities in the urban and mostly rural areas created by oil palm industry. Previous study done by Ming and Chandramohan (2002), found that oil palm industry can contribute more to employment and increase income of poor population if it is sustainably managed.

Accordingly, with the previous research done by Noormahayu, Khalid and Elsadig (2009), in using primary data collected from 200 farmers in the administrative district of Sungai Panjang in the

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state of Selangor and using Cobb Douglas method; in which this method has been proven to be dependable to provide reasonably accurate relationship between oil palm and GDP; found that oil palm significantly contributes to Malaysian GDP. This is because of the discovery on the innovation of biofuel and hence, the government encourages the production of oil palm. At the same time, there is an increase of petroleum price around the world including Malaysia, which encourages more demand on oil palm.

Besides, high returns from oil palm are motivating more farmers and smallholders in Malaysia to enter in oil palm industry compared to other agricultural industries. Furthermore, compared to other crops such as fruit and vegetables, oil palm produces slightly better income. However, the way oil palm contributes to GDP found by Noormahayu, Khalid and Elsadig (2009) is different with Okuneye (2003), which claims that oil palm contributed to Nigeria’s GDP by playing an important role in triggering infrastructural development in producing areas. The oil palm triggered industries such as transportation, food, manufacturing, telephone service provider, clothes, and education which indirectly contributed to Nigeria’s GDPs.

The price of oil palm keeps fluctuating over time. Due to the unstable price of oil palm, there are risks and uncertainties that would be faced by tree-corps farmers if it depends too much on this agriculture product. According to Arshad and Mohamed (1995), with the study of price discovery through crude oil palm and using traditional efficient market model and Univariate Box-Jenkins model, they found that Malaysian oil palm is subjected to significant price. However there is an unclear trend on the price of oil palm in the last three decades. Indeed, oil palm is more volatile compared to other commodities like cocoa, soybean and rubber at the international market.

Tree-corps farmers, shareholder, traders and producer should consider on the uncertainties and high risks in palm oil business world. To reduce this associated risk which tree-corps farmers, shareholder, traders and producer are exposed to, there should be one of the effective risk management strategies. Supported by Obado, Syaukat and Siregar (2009), they found that the cooking oil price should remain at an affordable level even though the price of the oil palm keeps fluctuating. When the prices of oil palm in the international market increase, there is also significant increase in cooking oil price for domestic market. The high increase in the trend of the oil palm price had a great implication on the agricultural and industrial sector, (Pleanjai, Gheewala and Garivait, 2004). This is due to higher cost of production either in agricultural or industrial sector.

2.2. Comparative Analysis of Forecasting Technique

Anticipating future behaviour of CPO is crucial in business, industry and government agencies. Therefore, appropriate model should be implemented in order to generate reliable forecast for CPO which can be a direction for policy makers. There are various and different forecasting techniques that have been introduced to analyse time series prediction. Normally, the best technique from the quality of available model (in term of error occurrence), data availability, and some predefine assumption were selected.

According to Sallehuddin, Shamsuddin, Hashim and Abraham (2009) forecasting approach can be divided into two categories which are Statistical and Artificial Intelligence (AI) based techniques. Examples of statistical forecasting are box-Jenkins, multivariate regression, multiple regression and exponential smoothing. However, AI paradigms include fuzzy logic, generic algorithm, neural networks and machines learning.

Usually, the method implemented for predicting time series data is ARIMA family which is widely known as Box-Jenkins time series model. Box-Jenkins method is a very powerful instrument in constructing accurate forecast small sample of forecasting. Method of Box-Jenkins also could avoid the problem of multivariate model. This is agreed by Ong, Huang and Tzeng (2005), who believe that the ARIMA models are flexible enough and involve judgement to describe the wide spectrum of descriptions of temporal rows and meet in practice. To discount judgement in the interpretation of quantitative approach of forecasting is definitely misguided, (Hanke and Wichern, 2009). This is

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because accurate and good forecasting techniques are also determined by unbiased judgement. On the other hand, forecasting involves judgment argued by Sadabadi, Shafiee and Karrari (2009), they with the argument that, if we includes judgement in identification stages, this will lead to the result unstable and bias.

However in reality, if there are advantages, there are also disadvantages. Box and Jenkins model have also pros and cons. This is because there are problems in determining appropriate order of model identification stage of ARIMA, such as identification stage of the parameters and residual from the fitted model. This is because, there will be difficulty for researcher to estimate autoregressive (AR) and moving average (MA) order (AR2 or AR3 or MA 2, etc.). Meaning to say we have employed “trial-and-error” method. The risk of incorrect model identification will create the wrong stage of model estimation and have to conduct model re-identification. This agreed by Hanke and Wichern (2009), ARIMA model relatively need large amount of data and it is not east to update the parameters of ARIMA model as new data becomes available. Compared to traditional forecasting approach such as exponential smoothing, ARIMA model needs large investment of time and resource in order to construct a satisfactory model.

Moreover, it is found that ARMA model out performs the persistence model. This is because ARMA model results compared to persistence model have more errors (Torres, Garcia, Blas, and Francisco, 2005). Besides, according to Valenzuela et.al (2008), there is also a problem in determining Akaike’s Information Criterion (AIC). This leads to the failure to choose an appropriate and the best model selection. This weakness will increase the risk of selecting models which consists a higher error. According to Maia, Carvalho, Ludermir (2008), if ARIMA is implemented to capture the non- linear structure data, there will be a major drawback, in which it will not provide satisfactory result. Worst come to worst, it will increase forecasting error. This is agreed by Khashei, Bijari, and, Ardali (2008), who assumed that the predicted value of the series to be linear in the ARIMA model. Due to this limitation, this will be totally inappropriate where underlying mechanism is non-linear. Therefore, to overcome the limitation of ARIMA model, there is a unique ability of the ANN in capturing the nonlinear estimation, indeed the ANN approach giving accurate for time series forecasting in real situation, (Khashei, Bijari, and Ardali, 2009).

Artificial Neural Network (ANN) was found to have stable performance progress with surprisingly low overhead (Duy, Sato, Inoguchi, 2009). This is because; compared to traditional forecasting approach, there is limitation due to inability in forecasting all the features of the history and nature of the computing system. Different scope of research in implementing artificial neuron network approach, conducted by Sallehuddin, Shamsuddin, Hashim and Abraham (2009) found that ANN not to be ‘always’ consistence because usually statistical methods are related with linear data, while ANN associated with nonlinear data. This is the main reasons why statistical method being successful in time series forecasting for several decades. However, they also agreed that ANN perform better with the reasons to ANN superior features in capturing nonlinear time series data. ANN provides effective and consistence in modelling nonlinear time series data without noise. This agreed by Hippert (2001), compared between ANN and traditional forecasting approach, ANN always perform better and become powerful if forecasting horizon is increased.

However, different finding by Maier and Dandy (1996), suggest ARIMA models are better suit for short term forecast and ANN better in predicting long terms forecast. However, ARMA according to Valenzuela, Rojas, Rojas, Pomares, Herrera, Huillen, Marqueza, and Pasadas (2008), it is not only better suit for short term forecast, but also requires data of the time series in question, this features lead to the advantageous to forecast a high frequency of time series data.

ANN has a several advantages compare to traditional Box-Jenkins model, ANN model much more complicated underlying time series characteristics. On the other hand, ANN model also have a “bad site”. This is because ANN model need large numbers of sample data due to its models required larger number of parameters. According to Khashei, Bijari, and Ardali (2009), this problem almost similar to the ARIMA weaknesses which is need high frequency of historical series of data. This is the major weakness of the ANN and ARIMA compared to hybrid and fuzzy logic model. Besides, there

70 International Research Journal of Finance and Economics - Issue 64 (2011)

are inexistence sets of rule for the sample size in a particular. This is due to the training of the network all depends on structure, thresholds and training data in hand.

However, it is found that ANN can also present large variety of problem such as over fitting and capture in local minima, as mention by Maia, Carvalho, and Ludermir (2008). This problem supported by Zhang, Patuwo, and Hu (1999), they found that over fitting problem is more likely occur in neural network models compared in another statistical models due to the usually other statistical model involve large parameters to be estimated. Therefore, to recover problem such as over fitted behaviour of ANN, it is better to expand large number of parameters time series data to be estimated. Different scope of view by Kim, Oh, Kim, Do (2004), problem such as over fitting behaviour by ANN seems not to be a problem, this is because over fitting by ANN is very beneficial in the investigation of such non stationary complicated financial time series. Indeed, it would be a key to success for complex financial time series analysis.

Proven by Cadenas and Rivera (2010), found that Hybrid model is more accurate and superior in forecasting the wind velocities compared to ANN and ARIMA models. Besides, the authors mention that as we adding more series of training vectors of the ANN model, it accuracy will be improve and perform better. ANN was found to be more accurate if the ranges of the data to be forecasted are short. This is proven with the finding by Sfetsos (2002), which presented a research paper on forecasting hourly wind speed by using ANN approach, hence employing ten minutes data which used multistep forecasting and average results were used conduct predictions. There are two independent data sets to be tested. They found that every ten minute data produced better root mean square error (RMSE) which is four times lesser than other models. Furthermore, with the development of the Modular Artificial Neural Network (MANN) will progress the accurateness of the predicting if we employ an appropriate technique, (Wu, Chau and Fan, 2010).

In addition, ANN compared to traditional forecasting approach, provide better forecast with a lower root mean square error in forecasting strong seasonality in time series. However if there is weak, changed network structure will be better, Hamzace (2008). Moreover, according to Rojas, et.al (2007), ANN not only have an ability to forecast nonlinear time series data, but also the residual among the linear output gained by the ARMA system.

Box-Jenkins and ANN can be considers success in predicting in linear and nonlinear time series data. However, the problem is, in reality, there is difficulty for us to decide the linearity of the time series data in order to implement Box-Jenkins or ANN method. There will be chances to increase the probability of forecasting error. Therefore, Hybrid model developed due to limitation of the Box- Jenkins and ANN method. Hybrid model seems to be goods strategy to overcome these limitations. This is because hybrid models can simultaneously model either linear or nonlinear. This agreed by Maia, Carvalho, and Ludermir (2008), hybrid model produce better forecast in their research paper compare to ARIMA and ANN methods. However, hybrid model really hard to employ because it involve complicated model.

3. Methodology 3.1. Box-Jenkins Approach (BJ)

The BJ approaches being developed by George Box and Gwilym Jenkins which applied the ARMA family to predicts the best fit of a time series prediction. The methodology of the BJ approaches is a technically sophisticated way of predicting the variable by considering the historical pattern of the time series, (Wilson and Keating, 2009). Below shows the models of the BJ approaches.

3.1.1. Autoregressive Model (AR) Autoregressive models are appropriate for stationary time series data. The equation for autoregressive is almost similar to moving average equation, except autoregressive estimates the dependent variable

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which depends on the historical data rather than the irregular residuals. However, AR is produced from a white noise series by using an equation (3.0) below: Y t =∅ 0 +∅ 1 Y t − 1 +∅ 2 Y t − 2 + ......... . +∅ p Y t −

p +

(3.0) Where, Y t

= the response variable at time t Y

t − p

= the response variable at time lags, these Y play important role in independent variable ∅

= coefficient autoregressive to be estimated ε

= error term, which represent the effects of the variable not explained by the model

3.1.2. Moving Average Model (MA) Equation 3.1 shows a moving average (MA) model predicting

Y t

(dependent variable) by using the historical data on the forecast errors in predicting

Y t

. Y t = ε t − ωε 1 t − 1 − ωε 2 t − 2 − ......... . −

ωε

q t −

(3.1) Where, Y t

= the response variable at time t, Y

t − p

= the response variable at time lags, these Y play important role in independent variable ε

= error term, which represent the effects of the variable not explained by the model ω

= the coefficient of moving average to be estimated.

3.1.3. Autoregressive Moving Average Model (ARMA) ARMA model is the combination between autoregressive and moving average. It is suitable to use the notation of ARMA (p,q). Term p is the order of the autoregressive part where q is the order of the moving average part. In modelling for linear and stationary time series data, researchers regularly employ the ARMA models due to its superiority, easy implementation, and robustness. General form of the ARMA model can be shown below.

Y t =∅ 0 +∅ 1 Y t − 1 +∅ 2 Y t − 2 + ......... . +∅ p Y t − p + ε t − ωε 1 t − 1 − ωε 2 t − 2 − ......... . −

ωε

q t −

(3.2) Where, Y t

= the response variable at time t, Y

t − p

= the response variable at time lags, these Y play important role in independent variable ∅

= coefficient autoregressive to be estimated ε

= error term, which represent the effects of the variable not explained by the model ω

= the coefficient of moving average to be estimated.

3.1.4. Autoregressive Integrated Moving Average Model (ARIMA) A great number of ARIMA model is developed. The general model is known as ARIMA (p, d, q). Where the p donates the number of autoregressive terms, while d known as the time series that has to be differenced before become stationary, and q known as moving average. The difference between ARMA and ARIMA is they are integrated. This is because most of the time series data are nonstationary. Where the assumption of the ARIMA approach is that, the time series data need to be stationary. Therefore, the time series data needs to be differentiated with the autoregressive or moving average approach.

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Generally, the property of ARIMA is similar to ARMA. Therefore, the equation of ARIMA is exactly like equation (3.2). The difference between ARIMA and ARMA is only “integrated or differencing”. This means, the time series data need to be polish into first difference or second difference before proceeding to another step (Hanke and Wichern 2009).

3.2. Artificial Neural Network Model (ANN)

A neural network usually consists of the interconnecting neurons. Each neuron or nodes are interconnected independently and it can be shown by the equation (4.1). Figure 1 show model building in order to conduct ANN approach.

Figure 1: ANN model building strategy

Postulate General Class of Models

Artificial Neural Network

Forecasting

Figure 2: Neuron construction

Source: More, A. and Deo, M.C., (2009), Forecasting Wind with Neural Network, Marine Structure 16, Elsevier, 35-49.

Y = f ⌈ ⌊ ∑

( xw 1 1 + xw 2 2 + ...

xw t t

)

⌉ ⌋

(4.1) Where, Y = is the output from the neuron x t

= are the input values w t

= are connection weights

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= is the bias value (threshold) f

= is the transfer function, typically known as sigmoidal function f ( x

)

1 1 +

e−

( x

)

3.2.1. Nonlinear Autoregressive (NAR) There are many applications for time series prediction in the neural network. An example of the application are nonlinear autoregressive with external (NARX), nonlinear autoregressive (NAR), and the nonlinear input-output. Using neural network in predicting the CPO prices by using the NAR is already acceptable. This form of the prediction is only using one series that is being conducted in these model. Figure 2 shows the construction of the NAR predictive model.

As we know, there is only one series involved; therefore, the future values of the time series which is V t

will be gathered from the past value of its own. This form of prediction can be written as follows

V t

= f [ V ( t − 1 ) , ... ., V ( t −

d ) ]

(3.3) (Source: Matlab guide version 2010b)

Equation 3.3 was adopted form the Matlab guide version 2010b. This model is better to forecast the prices and the financial instruments, but it must be ensure that the series of we using do not consist any of the companion series. Besides, NAR application is also better in predicting the in- sample test for the time series prediction.

Figure 3: Nonlinear Autoregressive (NAR) network

Input Nodes

Bias

Hidden Nodes

Bias

Output Nodes

Connection Weights

4. Result of the CPO Price Prediction Result of the daily, weekly and monthly forecast using BJ and ANN is shown in Table 1. The error occurrence for daily neural network with a 1-10-1-1 topology achieves lower MSE compared to

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ARIMA (2, 1, 1). In addition, using Diebold and Mariono (1995) prospective, the RMSE generated from the daily neural network shows an acceptable result. This is because, the daily predicted error is in the range of-1.2≤RMSE≤1.0. On the other hand, compared to ARIMA (2, 1, 1), it is not within the range of Diebold and Mariono (1995) prospective, which exceeds the acceptable criteria. Therefore, the model of ARIMA (2, 1, 1) is not suitable to forecast daily CPO prices. Overall, the neural network with 1-10-1-1 topology is better in forecasting daily CPO price compared to ARIMA (2, 1, 1).

Table 1: Forecasting schemes and their performance

Data Scheme used Network type Training algorithm Topology used MSE RMSE Daily Box-Jenkins ARIMA ARIMA (2,1,1) 1.8546 1.3618 Neural network Feed forward Numbers of delays, 2 1-10-1-1 0.0005 0.0224 Weekly Box-Jenkins ARIMA ARIMA (1,1,0) 0.0001 0.0100 Neural network Feed forward Numbers of delays, 7 1-20-1-1 0.1171 0.3422 Monthly Box-Jenkins ARMA ARMA (1,1) 0.0192 0.1386 Neural network Feed forward Numbers of delays, 2 1-15-1-1 0.0318 0.1783 Note: *Using the Diebold and Mariono (1995) prospective stat ranging (-1.2 to +1.0) indicate that all of the reported of

sample RMSE performers are statistically significantly different from another except for daily data on ARIMA.

The performance of the neural network degrades when it comes to measuring the weekly and monthly data of CPO prices. However, BJ approaches show much better forecasting performance when it comes to weekly and monthly basis. In a weekly data, the BJ approach produces 0.0001 of the MSE in the ARIMA (1, 1, 0) model which indicates smaller errors than neural network with reported MSE of 0.1171. Therefore on a weekly basis, ARIMA (1, 1, 0) shows superiority in weekly CPO prices compared to neural network. Analysis based on Diebold and Mariono (1995), the RMSE reproduced by the ARIMA (1, 1, 0) is satisfactory.

Moreover, in a monthly basis, we compared ARMA (1, 1) and the neural network with 1-15-1- 1 topology. The results suggest that the monthly RMSE of the ARMA and ANN show the acceptance level based on Diebold and Mariono (1995). However, the ARMA (1, 1) shows better result compared to ANN as 0.0192<0.0318. Therefore, ARMA (1, 1) model is appropriate to forecast monthly CPO prices.

4.1. Daily Forecasts

The ARIMA and the neural networks were developed to forecast daily CPO prices. The CPO prices were collected from 3rd January 2006 to 30th December 2010 which consists of 1236 observations showing volatile movement. In order to certify the data is stationary, after conducting the unit root test, we converted the CPO prices into log form. Figure 4 presents the actual daily CPO prices and ANN prediction almost accurate. Compared to ARIMA (2, 1, 1), the forecast daily CPO prices is not parallel with the actual price. This proves that the ANN is better in predicting the daily CPO prices with high frequency time series data.

The outliers identified in the first month towards the middle year of 2006 are considered as unpredictable by the ANN. The potential explanation is that in 2006 Malaysian CPO prices were recovered due to the anticipated demand from the biodiesel industry coupled with the high prices of the soybean prices.

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Figure 4: Time history comparison of the forecasted and observed daily CPO prices

4 2006 2007 2008 2009 2010

Daily ARIMA and NN model From the daily forecast, model being compared are ARIMA (2, 1, 1) and neural network with a 1-10-1- 1 topology. The ARIMA (2, 1, 1) was fitted to training part of the series and used to predict daily CPO prices with respect of the testing part of observations. The ARIMA (2, 1, 1) generated from the first differencing of the log CPO and combined with the second and first order of the AR and MA equations. However, the prediction of the daily ARIMA (2, 1, 1) is not as good as the prediction of the ANN.

The NN model perform better in daily CPO price prediction due to the ANN only reproduced 0.0005 of the MSE which is less than ARIMA (2, 1, 1) with the 1.8546 of MSE. The construction of the daily ANN shown in the Figure 5 and the output (predicted) of the ANN were generated from the 10 hidden layers and 1:2 of the delays of the neuron.

Figure 6 and 7 show the comparison of the regression line between the ARIMA and ANN respectively. It is clearly shown that the ARIMA (2, 1, 1) model is not accurate as ANN predictions. Besides, ANN prediction shows small outliers effect and almost perfect prediction compared to the ARIMA prediction of daily CPO prices. The value of R generated by the NN is 0.9906 which is higher than the 0.6406 generated from the ARIMA (2, 1, 1).

Figure 5: Daily ANN topology and showing the weights and biases at each node.

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Figure 6: Scatter of forecasted and observed daily

CPO prices (ARIMA)

Figure 7: Scatter of forecasted and observed daily

CPO prices (ANN)

8.4

8.2

8.0

7.8

7.6

7.4

R =0.6406 7.2 7.4 7.6 7.8 8.0 8.2 8.4

7.2

R =0.9906

7.2 7.4 7.6 7.8 8.0 8.2 8.4

4.2. Weekly forecasts

The analysis of data corresponds to the weekly CPO prices. The data range is from 3

January 2006 to 30th December 2010 with 286 observations of CPO prices in a weekly basis. Figure 8 shows the CPO prices transformed into log form on a weekly basis.

Figure 8: Time history comparison of the forecasted and observed weekly CPO prices

10.5

10.0

9.5

9.0

8.5

8.0

7.5

7.0

50 100 150 200 250

Weekly ARIMA and NN Model The models which are being compared are ARIMA (1,1,0) model and ANN model with a 1-20-1-1 topology using weekly data of CPO prices. This is proved in Table 1 where the MSE of ARIMA (1,1,0) is 0.0001, less than ANN which is 0.1171. The depreciation of the ANN performance is due to the dispersion matter. Even though previous findings highlight that the ANN perform better in the nonstationary time series data, but its performance become worse as the time series data frequency declines.

Figure 9 and 10 illustrate the performance of the ANN depreciates as data frequency is low. But the performance of the ARIMA is still not in the satisfactory level in the weekly data, which can be considered moderated which is between high and low frequency data. Furthermore, the value of R of the ARIMA is still low even though it has low MSE compared to ANN which has high value of R and MSE. Where, the ARIMA MSE is 0.001 while the ANN is 0.1171. On the other hand, the value of R

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for the ANN is higher than ARIMA which is 0.7260 and 0.6672 respectively. This proved that the value of R of the ANN becomes inaccurate as the dispersion becomes wider. In contrast to ARIMA, the performance becomes better as the dispersion of the time series data becomes wider.

Figure 9: Scatter of forecasted and observed weekly

CPO prices (ARIMA)

Figure 10: Scatter of forecasted and observed weekly

CPO prices (ANN)

9.20

8.85

7.2 7.6 8.0 8.4 8.8 9.2 9.6 10.0

10.4

9.15

10.0

9.10

9.6

9.05

9.2

9.00

8.8

8.95

8.4

8.90

8.0 R =0.6672

7.6

R 7.2 7.6 8.0 8.4 8.8 9.2 9.6 10.0

=0.7260

4.3. Monthly Forecasts

The analysis using monthly CPO prices from January 2006 to December 2010. Thus, this time series correspond with 60 observations of CPO prices in Malaysia to be used for the forecasting. Figure 11 shows the monthly performance of historical price of CPO against the times.

Based on Figure 11 above, it clearly shows that the performance of the ANN degrades as the dispersion of the time series become wider. Besides, the accuracy of the ARMA (1, 1) becomes more accurate in the monthly basis. The volatility movement of the actual CPO prices followed the predicted price using ARMA (1,1) model. On the other hand, the curved shape of the ANN and the actual observed is less similar but as the actual CPO prices increase, theANN curve follows.

Monthly ARMA and NN Model ARMA (1, 1) and neural network with a 1-15-1-1 topology are being used to forecast monthly CPO prices. The ARMA (1,1) model performance shows superiority compared to ANN prediction. In addition, the MSE of the ARMA model is smaller compared to the ANN models. Hence, the ARMA reproduce only 0.0192 MSE which is less than ANN with the 0.0318 MSE, the ARMA model being selected to forecast monthly CPO price prediction and not the ANN model.

Figure 12 and 13 presents the scatterplots of both models’ performances of ARMA (1,1) and the ANN with 1-15-1-1 topology respectively. The general results suggest that traditional ARMA model seem to be efficient when dealing with monthly data. Furthermore, the value of the R construction for every model is stated in Figure 12 and 13 revealed

Using the error performance, the MSE of ARMA model is 0.0198 while the ANN is 0.0318. This means that the error for every prediction of ARMA (1,1) is better in predicting the monthly CPO prices. On the other hand, the value of the R of the ARMA (1,1) model is higher than ANN which indicates 0.8652 and 0.7260 respectively. Using Diebold and Mariono’s (1995) prospective stat ranging (-1.2 to +1.0), it indicates that the reported RMSE performer sample is significantly different statistically for monthly CPO prices prediction.

78 International Research Journal of Finance and Economics - Issue 64 (2011)

Figure 11: Scatter of forecasted and observed monthly CPO prices (ARMA)

Figure 12: Scatter of forecasted and observed

monthly CPO prices (ANN)

11.2

10.2

10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4

11.1

11.0

10.9

10.8 10.8

10.7

10.6

10.5

10.4

10.3 R =0.8624

10.2

R =0.8487

10.0 10.2 10.4 10.6 10.8 11.0 11.2 11.4

5. Conclusion The foregoing sections deal with the problem in choosing the appropriate technique of the forecast (BJ and ANN). The CPO price predictions were forecasted on a 1 day, 1 week, and 1 month basis using data stretching from 3

January 2006 to 30

December 2010. From the result scheme and performance of both models, we can conclude that the artificial neural network perform better for the high frequency data such as daily, hours, minutes and per-second basis. This is because the ANN perform better compared to BJ approach in a high frequency time series data, and degrade if the times series data were in low frequency data. In addition, it is noticed that in conducting the high frequency data for ANN it required a trial and error on the hidden layers and epochs. Should this not be conducted, there would be an over fitting problem.

On the other hand, BJ approach is also better in performing high frequency time series data, but not as accurate as neural network. However, when it comes to low frequency data which is on a monthly basis, the performance produced more accurate prediction than ANN.

Besides that, the dispersion matter also played an important role in the accuracy of ANN and the BJ prediction. For example, based on literature reviews, most of the researcher such as More and Deo (2003) with the research title “Forecasting wind with neural network”, claimed, that the neural networks produced much more accurate forecasts compared to the traditional time series model of ARIMA. However, with the result revealed in the Table 1, it is clearly seen that neural network only produced superiority in high accuracy on a daily basis which is narrow dispersion time series data (high frequency), but degrades as the wider dispersion of the time series and the superiority of the neural network is replaced by ARMA family based on monthly data.

Concurrent with the research conducted by Sallehuddin, Shamsuddin, Hashim and Abraham (2009), it was founded that ANN is not ‘always’ consistent because statistical methods are usually related with linear data, but the neural network can be associated is with nonlinear data. However, from our result of the forecast, when the time series data is consisted of the linear and nonlinear pattern, the neural network performance degrades as well. The neural networks only perform superior accurate prediction in the nonlinear and narrow dispersion (high frequency) of the time series data. Besides, the Box-Jenkins only gives better prediction when the prediction deals with the low frequency of the time series data. Therefore, in order to produce more accurate prediction when there is existence of the linear and nonlinear pattern in the time series, it is best to conduct fuzzy logic approach.

International Research Journal of Finance and Economics - Issue 64 (2011) 79

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