A Hybrid Model of Artificial Neural Network and Genetic Algorithm in Forecasting Gold Price

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1 A Hybrid Model of Artificial Neural Network ad Geetic Algorithm i Forecastig Gold Price Azme Khamis ad Phag Hou Yee Abstract The goal of this study is to compare the forecastig performace of classical artificial eural etwork ad the hybrid model of artificial eural etwork ad geetic algorithm. The time series data used is the mothly gold price per troy ouce i USD from year 1987 to A covetioal artificial eural etwork traied by back propagatio algorithm ad the hybrid forecastig model of artificial eural etwork ad geetic algorithms are proposed. Geetic algorithm is used to optimize the of artificial eural etwork euros. Three forecastig accuracy measures which are mea absolute error, root mea squared error ad mea absolute percetage error are used to compare the accuracy of artificial eural etwork forecastig ad hybrid of artificial eural etwork ad geetic algorithm forecastig model. Fitess of the model is compared by usig coefficiet of determiatio. The hybrid model of artificial eural etwork is suggested to be used as it is outperformed the classical artificial eural etwork i the sese of forecastig accuracy because its coefficiet of determiatio is higher tha covetioal artificial eural etwork by 1.14%. The hybrid model of artificial eural etwork ad geetic algorithms has better forecastig accuracy as the mea absolute error, root mea squared error ad mea absolute percetage error is lower tha the artificial eural etwork forecastig model. Idex Terms Artificial Neural Network; Forecastig; Geetic Algorithm; Gold Price; Machie Learig. I. INTRODUCTION Gold is oe of the most precious elemets o earth. After that, activity of gold price tradig is become more commo ad hece gold price fluctuates. Gold price per troy ouce shows the steady upward tred sice the early of 2008 because demad icreases as i [1]. Accordig to [2], the gold price plays a importat role i ecoomic. Most of the commodities are correlated with gold price. May researchers claim that gold price is a importat idicator because gold is oe of the most popular fiacial istrumets. For istace, [3] devotes forecastig of gold price is a essetial issue because gold price serves as the expectatio of ivestors ad the reflectio of the tred of the world s ecoomic. Moreover, [4] claims that forecastig gold price is beeficial to the ivestors ad compaies. With data-decisio makig, ucertaity ca be decreased. Therefore, forecastig the future price of gold by usig suitable models is essetial. There are a lot of gold price forecastig model proposed by the researchers. As a example, [5] discussed o Published o Jue 8, Az. Khamis ad P. H.Yee are with Departmet of Mathematics ad Statistics, Faculty of Applied Sciece ad Techology, Uiversiti Tu Hussei O Malaysia, Malaysia. ( azme@uthm.edu.my, houyee940826@gmail.com). forecastig mothly gold price by usig liear regressio model. I additio, [6] proposed Box-Jekis model to forecast gold price. I the research, ARIMA (0,1,1) is the optimal forecastig model for gold price. Box-Jekis model is supported by [7]. I additio, machie learig techiques such as artificial eural etwork (ANN) [8] ca be used to forecast gold price. I [8], USD idex, silver price, iterest rate, oil price ad stock market idex are used as the predictor variables of the ANN model to predict gold price. ANN is effective i forecastig. I previous studies, ANN is applied i differet field. I [9], the result shows ANN has ability to hadle complex model, it ca predict electricity price effectively despite of the volatility of the data. Moreover, ANN ca be used i modellig. A study [10], ANN is used to model palm oil yield ad the result is compared with multiple liear regressio model (MLR). The result shows ANN has outperformed MLR i predictig palm oil yield. However, [11] claims that ANN may lead to local miima ad should be overcome. GAs ca be used to overcome the local miima issue i ANN [12]. I [13], ad [14], GAs was used to improve the learig algorithm of ANN ad result shows GAs improved ANN model. Hece, by combiig these two techiques ca be useful i solvig the real-world problem especially i forecastig field. The activity-based costig ad assig quatities of idirect cost behave o-liear patter. Though the hybrid model uses fewer cost drivers tha traditioal ANN, it has outperformed the traditioal model [14]. The hybrid model is better because it will ot be iterrupted by the variatios i the umber hidde odes. As a result, it ca yield better performace i allocatig the idirect cost. The weakess of this research is that the data used is simulated data. The model may perform well for the studies but it may ot be applicable i the actual problem i life as the real-life problem may be affected by other exteral factors. I additio, the hybrid model of ANN ad GAs ca be employed to forecast gold future price. For istace, [12] suggested by equippig GAs with ANN as it ca be useful to cope the problem of the scarce prior kowledge about the structure of problem domai. The hybrid model ca solve the problem by simulatig the o-liear models. Improvemet of the hybrid model compare to the traditioal ANN model is show i the result of the hybrid model yielded forecast with lower error [12]. The hybridizatio model of ANN ad GAs ca perform effectively i the evirometal field as well. A study coducted by [15] optimize the feedforward etwork i ANN couplig the GAs ad back propagatio learig to forecast raifall. GAs determies the suitable iput for the forecastig raifall etwork structure. By itegratig GAs with ANN, the forecast performace is more reliable tha DOI: 10

2 the ordiary ANN model as there was improvemet for the error. Gold price is hard to be predicted as there are may cotributig factors affectig gold price. Furthermore, gold is oe of the most importat fiacial istrumets. By havig a accurate gold forecastig model, Malaysia govermet ad ivestors ca make a better decisio. Hece, there are tos of forecastig model ca be used to forecast gold price. Oe of the most popular techiques is by usig ANN. However, the ANN forecastig model has limitatios. As a result, by usig mothly gold price per troy ouce from year 1987 to 2016 provided by World Gold Coucil, this research aims to propose acquire a ANN forecastig model ad to acquire the hybrid ANN ad GAs forecastig model. Forecastig performace of covetioal ANN forecastig model ad the ANN ad GAs hybrid model will be evaluated by usig suitable forecastig accuracy measures. Fially, the best model will be proposed to forecast the mothly gold price per troy ouce. propagatio, the weight of iput layer to the output layer is revised accordigly to the requiremet. Φ = 1 1+е i=1 (y i w i ) (2) where y t is the gold price, w i is the associated weight, Φ is the activatio fuctio. II. RESEARCH METHODOLOGY The gold price per troy ouce data i USD startig from Jauary 1987 to December 2016 was obtaied from the official website of World Gold Coucil. The data was separated by usig proportio. Eighty percet of the data (288 observatios) was used for traiig of the model. Meawhile, the other twety percet of the data, which is 72 observatios was reserved for testig of the forecastig mode. ANN Forecastig Model: Before costructig the ANN, autocorrelatio plot ad partial autocorrelatio plot were used to determie the sigificat lag ad seasoality of mothly gold price per troy ouce data. Moreover, the gold price per troy ouce is ormalized to esure stadardizatio as (1) [8]. ormalized Y t = Y t Y mi Y max Y mi (1) where Y is the gold price at t, Ymax is maximum gold price ad Ymi is the mea of observatio value. ANN is a computatioal model that cosists of three fudametal layers which are iput layer which are iput layer, hidde layer ad output layer. I feedforward NN, uidirectioal trasferrig of data occurs from the iput layer to the hidde layer ad evetually reaches the output layer. The architecture of ANN i this research is show i Fig. 1 [16]. The iput ode value is duplicated ad multiplied by the correspodig weight ad its summatio is kow as activatio value. Subsequetly, activatio fuctio is applied to the activatio value to obtai output. The activatio used i this research is sigmoid fuctio as (2). The sigmoid fuctio has rage from 0 to 1 ad it is effective for the weight updatig process i the traiig algorithms of ANN [16]. The output value is obtaied by the summatio of the value of hidde ode with its correspodig weight. The the result is compared with the targeted result i order to improve the model. The margi of error of the output is determied before the chage i the output weight of the ANN model. The weight of the hidde layer to the output sum is revised by usig delta sum to decrease the margi of error. I additio, i back Fig. 1. Feedforward ANN Architecture The iput value for the ANN is the mothly gold price per troy ad its sigificat lag. I this research, the ANN model with two hidde layers has bee costructed by usig back propagatio learig (Fig. 1). Sigmoid fuctio is the activatio fuctio used to trai ad calculate the output. The margi of error of the output is determied i order to revise the weight of euros. The learig iteratio is termiated whe the improvemet is ot sigificat. III. HYBRID ANN AND GAS FORECASTING MODEL For the hybrid model, GAs is used to optimize the error by revisig the weight of euros. First ad the foremost, the ANN model is selected based o the lowest root mea squared error (RMSE). The, weight of the euros i ANN is traied by usig GAs operators icludig selectio, crossover, mutatio ad evaluatio. The weight of the euros i the best ANN model are ecoded as strig ad it is evaluated based o the fitess fuctio. Whe it fulfills the termiatio coditio, GAs will stop. Otherwise, it will cotiue with selectio, crossover ad mutatio. The fitess fuctio is based o RMSE equatio (5). Selectio operator i GAs will select the chromosomes from the populatio chromosomes with higher fitess ad pass it to ext geeratio for crossover process. The lower the RMSE, the higher the fitess ad it has higher chace to be selected to ext geeratio. There is a additioal operatio i selectio process, which is elitism process. It is used to prevet the best chromosome lost from selectio process. After the selectio process, GAs cotiue the crossover ad mutatio process. The objective of crossover is to create ew idividual by combiig two idividuals based o the probability. Crossover is adapted to coverge the solutio to certai poit. Sigle-poit crossover is used i this research. Two ew offsprig are formed after the exchage of the strig has bee performed at a sigle-poit of the two parets DOI: 11

3 chromosome. Sigle poit crossover will produce two offsprig. The, mutatio occurs after the crossover process i which it ivolves flippig of some bits i a chromosome to avoid covergece. The flippig of the chromosomes is to geerate a ew chromosome. After oe iteratio, the fitess value will be evaluated ad the evolutioary GAs cycle is termiated whe the satisfied solutio is obtaied [17]. I this research, the optimal combiatio of selectio ratio ad mutatio rate is determied by trial ad error. The model selectio is based o the coefficiet of determiatio value equatio (3) [8]. After the model was built, R 2 value ad RMSE is obtaied. R 2 is used to determie the fitess of the forecastig model i this research. Whe the R 2 value is higher, the more ucertaity is explaied by the model. I additio, RMSE is used for model selectio. RMSE is the square root of the average squared error. The lower the error, the higher the accuracy of the forecastig model. Hece, the model with higher coefficiet of determiatio ad lower RMSE will be chose as the forecastig model. After model is selected, ormality test is doe to esure the model is suitable to be used to forecast mothly gold price per troy ouce. R 2 = 1 (y t y t ) (y t y ) where Y t is the actual observatio value, y t is the forecasted value ad y is the mea of observatio value. (3) V. RESULTS AND DISCUSSIONS ANN Model Buildig: Three ANN models were built by usig sigificat lag of gold price per troy ouce. The ANN 1 s iputs are gold price per troy ouce ad lag 1. While ANN 2 s iputs are gold price per troy ouce ad lag 2 ad ANN 3 has gold price, lag 1 ad lag 2 as iput. The epochs take to build the model 1, 2 ad 3 is 805 epochs, 790 epochs ad 801 epochs respectively as show i Table I. This shows ANN 2 is most efficiet amog the three models. O the other had, R 2 value idicates ANN 1 has better fitess compare to the other two models % of the forecast value is explaied by the mothly gold price per troy ouce ad lag 1 of gold price. However, model 2 has R 2 value 74.88%. This meas that model 2 does ot explai the forecast value as good as model 1. The R 2 value of model 3 falls betwee model 1 ad % of mothly forecastig gold price explaied by the model. The RMSE of ANN 1 is ad it is lowest RMSE amog the three models. Based o the R 2 ad RMSE value, model 1 that cotais mothly gold price ad lag 1 of gold price per troy ouce ca be cocluded as the best model amog the three possible models because it has highest R 2 value ad with lowest RMSE. The the ANN 1 1 will be used to hybrid with GAs. TABLE I: COMPARISON OF ANN TRAINING MODEL Model Iput Variable Epoch RMSE R 2 (%) ANN 1 Gold price, Lag ANN 2 Gold price, Lag IV. FORECASTING ACCURACY MEASURES Performace of the forecastig model is assessed by usig mea absolute error (MAE), mea absolute percetage error (MAPE) ad RMSE. MAE is the average of the absolute error, where the error is the differece betwee the actual observatio value ad the correspodig forecast. The higher the MAE ad RMSE, the lower the accuracy. The value of MAPE is betwee 0% to 100%, where the forecast accuracy is high whe the MAPE is lower. Whe the forecastig model has lower MAE, MAPE ad RMSE value, the more accurate the model is. MAE = t=1 Y t F t RMSE = t=1 (Y t F t )2 Y t MAPE = Y t F t (4) (5) 100 (6) where Y t is the actual observatio value, F t is the forecasted value ad is the umber of o-missig data poits. Aderso-Darlig (AD) test is used to assess the residual of the forecastig model. Whe the p-value of the residual is larger tha 0.05, ull hypothesis is ot rejected, where the residual follows ormal distributio. Normality testig is doe to esure the forecastig model is suitable to be used i the future. ANN 3 Gold price, Lag 1, Lag GA-NN Model Buildig: The weights of euros i ANN 1 is hybridized by usig GAs with differet crossover probability ad mutatio probability. The crossover probability that chose for this research is 0.7 ad 0.8. Moreover, 0.01 ad 0.02 probability were used for mutatio probability. The RMSE for GA-NN 1, GA-NN 2, GA-NN 3 ad GA-NN 4 are 12.37, 1016, ad respectively. GA-NN 2 has the best forecastig performace as it has the lowest RMSE. Moreover, as depicted i Table II, R 2 of GA-NN is 92.18% which is the highest amog the four hybrid models. This idicates GA-NN 2 has higher fitess compare to the other forecastig model. The crossover rate ad mutatio rate of GA-NN 2 is 0.7 ad It is chose to compare the forecastig accuracy with the classical ANN 1. TABLE II: COMPARISON OF GA-NN TRAINING MODEL Model Crossover Mutatio Rate Rate RMSE R 2 GA-NN % GA-NN % GA-NN % GA-NN % DOI: 12

4 VI. COMPARISON OF ANN AND GA-NN FORECASTING MODEL After diagostic checkig o the residual of ANN 1 ad GA-NN 2, both models were used for model testig. From AD test, both models are suitable to be used as they have ormally distributed residuals. The compariso of forecastig performace betwee the two models are made based o MAE, RMSE ad MAPE. Moreover, R 2 is used to determie the fitess of the forecastig model. ANN 1 ad GA-NN 2 forecastig model s MAE value are ad respectively. GA-NN 2 s MAE is lower tha ANN 1 s MAE by Furthermore, ANN 1 s RMSE is While RMSE of GA-NN 2 is which is lower tha ANN s RMSE by I additio, ANN 1 model has the higher MAPE value tha GA-NN 2 model o average, ANN 1 model s forecast is off by %. O the other had, MAPE value of GA-NN 2 is %. By usig R 2 value, GA-NN 2 model has better fitess compare to the ANN 2 model as R 2 of GA-NN 2 is higher tha ANN 1 by 1.14%. As a result, GA-NN forecastig model is outperformed ANN model as it has higher forecastig accuracy ad better fitess. The result shows GAs ca improve the forecastig performace of ANN model because the forecastig performace of GA-NN is outperformed the traditioal ANN forecastig model. GAs is a global searchig techique that is commoly used to geerate high quality solutio. The improvemet of the forecastig model is due to the global search ability of GAs i optimizig the weights of the euros i ANN. GAs prevets ANN falls ito local miima. TABLE III: FORECASTING PERFORMANCE OF ANN AND GA-NN MODEL Model MAE RMSE MAPE R 2 ANN % GA-NN % I short, the gold price per troy ouce has tred from year 1987 to 2016 ad it is quite volatile. Yet the gold price per troy ouce ca be predicted by usig suitable forecastig model. Gold price per troy ouce ad lag 1 of gold price per troy ouce were used for classical artificial eural etwork model ad the hybrid of artificial eural etwork ad geetic algorithm model buildig. As show i the result, hybrid GA-NN model has better forecastig accuracy compare to classical ANN as hybrid GA-NN 2 model has lower MAE, RMSE ad MAPE value. As a result, GA-NN 2 is suggested to be used i forecastig mothly gold price per troy ouce. VII. CONCLUSIONS I this study, two forecastig models are proposed to forecast the gold price per troy ouce for year 1987 to The first forecastig model is classical artificial eural etwork forecastig model with two hidde layers ad 5 hidde odes i each hidde layer traied by back propagatio. The the secod forecastig model has the same architecture with the first forecastig model ad the model is traied by usig geetic algorithms (GAs). GAs is used to optimize the weight of euros i ANN. ANN 1 was used to hybrid with GAs with differet parameter. Four GA- NN models were proposed ad GA-NN 2 was chose as it has best fitess ad accuracy performace. The crossover rate ad mutatio rate used for GA-NN2 were 0.7 ad 0.02 respectively. The R 2 value of GA-NN 2 is which is highest amog the four GA-NN models. I term of forecastig accuracy, GA-NN 2 has the best forecastig performace because it has the lowest RMSE. The RMSE for GANN 2 is GA-NN forecastig model is more accurate compare to ANN model as it has lower MAE, MAPE ad RMSE of both model. Moreover, R 2 of GA-NN is higher tha ANN model by 1.14%. This shows the GA-NN model has better fitess for mothly gold price compare to ANN model. Hece, the forecastig performace of hybrid model of ANN ad GAs is outperformed the covetioal ANN forecastig model. This study ca coclude that GAs ca improve the performace of ANN model because GAs is a global searchig techique that is commoly used to geerate high quality solutio. The results of this research show GA-NN forecastig model is outperformed ANN model with back propagatio learig because GA-NN forecastig model ca produce the mothly gold price forecast with lower error. The improvemet of the forecastig model is due to the global search ability of GAs i optimizig the weights of the euros i ANN. ACKNOWLEDGMENT This article is a part of research coducted by the first author at Departmet of Mathematics ad Statistics, Faculty of Applied Scieces ad Techology, Uiversiti Tu Hussei O Malaysia, Malaysia. The author would like to express sicere gratitude to the Dea ad colleagues of the faculty for their support ad ecouragemet to realize this study. Thaks are also exteded to the aoymous reviewer ad the editor for their costructive cotributios to the mauscript. REFERENCES [1] S. Shafiee ad E. Topal, A Overview of Global Gold Market ad Gold Price Forecastig, Resources Policy, 35(3), pp , [2] H. Mombeii ad A. Yazdai-Chamzii. 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5 [8] H. Mombeii ad A. Yazdai-Chamzii, Modelig Gold Price Via Artificial Neural Network. Joural of Ecoomics, busiess ad Maagemet, 3(7), pp , [9] H. Y. Yami, S. M. Shahidehpour ad Z. Li, Adaptive Short-Term Electricity Price Forecastig Usig Artificial Neural Networks i The Restructured Power Markets. Iteratioal joural of electrical power ad eergy systems, 26(8), pp , [10] A. Khamis, Z. Ismail, K. Haro ad A. T. Mohammed, Neural Network Model for Oil Palm Yield Modelig. Joural of Applied Scieces, 6(2), pp , [11] D. J. Motaa ad L. Davis, Traiig Feedforward Neural Networks Usig Geetic Algorithms. I IJCAI 89, pp , [12] S. Mirmirai, ad H. C. Li, Gold Price, Neural Networks ad Geetic Algorithm. Computatioal Ecoomics, 23(2), pp , [13] K. J. Kim ad I. Ha, Geetic Algorithms Approach to Feature Discretizatio i Artificial Neural Networks for the Predictio of Stock Price Idex. Expert systems with Applicatios, 19(2), pp , [14] K. J. Kim ad I. Ha, Applicatio of A Hybrid Geetic Algorithm ad Neural Network Approach i Activity-Based Costig." Expert Systems with Applicatios, 24(1), pp , [15] M. Nasseri, K. Asghari, ad M. J. Abedii, Optimized Sceario For Raifall Forecastig Usig Geetic Algorithm Coupled With Artificial Neural Network. Expert Systems with Applicatios, 35(3), pp , [16] S. Hayki, ad N. Network, A Comprehesive Foudatio. Neural Networks, 2, pp. 41, [17] M. Mitchell, A itroductio to geetic algorithms. Eglad: MIT press, DOI: 14

CHAPTER 3 RESEARCH METHODOLOGY. Chaigusin (2011) mentioned that stock markets have different

20 CHAPTER 3 RESEARCH METHODOLOGY Chaigusi (2011) metioed that stock markets have differet characteristics, depedig o the ecoomies omie they are relateded to, ad, varyig from time to time, a umber of o-trivial