Analysis of I-Series, An Appraisal and Its Models

Transcription

1 Vol. No.2, pp.-, June 203 MODELING TO ANTICIPATE WORLD PRICE OF EACH OUNCE OF GOLD IN INTERNATIONAL MARKETS Mohammad Rikhegar Business Managemen, MA Suden Islamic Azad Universiy, a Souh Tehran Branch Hamed Asgari Business Managemen, MA Suden Islamic Azad Universiy, a Souh Tehran Branch Hamid Bagheri Business Managemen, MA Suden Islamic Azad Universiy, a Souh Tehran Branch Rasoul Ejraee English Language Teaching, MA Suden Islamic Azad Universiy, a Cenral Tehran Branch Hanie kasechi Business Managemen, MA Suden Islamic Azad Universiy, a Souh Tehran Branch Dr. Mahnaz Rabiei Economics, Ph.D Faculy member of Islamic Azad Universiy, a Souh Tehran Branch

2 Vol. No.2, pp.-, June 203 Absrac: Any change in sale price may affec cusomers, disribuers and sellers. Anicipaing fuure prices is one of he bes ways o face appropriaely such hese price changes in he marke. Time series have wide range of applicaion in various fields such as economy, managemen and markeing. Time series is a very imporan ool o analyze a collecion of observaions which are recorded as daily, weekly, monhly and annually repors. In his paper, he world price of each ounce of gold during 338 coninuous monhs are considered (Average per monh) and he arge is o assess he behavior of daa and o release a suiable model for his daa o anicipae world price of each ounce of gold during upcoming monhs by means of analysis of ime series. The firs sep o analyze ime series is o draw daa. Nex sep is o recognize effecive parameers on he series (rend, cycle and seasonal) and o remove hem from ime series and a las o process a saic model on ime series. We drew auocorrelaion funcion (ACF) and parial auocorrelaion funcion (PACF) for daa. Auo-regression model (AR), moving average model (MA) and a combinaion of AR and MA models (ARIMA, ARMA) were seleced as he grade of recogniion model and appropriae model. Afer all sages o analyze ime series and creaion of remained parameers and afer consideraion of finess of represened model, anicipaion of world price of gold for each ounce will ake place. In his regard, he resul of considering he daa in his paper produces informaion for fuure o make appropriae and profiable decision based on curren daa. The process is done by means of MINITAB sofware. Keywords : Time Serise,Forecas, ARIMA,ACF, PACF INTRODUCTION Nowadays, deerminaion and rend of he how of price flucuaions is one of he mos crucial issues being ineresed by financial economiss and analyss and which has been lead o a variey of differen views in his maer.() The reacion owards he changes of producs price is o be one of presence and peneraion in he marke. Any change in sale price may affec cusomers, disribuers and sellers and ha migh pave he way for he governmen s reacions as well. (2). One of he ways for facing appropriaely such flucuaions in prices is o anicipae he producs prices in he fuure. Hisorically, gold has been considered a fronier-less currency, ha may be raded a any ime, virually under all circumsances. Gold proved o be he mos effecive way o collec cash during he sock exchange crash in 987, and once again in 997 and 998 during he Asian crisis. In boh Gulf wars, he demand for gold increased significanly and hence he need o mainain a small proporion of a porfolio in gold could be invaluable in momens when cash is essenial. Is imporance lies in reflecing he expecaions of he invesors, marking he rends and expecaions of growh and decline of he world economies (3). Many derivaives of gold rading in inernaional gold markes are also raded, such as gold fuures, gold opions, gold forward conracs, and so on (4)(). Remarkably, since he price of gold varies wihin a limied range, gold is able o reduce he effec of inflaion, conrol he rise of price and help carry ou consricive moneary policy (Asalakisa & Valavanisb, 2009).(6) 2

3 Vol. No.2, pp.-, June 203 Time series 3 have varian immeasurable applicaions in such fields as saisics and engineering; managemen; weaher; markeing as well as economics and ec. i can be found ha in he real world here are many insances in differen fields in which a collecion of daily, weekly, monhly, and annually observaions are recorded. Time series are regarded as imporan ools in analyzing such observaions. A ime series is a collecion of observaions which has been organized in a chronological order. To pu ha in oher word is ha he ime series are defined as he daa collecion based on an observaion of a phenomenon in a period of ime. Briefly, he purpose of ime series analysis is as,. Exploring and idenifying he probable model of daa, and 2, anicipaing he values of ime series. In a ime series, firs, we recognize he pas behavior of he probable model of series which include he daa, hen we suppose ha he daa will be having he same behavior and be subordinaed by he daa fiing model, herefore; we ry o anicipae he fuure values of ime series. Meanwhile, he modeling of a descripion of a behavior of ime series, mahemaically, includes he following hree general sages as,. idenifying he primary model, 2. esimaing he idenified model s parameers, and 3. invesigaing he model 4.(7) In he sudy, he modeling of ime series is done by Box- Jenkins approach. To analyze he ime series, he wo following approaches are sough as,. he analysis in ime range and, 2. he analysis in frequency range. In he presen sudy, we are o make use of he former approach which is described very briefly below: ime series analysis on he basis of auocorrelaion coefficien is referred o as he analysis in ime range. To do so, we are o use auocorrelaion funcion, auocorrelaion, and parial auocorrelaion for sudying he gradual fulfillmen of a ime series regarding he parameer s paerns. In he curren sudy, we ry o make he whole presen correlaions in observaions ou of a model, since he oher remaining will be uncorrelaed. Saemen of problem and he relevan daa The values of daa concerning he world price of each ounce of gold in Dollar during he coninuous 338 monhs i.e., from he early 98 o he end of February 203, has been aended (Average per monh) o.(8)the purpose is o examine he behavior of daa and o release an appropriae model for he sudy s daa and o presen world price of each ounce of gold during upcoming monhs by means of analysis of ime series.. Granger,C.W.J. Forecasing Sock Marke Price: Lesson For Forecaser, 99 For furher informaion on reference No Cuer, F. (93). Markeing Managemen. 3. Time series 4. Box- Jenkins Time Series Analysis METGHODLOGY 3

4 Vol. No.2, pp.-, June 203 Time series analysis: To draw he daa is he firs sage in ime series analysis and ha is done by using he saisical program i.e., Miniab as he figures shows. (9) Describing behavior of ime series: To deermine parameers of he variable in ime series, and o remove hem for having saic daa, and finally afer having saic daa, some appropriae models on daa go o he daa finess (0). To he figure, i is showed ha he daa have he process and ha means he daa is no saic, herefore; i is needed o make hem saic, firs. Figure : ime series analysis graph A ime series migh be saic in eiher average or correlaion. The proper soluion o make a ime series saic is o differeniae ha ime series. For ha ime series which have a sor of non-saic variance, say, variance is no saic; he suiable resoluion migh be Box-Cox Transformaion. I should be aken ino accoun ha non-saic variance should firs be examined. Where Rounded Value = - 0.0, by using Box-Cox Transformaion 3 for creaing saic daa, he following ransformaion is done on he primary daa: w = /SQRT (X). x Time Series Plo of x Index B o x -C o x P lo o f x 4 0 L o w er C L U p p er C L L am b d a ( u sin g 9.0% c o n fid en c e) 3 E sim ae L o w er C L U p p er C L R o u n d ed V alu e SDev Lim i La mb d a 0 2 To examine saic in variance, we firs are o draw Time Series Plo for W and ACF 4. 4

5 Vol. No.2, pp.-, June 203 T i m e S e r i e s P l o o f w w In d e x Figure 2: graph ime series for variable W A u o c o r r e l a i o n F u n c i o n f o r w ( w i h % s ig n i f ic a n c e li m i s f o r h e a u o c o r r e l a io n s ) Auocorrelaion L a g Figure 3: graph ACF for W. Javadi Sabbaghian, r and Bagher Sharifi Chefield, C. an inroducion on ime series analysis. 3. Box-Cox Transformaion 4. Auo correlaion Funcion As i shows, he values of auocorrelaion funcion have a slow endency owards zero. This ype of behavior resuls in non-saic in ime series average. So i is recommended ha we differeniae he ime series o mee saic. We draw, hen, auocorrelaion and parial correlaion for he differeniaed ime series as below:

6 Vol. No.2, pp.-, June 203 A u o c o r r e l a i o n F u n c i o n f o r d ( w ) ( w i h % s i g n i f i c a n c e li m i s f o r h e a u o c o r r e l a i o n s ) Auocorrelaion L a g Figure 4: graph ACF for dl(w) P a r i a l A u o c o r r e l a i o n F u n c i o n f o r d ( w ) ( w i h % s i g n i f i c a n c e l i m i s f o r h e p a r i a l a u o c o r r e l a i o n s ) Parial Auocorrelaion L a g Figure : graph PACF for dl(w) Alhough here is no seasonal observaion in he graphs, we will no uilize seasonal differeniaion in nex seps. Deermining ype and order of he model and examining he saisical models: Typically, for deermining and recognizing ype and order of he models ACF and PACF 2, here ARIMA, ARMA, AR, MA should be chosen, firs. The huge usage of hese ypes of models could be referred o as heir capaciy in making correlaion 3 among he presen ime values and he pas ime as well as heir simpliciy in srucures.() 6

7 Vol. No.2, pp.-, June 203 Examining he ypes of models Regarding he obained ACF and PACF graphs (fig. 4, fig. ), we ry o examine hem o release a proper model Model fi: Having recognized he experimenal model for ime series, we esimae parameers of model. Since he P-Value, we are no o accep H 0 of he saic saemen, herefore; he gained model is : ARIMA 6 or ARI 6 (,2) d ( B ) W φ2 ( B ) W = θ 0 + Z = θ 0 θ q ( B) Z 2 ( 0.33B B ) w = Z w.33w w w 3 = Z φ ρ + w = / x. Auo correlaion Funcion 2. Parial Auo correlaion Funcion 3. Correlaion 4. Salas e. Al, (996). Auo regressive Inegraed Moving Average 6. Auo regressive Inegraed Examining he model s being proper: N o r m a l P r o b a b ili y P lo R e s i d u a l P l o s f o r w V e r s u s F i s Percen Residual R e s i d u a l F i e d V a l u e H is o g r a m V e r s u s O r d e r Frequency 7 2 Residual R e s i d u a l O b s e r v a i o n O r d e r Figure 6: Residuals Plos for W The Residuals analysis: We ry o use he Residuals analysis of he model fi o examine he model s being proper. If any missing in recognizing he experimenal model, he Residuals analysis shows ha missing. A) examining he normaliy of he Residuals: we accep he Residual hypohesis by considering he 7

8 Vol. No.2, pp.-, June 203 normal probabiliy and Residuals hisogram. B) examining he hypohesis of he variance of Residual s being saic: his hypohesis is acceped regarding he presence of non-consruced in he Residuals versus he fied values 2. C) drawing he Residuals graph versus ime: by drawing he Residuals versus he Order of daa 3 and observing ha he Residuals have no specific srucure, so we accep he model s being proper. D) examining hypohesis of he residuals independence: based on he gained graphs, we accep his hypohesis. Fig. 7: ACF of Residual Plos for w ACF of Residuals for w (wih % significance limis for he auocorrelaions) fig 8: PACF of Residual Plos for w PACF of Residuals for w (wih % significance limis for he parial auocorrelaions) Auocorrelaion Parial Auocorrelaion Lag Lag Ber-Mana es. Based on K2s aken ou of Legs and he value of K2 and based on K2 in a significan level of 0.0 and ye based on he P-Value ou of Legs all of which are > 0.0, i shows ha we rejec he H 0 or, say, non-sufficiency model, and hen, we accep he very model by considering he confidence level of Acceping ha hypohesis means ha ha is a sor of non-correlaion for all correlaions peraining o he Residuals, and his shows sufficiency of he model.. Normal Probabiliy Plo of he Residuals Hisogram of he Residuals 2. Residuals versus he Fied Values 3. Residuals versus he Order of he Daa Choosing model based on AIC crieria : This model is based on he noion ha a model can be chosen, among he oher models, if and only if i has he leas AIC coefficien.(2). In examining a model s being proper, he over fiing approach 3 is aken ino accoun, and since he exra saisic is significan, so we uilize he AIC crieria for recognizing he suiable model. As i shows, he AIC crieria for he firs model is lower, and ye i includes less parameers. So his model is chosen as a suiable model. Table : he AIC value of he models on condiions. 8

9 Vol. No.2, pp.-, June 203 مدل MS AIC (2,,0) (0,,2) (3,,) (3,,2) (2,2,2) Forecasing: In his sudy, we will anicipae he nex six sages by using Miniab Sofware. Since forecasing farher sages are somehow far away from exacness and are no close o realiy, we end o fewer sages which are much probabiliy o realiy. When forecasing he daa, he forecas akes place in average, bu Confidence Limis has he imporance of indicaing he majoriy and minoriy of each daa wheher hey are good. Therefore, Confidence Limis are much beer han he usual forecas. These forecass are relaed o he ransformed ime series. To gain he real ime series forecas, we apply he following formula: w =.33w 0.287w w Z. AIC 2. Mongomery, Johnson, and Gardiner. Forecas and ime series analysis 3. Over Fiing 4. Forecas. Confidence Limis The anicipaed values are in he able as below: Forecas (w) Forecas (X) Upper (X) Lower (X) x = / w ) ( 2 9

10 Vol. No.2, pp.-, June 203 T i m e S e r i e s P l o f o r w ( w i h f o r e c a s s a n d h e i r 9 % c o n f i d e n c e l i m i s ) w T im e CONCLUSION AND SUGGESTIONS If he forecas lass for a long ime and ha is on Confidence Limis, which is imporan no longer because he paern may be changed or may some evens occur and finally change he process of daa moving. 2) he forecas indicaed ha he increasing rend of one monh before reforecas begins has a coninuously process. 3) regarding ha here are some consiuens(a: process or long erm endency, b: rounded changes, c: seasonal changes) which are used for describing behavior of a ime series, ha would beer be recommended he usage of his model o forecas economical issues. 4) making he saisical enry daa saisic as one of he condiions for resolving he forecas problems by using ime series should be considered. ) ype of he eclecic model(ar, MA, ARMA, and ARIMA) as forecas funcion and processing in problems is highly focused and ha can influence he exacness of oupu responses. References Anonino Parisi, Franco Parisi, David D ıaz,2007, Forecasing gold price changes: Rolling and recursive neural nework models, J. of Muli. Fin. Manag., 8, Asalakisa, G. S., & Valavanisb, K. P. (2009). Suveying sock marke forecasing echniques- Chefield, C.(372) an inroducion on Time Series Analysis. Translaed by: Noroumand, H., A., & Bozorgnia, A. Ferdousi Universiy of Mashhad publicaions. Fillip, K. (93). Markeing Managemen. Translaed by: Forouzande, B. Amoukhe publicaions. Granger,C.W.J. Forecasing Sock Marke Price: Lesson For Forecaser, Working Paper; San Diago: Universiy of California, Deparmen of Economics,99,pp Grudniski, G., & Osburn, L. (993). Forecasing S& P and gold fuures prices: an applicaion of neural neworks. Journal of Fuures Markes, 3(6), Javidi Sabbaghian r and bagher Sharifi m.random Modeling Applicaion in River Flow Simulaion and Esimaion of Mean Annual River Discharge by Time Series Analysis.2009 Khalozadeh, H., & Khaki, A. Assessing he Forecasing Sock Price and releasing non-linear Model based on Nerve Nework. Economics Research Journal, 64(43-8), Fall & Winer

11 Vol. No.2, pp.-, June 203 Khorami, M., & Bozorgnia, A. (386). Time Series analysis by means of Miniab Sofware. Sokhan Gosar publicaions. Mongomery, Johnson, & Gardiner. (373). Forecas and Time Series Analysis. By: Faeme, GH., M., T. San ai Universiy of Amirkabir (polyechnic, Tehran). Shafieea, S., & Topalb, E. (200). An overview of global gold marke and gold price forecasing. Resources Policy, 3(3), Par II: Sof compuing mehods. Exper Sysems wih Applicaions,36(3, Par 2), Auhors addresses : Mohammadrikhegar@yahoo.com Hamed.askari@yagoo.com Hamidbb@yahoo.com Rasoulejraee@gmail.com