Forecasing Sock Exchange Movemens Using Arificial Neural Nework Models and Hybrid Models Erkam GÜREEN and Gülgün KAYAKUTLU Isanbul Technical Universiy, Deparmen of Indusrial Engineering, Maçka, 34367 Isanbul, Turkey. erkamguresen@gmail.com kayakulu@iu.edu.r Absrac: Forecasing sock exchange raes is an imporan financial problem ha is receiving increasing aenion. During he las few years, a number of neural nework models and hybrid models have been proposed for obaining accurae predicion resuls, in an aemp o ouperform he radiional linear and nonlinear approaches. This paper evaluaes he effeciveness of neural nework models; recurren neural nework (RNN), dynamic arificial neural nework (DAN) and he hybrid neural neworks which use generalized auoregressive condiional heeroscedasiciy (GARCH) and exponenial generalized auoregressive condiional heeroscedasiciy (EGARCH) o exrac new inpu variables. The comparison for each model is done in wo view poins: MSE and MAD using real exchange daily rae values of Isanbul Sock Exchange (ISE) index XU10). 1. Inroducion The financial ime series models expressed by financial heories have been he basis for forecasing a series of daa in he wenieh cenury. Ye, hese heories are no direcly applicable o predic he marke values which have exernal impac. The developmen of muli layer concep allowed ANN (Arificial Neural Neworks) o be chosen as a predicion ool besides oher mehods. Various models have been used by researchers o forecas marke value series by using ANN (Arificial Neural Neworks). Engle (198) suggesed he ARCH(p) (Auoregressive Condiional Heeroscedasiciy) model, Bollerslev (1986) generalized he ARCH model and proposed he GARCH (Generalized ARCH) model. By considering he leverage effec limiaion of he GARCH model, he EGARCH (Expo-
130 Erkam GÜREEN and Gülgün KAYAKUTLU nenial GARCH) model was proposed (Nelson 1991). Despie he populariy and implemenaion of he ANN models in many complex financial markes direcly, shorcomings are observed. The noise ha caused by changes in marke condiions, i is hard o reflec he marke variables direcly ino he models wihou any assumpions (Roh 007). During he las few years research is focused on improving he ANN s predicion performance. The objecive of his sudy is o compare classical ANN models and new ANN mehodologies wih hybrid ANN models, such as GARCH-ANN and EGARCH- ANN models. The mehods are compared by using MSE (Mean Square Error), MAD (Mean Absolue Deviaion) and % MAD (Mean Absolue % Deviaion). The remaining secions of his paper are organized as follows: Secion provides a brief review of relaed sudies. Secion 3 inroduces he models used in his sudy and Secion 4 provides resuls of each model using daily exchange raes of Isanbul Sock Exchange (ISE) index XU100. Final secion concludes he sudy wih fuure researches.. Brief review of research on ime series ANN models have been used by researchers. A brief lieraure survey is given in Table 1. This survey clearly shows ha ANN mehods ouperform he classical mehods. Hybrid mehods ha use boh classical mehods wih ANN have poenial o avoid deficiencies in classical mehods. Many researchers poined ha hybrid mehods are promising for fuure sudies and wih using hybrid mehods advanages of each mehod can combine.
Forecasing Sock Exchange Movemens 131 Table 1. Financial Time Series Researches (ANN and Hybrid Models)
13 Erkam GÜREEN and Gülgün KAYAKUTLU 3. ANN and Hybrid ANN Models 3.1. Mulilayer Percepron (MLP) This model uses las four values of a ime series as inpus and generaed by using NeuroSoluions 5.06 sofware. MLP has wo layers using anh neurons. The number of neurons in each layer and learning rae are calculaed by geneic algorihm using he same sofware. 3.. Lagged Time Series (LTS) This model is generaed by using NeuroSoluions 5.06 sofware o use lagged values of he financial ime series. LTS has layers wih anh neurons and each layer have lagged connecions. The number of neurons in each layer and learning rae are calculaed by geneic algorihm using he same sofware. 3.3. Recurren Neural Nework (RNN) This model is generaed by using NeuroSoluions 5.06 sofware o have layers wih anh neurons and each layer consising of recurren connecions. The number of neurons in each layer and learning rae are calculaed by geneic algorihm using he same sofware. 3.4. Dynamic Archiecure for Arificial Neural Neworks (DAN) This model is developed by Ghiassi and Saidane (Ghiassi and Saidane 005) and compared wih he classical ANN models using a known ime series (Ghiassi e al. 005). Figure 1 shows he srucure of DAN. DAN uses all inpu daa a a ime o rain he nework. Training begins wih a special F 0 node capures he lineariy using classical linear regression. The raining process sops when a desired level of accuracy is reached. Each ime a nonlinear relaion is hi, a new hidden layer is added. Each hidden layer has 4 nodes: one C node, one CAKE node (in Figure 1, F nodes) and wo CURNOLE nodes (in Figure 1, G and H nodes). A CAKE (Curren Accumulaed Knowledge Elemen) node capures he previous layers using he CAKE node a he previous layer.
Forecasing Sock Exchange Movemens 133 Wih a linear combinaion of CURNOLE (Curren Residual Nonlinear Elemen) nodes, C node and previous CAKE node, exising CAKE node provides he resuls. Unil he desired level of accuracy reached new hidden layers coninue o be added o he model. Afer he special linear layer (F 0 ) DAN uses i s where i is he angle beween he observaion vecor i and a defined reference vecor. DAN uses he rigonomeric ransfer funcions o capure he nonlineariy. Each G and H nodes a layer k uses he given formula: G k (X i ) = Cosine( i i ), H k (X i )=Sine( i i ) [1] Using he given formula of G k (X i ) and H k (X i ) we can use he following formula for F nodes: F k (X i ) = a k + b k F k-1 (X i ) + c k Cosine( i i ) + d k Sinse( i i ) [] Fig. 1. The DAN Nework Archiecure (Ghiassi and Saidane 005)
134 Erkam GÜREEN and Gülgün KAYAKUTLU 3.5. GARCH - ANN Models Mos of he financial series models are known o be easily modelled by GARCH(1,1), so his research uses he exraced variables from GARCH(1,1) as Roh suggess (Roh 007). The GARCH(1,1) has he following formula: = 0 + 1-1 + 1-1 [3] Where is volailiy a, 0 is he non-condiional volailiy coefficien, -1 residual a -1, -1 is he variance a -1. The newly exraced variables are as follows (Roh 007): = 1-1 -1 = 1-1 We use hese new variables as addiional inpus for every ype of ANN given above. 3.6. EGARCH - ANN Models EGARCH has he leverage effec wih he following formula: ln ln 1 1 1 [4] 1 1 Where is he non-condiional variance coefficien, ln is he log value of variance a -1, ( -1 / -1 - (/) ) is he asymmeric shock by leverage effec, and ( -1 / -1 ) is he leverage effec. The newly exraced variables are as follows (Roh 007): ln = ln -1 LE (leverage effec) =( -1 / -1 - (/) ) L(leverage) = ( -1 / -1 ) 4. Forecasing ISE XU100 Index In his research daily sock exchange raes of ISE index XU100 from January 003 o March 008 are used. Graph of he daa is given in figure. Firs 113
Forecasing Sock Exchange Movemens 135 days are used for raining and cross validaion and las 160 used for esing. For hybrid models also new variables exraced from GARCH and EGARCH are calculaed using MS Excel. For MLP, LTS, RNN, GARCH-MLP, GARCH-LTS, GARCH-RNN, EGARCH-MLP, EGARCH-LTS and EGARCH-RNN NeuroSoluions 5.06 sofware is used. For calculaing DAN, GARCH-DAN and EGARCH-DAN MS Excel is used. Resuls are given in able. GARCH-DAN have he smalles raining MSE and MAD, followed by EGARCH-DAN and DAN. In all he oher hybrid models, raining MSE and MAD values are increased. However, GARCH-DAN and EGARCH-DAN have smaller raining MSE and MAD, DAN has smaller esing MSE and MAD. DAN based neural neworks ouperformed he oher neural neworks. Hybrid RNN models decrease he raining error bu increase he esing errors. Fig.. ISE XU100 closing values from January 003 o March 008
136 Erkam GÜREEN and Gülgün KAYAKUTLU Table. Resuls of ANN and Hybrid Models Training Tes MSE MAD MAD % MSE MAD MAD % MLP 33,11.4 431.074.0378 5,540,545.9,04.031 3.87061 LTS 4,040,90. 1,70.136 8.091805 4,053,666. 3,114.716 6.0167 RNN,15,589. 1,073.56 6.18388 30,78,867.0 4,748.948 8.847816 DAN 6,130.4 370.661 1.40897 1,176,015.7 840.700 1.67989 GARCH- MLP 468,83. 514.5.67341 7,14,780.4,317.443 4.38835 EGARCH- MLP 450,787. 51.06.705861 8,651,756.5,547.34 4.797743 GARCH- LTS 4,793,11.9 1,344.516 7.01188 8,679,183.4 8,59.680 15.56614 EGARCH- LTS 7,68,783.3 1,771.43 9.80969 86,388,074.0 8,383.7 15.77058 GARCH- RNN 1,588,036.6 839.538 4.413098 40,95,40.9 5,61.619 10.5457 EGARCH- RNN,331,406.0 806.84 4.5458 46,95,7.1 5,970.485 11.158 GARCH- DAN 61,378.6 370.18 1.4039 1,178,80.5 84.373 1.68031 EGARCH- DAN 61,918. 370.416 1.405955 1,177,07.3 841.188 1.680164 5. Conclusion This sudy is in search for reducing he shorcomings of using ANN in predicing he marke values. Wih his aim Hybrid models are developed and invesigaed. In order o presen he differences in accuracy of predicion, all he models are applied on he same se of daa rerieved from Isanbul Sock exchange. This sudy shows ha DAN is powerful neural nework archiecure. Hybrid models using GARCH and EGARCH can decrease he raining error bu do no guaranee a decrease in esing errors. The lowes error is achieved by DAN based hybrid model, which also shows ha DAN has greaer noise olerance. The achieved resuls indicae ha DAN model is o be focused in he fuure sudies o improve he noise olerance. More aenion is o be given o he hybrid models in defining he hybridizaion procedure clearly.
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