1. Introduction. Do Van Thanh 1 *, Nguyen Minh Hai 2 and Do Duc Hieu 3. Abstract

Transcription

1 Indan Journal of Scence and Technology, Vol (), DOI: /st/08/v/04908, January 08 ISSN (Prnt) : ISSN (Onlne) : Buldng Uncondtonal Forecast Model of Stock Market Indexes usng Combned Leadng Indcators and Prncpal Components: Applcaton to Vetnamese Stock Market Do Van Thanh *, Nguyen Mnh Ha and Do Duc Heu 3 Faculty of Informaton Technology, Nguyen Tat Thanh Unversty; dvthanh@ntt.edu.vn Faculty of Basc Scences, Industral Unversty of Ho Ch Mnh Cty; nguyenmnhhadhcn@uh.edu.vn 3 Faculty of Informaton Technology, Unversty of Scence and Technology of Ha No; Vncentdo30@gmal.com Abstract Obectves: The goal of ths paper s to propose a new approach to buld uncondtonal forecast models of stock market ndexes n the context of hgh dmensonal nput data set. Methods: The methodology of buldng these models s to combne the method of leadng ndcators and the Prncpal Component Analyss technque (PCA) for dmensonalty reducton and to use the multple regresson method on the new data set of reduced dmenson. The real data set collected by month of 93 economc-fnancal varables were used to buld a forecast model of Vetnamese stock market ndex VNINDEX. Fndngs: The absolute error percentage of the out-of-sample forecasts for the next 4 perods of the model bult under the proposed methodology s no more than.6%. Applcatons: The methodology proposed can also be appled to buld the uncondtonal forecast models for the stock prces as well as many other fnancal-economc ndcators. Keywords: Dmensonalty Reducton, Hgh Dmenson Data, Leadng Indcator, PCA, Uncondtonal Forecast Model, Stock Market. Introducton Stock market forecast s very mportant and s always concerned. Stock market forecast ncludes the two man ssues: forecastng the stock market ndex and stock prces. Stock market forecast s alway regarded as a challengng task of the fnancal tme seres forecast process. There had been a lot of varous techncal approaches to forecast stock markets such as Neural Network, Hden Markov Model, Neutro Fuzzy Inference System, Genetc Algorthm, Tme Seres Analyss, Regresson, Rough Set Theory, etc. Some lmtatons of these approaches are also ntroduced 3. In recent years, some machne learnng technques to analyss and forecast stock markets are of nterest more as Mnng Assocaton Rules 4, Prncpal Component Analyss 5, Support Vector Machne 6. It can *Author for correspondence

2 Buldng Uncondtonal Forecast Model of Stock Market Indexes usng Combned Leadng Indcators and Prncpal Components: Applcaton to Vetnamese Stock Market be seen that the approaches presented 8 only forecast the drecton of the stock market, not forecast concrete values for ths market. It can be sad that so far n the forecastng technques gvng concrete forecast values, the regresson technque s stll consdered one of the most mportant technques and most wdely used. The multple regresson technque to buld forecast models of stock market ndexes as well as of stock prces s consdered as the econometrc techque approach 8. Then only a few economc and fnancal varables (measured at dscrete tme ntervals), as well as stock transacton data varables are selected to be explanaton varables n forecast models. Whle number of stocks traded on a stock market n general s very bg and there are also a lot of economc and fnancal varables affectng the volatlty of a stock market. Hence t s mpossble to buld forecast models of stock market ndexes wth full of such explanaton varables. To buld the forecast models of stock market ndexes by the multple regresson method, they usually use a few stated varables to take nto forecast model. The selected varables often have hgh correlaton coeffcents wth the stock market ndex. However, the correlaton coeffcent cannot show the causalty among varables and there are much evdences ndcate that the correlatons are less obvously meanngless 9. In fnancal and economc felds, there usually exst several ndcators (or varables) so that ts fluctuatons have stable relatonshps wth the fluctuatons of some other ndcators 0. These relatonshps are usually found out through forecast models. Therefore, nformaton of some ndcators (called mpact ones) can be used to montor and forecast some other ndcators. The mpact ndcators are classfed nto 3 categores: leadng ndcators, concdent ndcators and laggng ndcators. In buldng forecast models, one nterested especally n the frst categores. Leadng ndcators are often used n early warnng systems and buldng uncondtonal forecast models, here no need to forecast values of explanaton varables n the model, whle concdent ndcators are often used to buld condtonal forecast models, here must forecast future values of explanaton varables before mplementng forecast. The authors have proposed the methodology buldng forecast models of stock market ndexes by days of week 3. In these models, explanaton varables are stock transacton data ones whch are leadng ndcators of a stock market ndex and have a hgh correlaton coeffcent wth ths ndex. Then the bult model s an uncondtonal forecast one. Testng the Vetnamese stock market ndex forecast model bult accordng to ths methodology shows that forecast accuracy by the model s qute hgh. However, accordng to ths approach, only few leadng ndcators are used as explanaton varables, therefore a lot of nformaton n the other leadng ndcators has not taken nto the forecast model yet, whle forecast results by model wll be more accurate f the model has more nformaton 4. Feature selecton ams at dentfyng the most relevant nput varables wthn a dataset. Feature selecton s comprsed of feature evaluaton, feature constructon and feature transformaton. For tme seres data, the am of feature evaluaton s to detect the nput varables and dynamc lags that capture the regular tme seres components of level, trend and/or seasonalty, whle remanng adaptve to change of stochastc components. Feature constructon ams at createng new features from the nput orgnal varables and the goal of feature transformaton n tme seres s to adequate pre-processng of features n order to facltate better modellng 5. Recently there exst some man approaches for feature selecton such as the algorthm of Self-Organzng Indan Journal of Scence and Technology

3 Do Van Thanh, Nguyen Mnh Ha and Do Duc Heu Feature Maps (SOFM), the algorthm explotng the concept of Partal Mutual Informaton (PMI), the technque of Prncpal Component Analyss (PCA), the algorthms for Maxmum Varance Unfoldng (MVU) 6 and combnng flter and wrapper approach, etc., PMI crteron s used to select the regressors whch carry the maxmal non redundant nformaton to be used to buld a forecast model. PMI s the nonlnear statstcal analog of partal correlaton. It represents the nformaton of of two random varables between two observatons that s not contaned n a thrd one. The algorthm SOFM s used to classfy nput vectors (varables) accordng to how they are grouped n the nput space. Flters employ statstcal tests for feature selecton whle wrappers use the underlyng algorthm to compute forecasts for feature subsets. Combnng the flter and wrapper approach as well as usng the algorthms SOFM and PMI for feature selecton for nput data of stock market can not provde nformaton about the causalty between nput varables as well as between these varables wth the stock market ndex. Algorthms for MVU are nonlnear dmensonalty reducton ones 7. These algorthms are used for learnng fathful low dmensonal representatons of hgh dmensonal data by mappng hgh dmensonal nput data to low dmensonal outputs. PCA performs ths mappng by proectng hgh dmensonal data nto low dmensonal subspaces. PCA works very well f the most mportant modes of varablty are approxmately lnear and works poorly f these modes are nonlnear 8. In the case, the nputs are data of the causal varables for the stock market ndex, usng PCA for feature selecton wll be more sutable than the algorthms for nonlnear dmensonalty reducton because the hgh dmensonal observatons (of the causal varables) are very well reconstructed from ther low dmensonal lnear proectons (observatons of the prncpal components), so the most mportant modes of varablty of nput data are approxmately lnear. PCA s a statstcal technque wdely used n data analyss. PCA summarzes a large and complex data set by creatng new varables, whch are lnear combnaton wth weghts of orgnal varables. The new varables are called prncpal components. They are orthogonal to each other; hence there not exst multcollnearty n forecastng equatons havng the explanatory varables to be the prncpal components. Usng Prncpal Components (PCs) has reduced the number of varables n the orgnal data set whle changes n the orgnal data set are stll captured as much as possble. The purpose of ths paper s to propose a methodology buldng uncondtonal forecast models of stock market ndexes wth utlzng nformaton as much as possble of hgh dmensonal nput data set usng combned the method of leadng ndcators and the Prncpal Component Analyss technque for feature selecton and then usng the multple regresson technque to estmate the forecast models n whch the stock market ndexes are dependent varable and selected prncpal components are explanatory varables. In the paper, an uncondtonal forecast model of stock market ndex by month s also bult by applyng the proposed methodology on statstcal data of Vetnamese stock exchange. In fact, the dea of buldng forecast models n ths paper s derved from the hgh frequency forecast model for GDP and CPI n US. In addton, not the same as, the nput data set for buldng forecast model n ths paper not only ncludes the all stock transacton data but also ncludes many other economc and fnancal data. The structure of the paper as follows: The next secton, secton wll ntroduce a methodology buldng uncondtonal forecast models of stock market ndexes by usng combned the leadng ndcator method and prncpal Indan Journal of Scence and Technology 3

4 Buldng Uncondtonal Forecast Model of Stock Market Indexes usng Combned Leadng Indcators and Prncpal Components: Applcaton to Vetnamese Stock Market component analyss technque. Secton 3 wll buld the VNINDEX s forecast model based on the proposed methodology and fnal Secton wll present some conclusons about some pros and cons of the methodology.. Methodology transformed nto statonary. Assume that the all varables Y and X ( =,,..., n) are statonary, test Granger causalty between the varables X and Y accordng to the equatons () and () below: n m Y= ax( ) + by( ) + u () = = The symbol Y s the stock market ndex varable. Y s a T vector varable, Y = (y, y,..., y m), y ( =,,..., m) s value of the stock market ndex Y at the tme pont, m s the number of observatons gathered n a lke dscrete tme ntervals. A = (X,X,...,X n ) s a vector matrx n whch elements are m-dmensonal column vectors. In other words, A= (x ), =,,..., m, =,,..., n, where x s a transacton value at the tme pont of the th stock transacton data varable or value of the th economc or T fnancal varable. Then X = (x, x,..., x m ). Data of the varables Y,X,X,..., X n n m observatons are the nput data to buld the forecast model of stock market ndex Y. The methodology buldng forecast models of stock market ndexes s descrbed n the Fgure and s summarzed as follows: Step : Fnd leadng ndcators of the stock market ndex Y n the set of nput data varables X, X,..., Xn Check the statonary of the all varables: Y and X ( =,,..., n). If a varable s not statonary, t must be p X= cx( ) + dy( ) + u () = = q where, the a, b, c, d are the parameters to be estmated by the OLS regresson method; X(-), Y(-) are varables X lagged steps and Y lagged steps respectvely; n, p, m, q are maxmum lag lengths of the varables X, Y and u( =, ) are resduals assumed to be whte nose. Only there exsts the causal relaton one way from X to n Y f a 0 and = m = d = 0. smlarly, only there exsts the causalty one way from Y to X f a = 0 and n = m d 0. = Varables X and Y are ndependent f a = 0 and m d = 0. When there exsts the causalty from X to Y, = then X s the cause of Y and X s called the leadng ndcator of Y. n = In the step, only the varables X have the causalty one way from X to Y wth hgh statstcal meanng (n general < 0%) are selected. The end result n ths step s to obtan the varables havng stable relatons wth the stock market ndex and are leadng ndcators of ths ndex. 4 Indan Journal of Scence and Technology

5 Do Van Thanh, Nguyen Mnh Ha and Do Duc Heu Fgure. Framework buldng forecast models of stock market ndexes. Indan Journal of Scence and Technology 5

6 Buldng Uncondtonal Forecast Model of Stock Market Indexes usng Combned Leadng Indcators and Prncpal Components: Applcaton to Vetnamese Stock Market Step : Select some varables n the set of the leadng ndcators to buld forecast model If the number of leadng ndcators of Y does not exceed the number of observatons then move to the Step 3 else: Fnd correlaton coeffcents between the stock market ndex Y and the leadng ndcators X ; Select the leadng ndcators havng hgh correlaton coeffcents, whch must exceed a threshold defned by users. Suppose h s the number of selected leadng ndcators, h mn (m, n). No loss of generalty, we assume that X ( =,,..., h) are the leadng ndcators. Then { } X, X,..., Xh s consdered the orgnal set of varables to buld uncondtonal forecast models of stock market ndex. Step 3: Determne the number of prncpal components to retan and retaned prncpal components Determne the correlaton matrx R of the selected leadng ndcators n the Step. Fnd Egen values and egenvectors of the matrx R. Arrange the Egen values n descendng order. Determne the number of prncpal components to retan by usng the commlatve proporton of Egen values. The retaned prncpal components are used to replace the orgnal set of leadng ndcators. The commlatve proporton of Egen values should range from 70% to 90% and then the retaned prncpal components can explan from 70%-90% changes n the orgnal data set. The retaned prncpal components are determned as follows: Assume PC, PC,, PC k are retaned prncpal components. It corresponds to the k largest Egen values and k egenvector V, V... V k respectvely. Vector V I ( =,... k) s the weght vector used to determne the prncpal component PC respectvely. Specfcally each V T s a h-dmensonal vector, V = ( v, v,..., vh ). PC s m-dmensonal vector whch s defned as follows: PC = v * Xˆ + v * Xˆ v * Xˆ (3) h h where, X ˆ s a standardzed vector of X, ˆ x x X = (4) s x, s are the mean and varance of the vector X, respectvely. Step 4: Buld uncondtonal forecast models of stock market ndexes Determne a maxmum lag length for each prncpal component PC by regressng the varable Y on ths prncpal component accordng to the formula: P Y = c + ay ( ) + a PC( ) + u (5) = And applyng the Schwarz Informaton Crteron (SIC) to select the maxmum sgnfcant lag. Dvde the orgnal data set nto two sets followng the observatons. The frst set s used to buld the forecast model and the second set s used to test performance of the bult forecast model. Regress the varable Y on k prncpal components PC, PC,...,PC k on the frst data set accordng to the formula: p p Y = a PC ( ) + a PC ( ) +... = = pk + a PC ( ) + by ( ) + c + u (6) = k k t here, u t s ndependent varable and whte nose, p ( =,,..., k) s the maxmum lag length of the PC respectvely. The estmaton process of the equaton (6) 6 Indan Journal of Scence and Technology

7 Do Van Thanh, Nguyen Mnh Ha and Do Duc Heu s teratve untl all estmated parameters a, b, n the estmated equaton has statstcal meanng (usually under 0%) and the resdual s an ndependent varable and a whte nose. In the estmaton process, the paper consders the resdual as an auto-regresson moved average process ARMA. Evaluatng performance of the bult forecast model s mplemented by usng ths model to forecast the second data set and then comparng the forecasted data wth the actual data n the second set. Its devaton wll ndcate the forecast qualty of ths model. If the forecast errors are small and accepted by users, re-estmate the forecast model on the total observatons and use the model to forecast n the next perods. The modelng s done n the envronment of EVIEW and can easly convert code from EVIEW language to the R one. 3. Applcaton to Vetnammese Stock Market Index 3. Data Set Data set of the 93 varables gathered by month, from January 00 to Aprl 06 (.e. 76 observatons) s used Table. The nput data varables for buldng the forecast model Data Varables propertes Source 78 varables: VNINDEX and 77 transacton data varables of all stocks. Stock codes are used as name of varables. 7 varables: consumer prce ndex (CPI), export turnover (EXP) and mport turnover (IMP), ndex of ndustral producton (IIP), USD prce ndex (USDI), gold prce ndex (GOLDI), exchange rate USD/VND (ER), Reflect the scale and fluctuaton of stock market Reflect the stuaton of domestc economc and fnancal polces FPT securtes center: General Statstcs Offce of Vetnam: varables: long-term lendng nterest rate, lendng nterest rate of three months. Reflect the domestc monetary polcy whch affect nvestment of Internatonal Monetary Fund IMF: external/data Indan Journal of Scence and Technology 7

8 Buldng Uncondtonal Forecast Model of Stock Market Indexes usng Combned Leadng Indcators and Prncpal Components: Applcaton to Vetnamese Stock Market Table Contnued 3 varables: The world prce of crude ol (POIL), rce (PRICE) and the prce of raw materals (PANF) for the agrcultural, forestry and fshery ndustres 3 varables: stock market ndex NASDAD, NIKKEI5, SP500 Reflect the world prces of raw materals affectng the domestc producton and nvestment Reflect the nternatonal economy and nvestments stuaton that affect the domestc stock market NIGEM model, Socal Economc Research Insttute n Brtsh, ac.uk/ Federal Reserve Bank of ST. Lous stlousfed.org/ to buld the forecast model. These varables are shown n the Table. 3. Buldng the Forecast Model Usng logart of natural radx to transform the nput data set and usng orgnal name of varables to name for varables n the transformed data set. Step : Fnd leadng ndcators of the stock market ndex VNINDEX n the set of nput data varables - Usng Augmented Dckey-Fuller test for testng statonary of the nput data varables, we see that the all stock transacton data varables are statonary; IMP varable s the level dfferental staonary, the all remanng fnan- Table. The leadng ndcators of dvnindex and statstcal meanng levels No Varable Meanng level Varable Meanng level Varable Meanng level. BHS *** FPT *** TMS ** BMP *** HPG *** TMT *** 3 BVH * HSG *** TNA *** 4 CII * ITD ** TNT *** 8 Indan Journal of Scence and Technology

9 Do Van Thanh, Nguyen Mnh Ha and Do Duc Heu Table Contnued 5 CLC ** KSA *** TSC *** 6 CTD *** KSB *** TYA ** 7 CTI *** LHG *** VIC ** 8 DAG *** LIX ** VNM *** 9 DHG *** MHC *** VNS *** 0 DLG ** NNC *** VSC *** DMC *** PGD *** dnasdad ** DRC *** SBT *** dnikkei ** 3 DRH *** SHI *** dsp500 ** 4 DVP ** TIE *** dusdi ** cal and economc varables as well as the VNINDEX varable are the level dfferental statonary. Denote dx s the level dfference of the varable X, d(x,) s the level dfference of X. - Testng Granger causalty accordng to the formulas (), () above wth the maxmum lag length for all vaables to be the same and to equal 5 (n = m = p = q = 5), we wll obtan 4 varables that are leadng ndcators of dvnindex wth statstcal meanng levels below 0%. In the 4 these varables there are only 4 economc and fnancal varables, the remanng varables are the stock transacton data ones. (Table ) ndcates the lst of 4 such varables wth meanng levels of hypothess H 0 : Varables n the left column s not Granger cause of dvnindex respectvely below 0%, where *, **, *** are Indan Journal of Scence and Technology 9

10 Buldng Uncondtonal Forecast Model of Stock Market Indexes usng Combned Leadng Indcators and Prncpal Components: Applcaton to Vetnamese Stock Market Table 3. Cummulatve values and proportons of Egen values statstcal meanng levels below 0%, 5% and % respectvely. Step 3: Determne the number of prncpal components to retan and retaned prncpal components Step : Select some varables n set of the leadng ndcators to buld forecast model Because the number of leadng ndcators for dvnin- DEX s 4, smaller than the number of observatons (76), ths step s stopped to move to the Step 3. Determne the correlaton matrx R of 4 varables n the Table. Fnd egenvalues of the matrx R, we wll see that there are egenvalues bgger than, the rest egenvalues are smaller than. It mples that we should select a maxmum of the frst prncpal components to replace the orgnal data set ncludng 4 varables n the Table. 0 Indan Journal of Scence and Technology

11 Do Van Thanh, Nguyen Mnh Ha and Do Duc Heu In more detals, analysng the cummulatve values of the egenvalues n the Table 3 shows that the cummlatve proporton of the frst 9 egenvalues s 7.%. Therefore n order to replace 4 varables n the orgnal data set (Table ) we can use the frst 9 prncpal components correspondng to the frst 9 egenvectors to be explanaton varables n the forecast model of VNINDEX. Then standardze the 4 varables n the Table accordng to the formula (4) and calculate the frst 9 prncpal components accordng to the formula (3) at the 76 observatons by month from January, 00 to Aprl, 06 we wll obtan the these prncpal components. Step 4: Buld uncondtonal forecast model for stock market ndex Regress DVNINDEX on the selected prncpal components accordng to the formula (5) and usng the Schwarz Informaton Crteron to defne the maxmum lag length for each prncpal component, we wll fnd out that the maxmum lag lengths of the prncpal components n the model are manly equal to and not exceedng. To buld and evaluate performance of the forecast model, we dvde the orgnal data set nto two sets. The frst data set ncludes the observatons from January 00 to December 05 to buld the model, the second data set ncludes the remanng observatons (frst 4 months of 06) to test performance of ths model. Regress dvnindex on the frst 9 prncpal components and consder the resdual of the estmated equaton as ARMA model, we get the forecast model n the (Table Table 4. The forecast model of VNINDEX Varable Coeffcent STD Error Meanng level PC(-) *** PC(-) *** PC3(-) * PC6(-) ** PC8(-) *** AR(3) *** MA() ** MA(3) *** R-squared: 0.39; Adusted R-squared: 0.3 DW Stat.:.89; SMPL: 7. Dependent Varable: d(log(vnindex)) Method: Least Squares Indan Journal of Scence and Technology

12 Buldng Uncondtonal Forecast Model of Stock Market Indexes usng Combned Leadng Indcators and Prncpal Components: Applcaton to Vetnamese Stock Market Table 5. % absolute error of forecast results Date VNINDEX VNINDEXF % absolute error 06M M M M ) (Appendx) wth the resdual of the estmated equaton to be the ndependent varable and the whte nose. To evaluate performance of the bult forecast model we use ths model to forecast the VNINDEX n the frst 4 months of 06 year. The percentages of absolute error of the forecast results are shown n the Table 5. We can see that the forecast accuracy s qute hgh. The forecasted result s more accurate f forecast pont s closer to the present tme. Ths also demonstrates the nature of the causalty, t s short-term relatonshps and n general, t changes qute quckly. 4. Concluson The paper has ntroduced brefly the methodology buldng uncondtonal forecast models of stock market by the multple regresson method va usng combned leadng ndcators and the prncpal component analyss to select and to create new varables explanng most of the changes of qute large set of orgnal canddate varables. The proposed methodology can also capture nformaton of unusual fluctuaton of some explanaton varables ncludng quanttatve varables (ts domans are number) as well as qualtatve varables (ts domans are categorcal). Ths methodology s sutable to buld short term forecast models. The forecast model of VNINDEX by month based on the proposed methodology gve forecast results wth qute hgh accuracy. The absolute error percentage of the outof-sample forecasts for the next 4 perods of the model s no more than.6%. Ths accuracy wll decrease f the forecast tme pont s far from the present tme. The forecast model of VNINDEX by month uses the transacton nformaton of all the stocks on the market, but uses only 5 economc-fnancal varables. The reason s that fnancal - economc data by month n Vetnam s not avalable. Ths stuaton s not the same for fnancal - economc data by quarter, year. In other words, buldng the model forecastng stock market ndexes for quarter and year based on the proposed methodology promses better results. Indan Journal of Scence and Technology

13 Do Van Thanh, Nguyen Mnh Ha and Do Duc Heu The methodology buldng uncondtonal forecast models of stock market ndexes n ths paper can be appled to buld short-term uncondtonal forecast models for many other fnancal-economc ndexes. 5. References. And AA, Imam M. The applcaton of fuzzy assocaton rule on co-movement analyze of Indonesan stock prce. Internatonal Conference on Computer Scence and Computatonal Intellgence (ICCSCI). Proceda Computer Scence. 05; 59: Crossref.. Carol AH, Chandrka KM. The selecton of wnnng stocks usng prncpal component analyss. Amercan Journal of Marketng Research. 05 Aug; (3): Cheng LH, Cheng YT. A hybrd SOFM-SVR wth a flterbased feature selecton for stock market forecastng. Expert Systems wth Applcatons. 009 Mar; 36(): Crossref. 4. Crone SF, Kourentzes N. Feature selecton for tme seres predcton a combned flter and wrapper approach for neural networks. Neuro Computng. 00; 73: Crossref. 5. Enders W. Appled Econometrc Tme Seres. 4th Edton. Wley; 04 Oct. 6. Graham E, Granger CWJ, Tmmerman A. Handbook of Economc Forecastng. Elsever BV. 03; :3. 7. Granger CWJ. Investgatng causal relatons by econometrc models and cross-spectral methods. Econometrca. 969 Aug; 37(3): Crossref. 8. Jon S. A tutoral on Prncpal Component Analyss. Verson ; 003 Mar. p Lawrence RK. Background to natonal economc forecasts and the hgh-frequency model of the USA. The Makng of Natonal Economc Forecasts. Edward Elgar, Cheltenham, UK- Northampton; 009. p Luca M, Fammetta O, Rccardo T, Eros P. A feature selecton method for ar qualty forecastng. Internatonal Conference on Artfcal Neural Networks; 00. p Mbeledogu NN, Odoh M, Umeh MN. Stock feature extracton usng Prncpal Component Analyss. Internatonal Conference on Computer Technology and Scence; 0.. Preeth G, Santh B. Stock market forecastng technques: A survey. Internatonal Journal of Advances n Scence and Technology. 04 Sep; (3): Thanh DV, Ha NM. Analyzng and forecastng a stock market ndex by usng leadng ndcators. Proceedngs of the 9th Natonal Conference on Fundamental and Appled Informaton Technology; 06. p Wang Y. Market ndex and stock prce drecton predcton usng machne learnng technques: An emprcal study on the KOSPI and HSI. Internatonal Journal of Busness Intellgence and Data Mnng. 03 Sep; 9(): Wang Z, Sun Y, Stockl P. Functonal prncpal components analyss of shangha stock exchange 50 ndex. Dscrete Dynamcs n Nature and Socety. 04; 04: Wenberger KQ, Saul LK. An ntroducton to nonlnear dmensonalty reducton by maxmum varance unfoldng. AAAI'06 Proceedngs of the st Natonal Conference on Artfcal Intellgence; 006. p Wllam HG. Econometrc Analyss. Prentce Hall, New York; 0. p Fnancal Forecast Center [Internet]. [cted 07 Sep 4]. Avalable from: Indan Journal of Scence and Technology 3