FORECASTING OF CURRENCY OUTFLOW AND INFLOWIN BANK INDONESIA BASED ON TWO LEVEL ARIMAX, FFNN, AND HYBRID

Transcription

1 Inernaional Journal of Managemen and Applied Science, ISSN: Volume-2, Issue-1, Special Issue-1, Oc.-216 FORECASTING OF CURRENCY OUTFLOW AND INFLOWIN BANK INDONESIA BASED ON TWO LEVEL ARIMAX, FFNN, AND HYBRID 1 ANDY FICE HADI, 2 R. MOH. ATOK, 3 SUHARTONO 1,2,3 Deparmen of Saisics, Insiu Teknologi uluh Nopember, Surabaya, 6111, Indonesia 1 andy_hadi@ymail.com, 2 moh_aok@saisika.is.ac.id, 3 suharono@saisika.is.ac.id Absrac: Currency is he rupiah currency issued by Bank Indonesia. As one means of paymen in cash, currency sill plays an imporan role where here are many people who choose o use currency for he purposes of economic ransacions. This is refleced in he increase of money in circulaion (UYD) and he flow of currency hrough Bank Indonesia. Bank Indonesia (BI) is he cenral bank of he Republic of Indonesia. BI is he only insiuion auhorized o circulae he rupiah o he public. Rupiah currency circulaion conduced by Bank Indonesia in accordance wih he need of he money supply. Therefore, forecasing he amoun of circulaion of currency required by BI. In research conduced forecasing he circulaion of currency in Eas Nusa Tenggara (NTT) using ARIMAX, Neural Nework, and hybrid ARIMAX-NN-GARCH. Crieria for selecion of he bes model is calculaed using and smape. Hybrid Model-FFNN ARIMAX is he bes model for forecasing he ouflow of currency while FFNN he model is he bes model for forecasing of currency. Keywords: TWO LEVEL ARIMAX, FFNN, HYBRID ARIMAX-FFNN, OUTFLOW, INFLOW I. INTRODUCTION Currency is he rupiah currency issued by Bank Indonesia (BI). As one means of paymen in cash, currency sill plays an imporan role. BI is he only insiuion auhorized o circulae he rupiah o he public. Increased need for currency usually occurs during periods of religious holidays such as IdulFiri, Chrismas and Chinese New. The need for currency also ends o be high a he end of he year, he school holiday period, and he new school year (Bank Indonesia, 213). Rupiah currency circulaion conduced by Bank Indonesia in accordance wih he need of he money supply. Therefore, proper forecasing of he value of he and ouflow of currency in a monh is required by he cenral bank as he basis for formulaing he need for currency in imes o come. The number of economic and business aciviies are subec o change depending on he number of days in a week. Because of he number of days vary from monh o monh and from year o year, he observaion of economic and business aciviy is influenced by calendar variaions. Effecs of variaion is mainly due o he amoun of he ransacion or working day of each monh, called he effec of working days (Hillmer, Bell and Tiao, 1981; Hillmer, 1982; Bell and Hillmer, 1983; Sullivan, Timmermann and Whie, 21; Al-Khazali, Koumanakos and Pyun, 28; Evans and Speigh, 21). Besides working day effecs, some fesivals or holidays, such as Eid, Easer, Galungan and Chinese New, so he AD calendar is based on he monh and day of he holiday calendar changed in BC each year. Because he business aciviy and consumer paerns can be influenced by holidays, he ime series of observaions can vary depending on wheher a paricular monh here is a holiday or no. Effecs such a calendar effec called holidays (Liu, 1986; Sullivan, Timmermann and Whie, 21; Seyyed, Abraham and Al-Hai, 25; Alagidede 28; Suharono, Lee and Hamzah, 21; Suharono and Lee, 211a). The exisence of he effec of calendar variaions required special handling. Liu (198) is a researcher who firs sudied he effec of variaions in he holiday wih he idenificaion and esimaion of he ARIMA model and sugges modificaions o he ARIMA model o include informaion on he holiday as a deerminisic inpu variables. Model ARIMAX is ARIMA model wih addiional exogenous variables, such as dummy variables for he effec of calendar variaions and deerminisic rend. Calendar variaions could be caused by heir working day variaions or variaions big day a religious / culural specific monh by monh unil he year-onyear (Suharono e al., 21). ARIMA and ARIMAX is one of he mos widely used mehod in he case of forecasing. The sudy uses a model ARIMAX ever underaken by Lee, Suharono, and Hamzah (21), which examines he influence of Eid effec on he sales of clohing Muslim men. Then Suharono, Lee, and Prasesyo(215) conduced a sudy using ARIMAX wo levels o examine he effec of Eid on sales Muslim dress. ARIMA models and ARIMAX an individual model. Zhang (23) inroduced a hybrid model combined linear ARIMA models a level one and a nonlinear model of Neural Nework (NN) a level wo. The hybrid model is used for he ime series daa is rarely found daa ha conain paerns of linear or nonlinear paerns alone bu ofen he daa obained wih he combined linear and nonlinear paerns. According Makridakis and Hibon (2), a hybrid model end o have beer accuracy han he individual models. Many approaches for dealing heerokedasisias. The righ model for analyzing he behavior of his kind is called he Auoregressive Condiional Heeroscedasiciy (ARCH) model. ARCH models firs inroduced by Engle (1982). Bollerslev (1986) enhance ARCH models o include also residual 219

2 Inernaional Journal of Managemen and Applied Science, ISSN: Volume-2, Issue-1, Special Issue-1, Oc.-216 variance in he pas. The model of his Bollserslev laer called Generalized Auoregressive Condiional Heeroscedasiciy (GARCH). Research on forecasing he and ouflow of currency never been done before by Karomah and Suharono (214) using monhly daa and ouflow of currency from 25 o 213 period, he resuls showed ha he bes model o predic neflow currency is a model-based combinaion ARIMAX variaion calendar and model of Auoregressive Disribued Lag (ARDL) -based ransfer funcion. Wulansari and Suharono (214) using daa neflow currency period , he resuls showed ha he model ARIMAX wih he effecs of calendar variaions and predicor variables Consumer Price Index (CPI) is he model wih he bes forecasing currency neflow. II. DETAIL EXPERIMENTAL Table 1.ouflow and characerisics s Mean S. Dev Min Max 252,37 238,81 4,11 158,3 Inflow 16,56 11,44 1,24 76,49 ouflow Daa and s s used in his research is he and ouflow of currency every monh from 23 o 214 in Eas Nusa Tenggara were recorded by Bank Indonesia. Daa will divided ino wo pars, namely in sample daa and ousample daa. Insample daa period saring in uary 23 unil December 213, while he ousample daa period are uary 214 unil December 214. Z : a period 1, Z : Inflow a period 2, Based on he daa exploraion is known ha here are effec of Eid a he he ouflow and of currency in Bank Indonesia Eas Nusa Tenggara. This research will be used ARIMAX wo levels, so ha he dummy variables ha form due o variaions in he calendar and o he seasonal paern is expressed as follows M s, is dummy variable for corresponding uni ime o capure he deerminisic rends, D, for he effec during even a ime and is he number of day before celebraion, D,-1 for he effec a one monh prior o evens 2.2 Analysis procedure 1 and daa modeling using wo level ARIMAX models. 2 and Inflow daa modeling using FFNN models. 3 and daa modeling using Hybrid ARMAX-FFNN 4 Comparing he accuracy of he hree mehod. III. RESULT AND DISCUSSION 3.1 Daa Exploraion These are characerisic of and ouflow daa in Bank Indonesia, Eas Nusa Tenggara Gambar 1Time Series Plo (a) (b) InflowUangKaral In figure 1 i can be seen ha he ouflow and paern conaining he effecs of calendar variaions. If eidaccurs in he mid or end of he mon, he ouflow will be an increase in he accurrence of Eid. Whereas, if Eid occurred a he beginning of he monh, he ouflow will increase in he previous monh. If eidfiri occur in mid or end of he monh, rose o one monh afer he Eid, whereas if Eid occurred in he early monhs, he increased during he monh 3.2 Two Level ARIMAX Model for and Inflow According o he Two Level ARIMAX explained in Two Level ARIMAX ournal [ ], he daa modeled using 132 raining daa. The ARIMAX model is ARIMAX model wih deerminisic rend and seasonal paern. The following resuls are he summary of wo level ARIMAX model for ouflow (Z 1, ) and (Z 2, ). a ARIMAX model for a.1 The firs level model Z 2,1 69 M 2,1 24 M 2, M 2, 41 4 M 1, 1, 2, 3, 4, 2, 5 49 M 2, 74 8 M 2, 6 9 1M 2, 49 5 M 5, 6, 7, 8, 2, 5 58 M 2, 5 76 M 2, 7 1M 3,16 3 M 9, 1, 1 1, 12,, D 2, 3 1D 2,2 8D 3, 9 O 6 3, 1 1 8, 2 9, A, 3 6 (1, B, B, 2 3 B )(1 1 a 1 2, 52 7 B ) 22

3 Inernaional Journal of Managemen and Applied Science, ISSN: Volume-2, Issue-1, Special Issue-1, Oc.-216 a.2 The second level model ˆ 1, ,58727 b ARIMAX model for b.1 The firs level model Z, 65 27, 717M 18,915M 1, 62M 2, 1, 2, 3, 8,828M 7, 758M 7,153M 9, 685M 4, 5, 6, 7, 9, 533M 7, 721M 9, 738M 6,119M 8, 9, 1, 11,,917M 1, 484D 16,179D 1,575D 12,, 1 2, 1 7, 1 8, 654D 1, , 1 D11, 1 18,715D13, 1, 99D18, 1 4, 2D 11, 1D 17,16D 1,98D 2, 1 22, 1 24, 1 29, 1 2, 18D 11, 258D 29,353D 2,178D, 2, 7, 9, 5,139D 5, 925D 9, 695D 2, 713D 11, 13, 18, 2, 1,398D22, -,623D24, 27D27, 1, 444D29, 28,831O 37, 772O 26, , 771O 1, A, A, A, T A, A, (1,86B,15B, 3 B )(1, 331 B ) b.2 The second level model ˆ 1 4,14, 126 ˆ 1 3,8, FFNN model for and Inflow In addiion o using Two Level ARIMAX models, in his research also used he mos popular NN model namely feed forward neural nework (FFNN). For example, he noaion means ha archiecure of FFNN is 3 inpu, 1 neuron in hidden layer, and 1 oupu. The inpu selecion based on he significan lag PACF. Based on he significan lag PACF from ouflow daa, hen he inpu used lag 5 and lag 12.The resul of obained using he FFNN model wih a variaion of he number of hidden neurons, are lised in able 3. Table 3.comparison of accuracy FFNN model for ouflow a Table 4.comparaion of accuracy FFNN model for Model FFNN In-sample Ou-sample ,914 9, ,45 5, ,12 5, ,869 7, ,846 5,29 Based on of insample, FFNN forecasing model wih 4 inpus, 5 hidden neuron, and 1 oupu is FFNN wih 4 inpus, 3 hidden neuron, and 1 oupu is he bes model. 3.4 Model Hibrida ARIMAX-FFNN Hybrid model is a mehod of combinaion of wo or more models in he funcion sysem. Hybrid ARIMAX-FFNN a linear model (ARIMA or ARIMAX) and hen residual modeled by nonlinear models (FFNN). So i is expeced o improve he accuracy of predicion. Firs, ouflow and daa modeled by ARIMAX, hen residual modeled wih FFNN. Inpu for FFNN based on he lag AR model. For ouflow he ARIMAX model is ARIMAX ([1,3,6],,)(1,,) 12, so he inpu for FFNN are lag 1, 3, 6, 12, 15, and lag 18. For, he ARIMAX model is ARIMAX ([1,3,8],,)(1,,) 12, so he inpu for FFNN are lag 1, 3, 8, 12, 13, 15, and lag 2. The resul of obained using Hybrid ARIMAX-FFNN for ouflow and are lised in able 5 and able 6. Tabel 5. Comparison of accuracy Hybrid model for ouflow Model In-sample Ousample ARIMAX-FFNN ,52 13,18 ARIMAX-FFNN ,24 131,34 ARIMAX-FFNN , ,665 ARIMAX-FFNN , ,56 ARIMAX-FFNN , ,233 Based on of insample, Hybrid ARIMAX- FFNN wih 7 inpus, 2 hidden neuron, and 1 oupu is Hybrid ARIMAX-FFNN wih 7 inpus, 3 hidden neuron, and 1 inpu is he bes model Based on of insample, FFNN forecasing model wih 2 inpus, 5 hidden neuron, and 1 oupu is FFNN wih 2 inpus, 2 hidden neuron, and 1 oupu is he bes model. For forecasing, he inpu selecion based on he significan lag PACF oo.based on he significan lag PACF from daa, hen he inpu used lag 1, 5, 6, and lag 12. The resul of obained using he FFNN model wih a variaion of he number of hidden neurons, are lised in able 4 Tabel 6 Model insample Ousample ARIMAX-FFNN ,918 13,319 ARIMAX-FFNN ,514 13,191 ARIMAX-FFNN ,92 13,747 ARIMAX-FFNN ,127 13,225 ARIMAX-FFNN ,751 13,648 Based on of insample, Hybrid ARIMAX- FFNN wih 7 inpus, 5 hidden neuron, and 1 oupu is Hybrid ARIMAX-FFNN wih 7 inpus, 2 hidden neuron, and 1 inpu is he bes model. 221

4 Inernaional Journal of Managemen and Applied Science, ISSN: Volume-2, Issue-1, Special Issue-1, Oc PERFORMANCE EVALUATION For forecas accuracy comparison, Two Level ARIMAX, FFNN, and Hybrid ARIMAX-FFNN, boh in-sample and ou-sample daa, are lised in able 7. The bes model based on he ou-sample accuracy. The bes model is model wih smalles value. Tabel 7. Daa Meode insample ousample ARIMAX 13,813 13,328 FFNN 132,1 186,44 Hibrida 121,24 128,665 Inflow ARIMAX 3,114 12,983 FFNN 6,12 5,75 Hibrida 2,514 13,191 Based on in-sample daa, ARIMAX model mosly yield beer forecas han oher mehod, i.e he bes predicion in Z 1,. moreover based on ousample daa, Hybrid model yield beer forecas han oher mehod. For, based on in-sample daa, Hybrid model mosly yield beer forecas han oher mehod. Moreover base on ou-sample daa, FFNN model mosly yield beer forecas han oher mehod. The elecion of he FFNN models as he bes model in predicing in he daa shows he i is no always ime series mehods are more difficul and has more complexiy level will always reurn forecass are more accurae han a simple mehod. I is he same wih research by Makridarkis and Hibon conained in he resul of M3 compeiion. Addiionally, we can compare he resuls via plos beween acual daa and forecass. Figure 3a, 3b, and 3c show comparison beween ouflow acual daa and each forecas model namely Two Level ARIMAX, FFNN, and Hybrid ARIMAX-FFNN.Figures4a, 4b, and 4c show comparison beween acual daa and each forecas model namely Two Level ARIMAX, FFNN, and Hybrid ARIMAX-FFNN. Figure 4. Time series plo ofouflow acual and forecass by (a) ARIMAX, (b) FFNN, dan (c) Hibrida ARIMAX-FFNN. Inflow Akual Hibrida ARIMAX-FFNN May Agu Aug Ag FFNN Oc ak ual arimax Dec akual ARIMAX 8 7 akual hibrida May Aug Oc Dec akual FFNN Figure 4. Time series plo of acual daa and forecass by (a) ARIMAX, (b) FFNN, dan (c) Hibrida ARIMAX-FFNN Ag 8 6 REFERENCES Ag [1] Alagidede, P. (28). -of-he-year and pre-holiday seasonaliy in African sock markes. Sirling Economics Discussion Paper 28-23, Deparmen of Economics, Universiy of Sirling. 222

5 Inernaional Journal of Managemen and Applied Science, ISSN: Volume-2, Issue-1, Special Issue-1, Oc.-216 [2] Bank Indonesia. (213). LaporanSisemPembayarandanPengelolaanUang 212, Bank Indonesia. [3] Bollerslev. (1986). Generalized Auoregressive Condiional Heeroscedasiciy. Journal of Economerica, 5, [4] Engle, R. F., (1982). Auoregressive Condiional Heeroscedasiciy wih Esimaes of he Variance of Unied Kingdom Inflaion, Economerica, 5, [5] F.J. Seyyed, A. Abraham and M. Al-Hai. (25) Research in Inernaional Business and Finance, 19, [6] Hillmer, S.C., Bell, W.R., and Tiao, G.C. (1981). Modeling Consideraions in headusmen of Economic Time Series. Proceedings of he Conference of Applied Time Series Analysis of Economic Daa. Ed. Arnold Zelner. U.S. Deparmen of Commerce, Bureau of he Census, [7] Hillmer, S.C. (1982). Forecasing Time Series wih Trading Day Variaion. Journal of Forecasing, 1, [8] Liu, L.M. (1986). Idenificaion of Time Series Models in he Presence of Calendar Variaion. Inernaional Journal of Forecasing, 2, [9] Makridakis, S,.danHibon, M. (2). The M3-Compeiion: Resul, Conclusions and Implicaion. Inernaional Journal of Forecasing, 16(4), [1] Sullivan, R., Timmermann, A., Whie, H. (21). Dangers of daa mining: The case of calendar effecs in sock reurns. Journal of Economerics, 15, Mahemaics, Saisics and is Applicaion (ICMSA 21). UniversiiTunku Abdul Rahman, Kuala Lumpur, Malaysia. [11] Suharono, Lee. M.H, danhamzah, N.A (21). Calendar Variaion Model Based on Time Series Regression for Sales Forecas: The Ramadhan Effec. In proceedings of he Regional Conferene on Saisical Sciences, [12] Suharonodan Lee, M. H. (211). Forecasing of ouris arrivals using subse, muliplicaive or addiive seasonal ARIMA Model. Maemaika, 27(2), [13] Suharono, Lee. M.H, danprasyo, D. (215). Two Level ARIMAX and Regression Models For Forecasing Time Series Daa Wih Calender Variaion Effecs. Innovaion and Analyics Conference and Exhibiion (IACE 215). [14] Wulansari, R. E., dansuharono, (214). PeramalanNeflowUangKaraldenganMeode ARIMAX danradial Basis Funcion Nework (SudiKasus Di Bank Indonesia). JurnalSainsdanSeni ITS, 3(2), D73-D78. [15] Zhang, G. P. (23). Time Series Forecasing Using a Hybrid ARIMA and Neural Nework Model. Neurocompuing, 5,