A New Hybrid Approach For Forecasting Interest Rates

Transcription

1 Avalable onlne at Proceda Computer Scence 12 (2012 ) Complex Adaptve Systems, Publcaton 2 Chan H. Dagl, Edtor n Chef Conference Organzed by Mssour Unversty of Scence and Technology 2012, Washngton D.C. A New Hybrd Approach For Forecastng Interest Rates Davd Enke*, Njat Mehdyev Davd Enke Department of Engneerng Management and Systems Engneerng Mssour Unversty of Scence and Technology Rolla, MO , USA Emal: enke@mst.edu Njat Mehdyev Department of Fnance and Informaton Management Techncal Unversty of Munch & The Unversty of Augsburg 86159, Augsburg, Germany Emal: njat.mehdyev@student.un-augsburg.de Abstract The dynamc, non-lnear, volatle and complex nature of nterest rates makes t hard to predct ther future movements. In order to deal wth these complextes, the authors propose a two-stage neuro-hybrd forecastng model. In the ntal data preprocessng stage, multple regresson analyss s mplemented to determne the varables that have the strongest predcton ablty. The selected varables are then provded as nputs to a Fuzzy Inference Neural Network to forecast future nterest rate values. The proposed hybrd model s mplemented usng data from the U.S. nterest rate market. Keywords: Regresson Analyss, Neural Networks, Interest Rate Forecastng, Hybrd Model 1. Introducton 1.1. Motvaton In addton to stock market predcton, one of the more challengng problems n the fnance area nvolves forecastng the future movements of nterest rates. The nonlnear and dynamc nature of nterest rates, as well as the dscontnutes and hgh frequency mult-polynomal tme seres components complcate the envronment for * Correspondng author. Tel.: E-mal address: enke@mst.edu Publshed by Elsever B.V. Selecton and/or peer-revew under responsblty of Mssour Unversty of Scence and Technology. Open access under CC BY-NC-ND lcense. do: /j.procs

2 260 Davd Enke and Njat Mehdyev / Proceda Computer Scence 12 ( 2012 ) predctng future returns. The nonlnear nature mples that the future nterest rates are related to ther past prces and have a very complcated relatonshp whch makes t hard, but not mpossble, to forecast the future returns. The Random Walk Hypothess mples that the past nterest rate values follow a martngale process, provdng no nformaton about the future, allowng one at best to only predct no change n the returns. LeRoy (1) consders that f the T-bll rates play some role for predctng future T-bll returns, whether small or large, then ther movement cannot be consdered random and the random walk hypothess fals. Followng ths, the results of Larran (2) ndcate that past returns can determne the future nterest rates. Furthermore, the relatonshp of the lagged nterest rates and future returns are nonlnear, but these lagged nterest rates are not the only determnants. The emprcal results of hs study reveal that fundamental factors also have to be consdered when developng nterest rate forecastng models Modelng Approaches There are numerous research frameworks, methodologes, and models that have been mplemented to predct future nterest rates, ncludng usng predctons from the futures market, forecasts usng surveys, no-change forecasts, and predcton wth tradtonal statstcal tools such as regresson analyss, ARIMA, GARCH, VAR, and Bayesan VAR (BVAR). Dorfman and McIntosh (3) suggest that structural econometrcs may not be superor to tme seres technques even when the structural modelers are gven the elusve true model. The nosy and complcated structure of hstorcal nterest rates, the errors n data collecton, tme lags, the recprocal dependency of the nput varables, and the need for the expresson of lngustc varables decrease the predcton ablty of tradtonal statstcal models. Most of these tradtonal models have dffcultes dealng wth non-lnearty, nonstatonary, and the dynamc envronment of nterest rate markets. Wth the ncreasng demand for more sophstcated models to overcome these phenomena, the use of Artfcal Neural Networks (ANN) has ncreased rapdly n part due to ther ablty to deal wth non-lnear problems. The use of ANN for modelng tme seres s also not mpacted by rregular samplng and shortness of the tme seres and has been wdely accepted as a powerful tool for modelng complex nonlnear and dynamc systems. Kang (4) found that ANN forecastng models perform qute well even wth sample szes smaller than 50, whle the Box Jenkns models (ARIMA) typcally requre at least 50 data ponts n order to forecast successfully. Ths data-drven approach s sutable for many emprcal data sets where no theoretcal gudance s avalable to suggest an approprate data generatng process (5). ANNs, partcularly Fuzzy Inference Neural Networks (FINN), are consdered very strong technques for envronments that cannot be easly modeled, even when hstorcal nput-output numercal data exst. Due to ts multdmensonal and non-statonary envronment, nterest rate predcton s very sophstcated and dffcult to model wth mathematcal expressons. Although ANNs offer many advantages over conventonal statstcal tools, there are mportant problems that need to be consdered. The frst lmtaton of ANN modelng s the uncertanty as to whch type of neural network should be chosen. Researchers have conducted numerous studes on neural network modelng for stock and nterest rate predcton, but there s no consensus about whch topology and data model to use. Another lmtaton s related to decreasng relablty, as more complcated networks requre numerous experments to overcome ths problem. The dffculty of ther learnng - to produce an adequate model for complex, multdmensonal, and dynamc systems - s one of the bggest dsadvantages of artfcal neural networks. Complex networks wth multple nputs, output, and hdden neurons wth forward and backward lnks can have very complex parametrc error functon spaces. There can also be a lmtaton related to the requred data structure. In general, the more data that s avalable, the more precse the results that are provded to and are delvered by the neural network. Ths can be a problem when there s not enough data to properly tran the network, as mght be the case for a new stock or new nterest rate product. Another lmtaton of neural network modelng concerns data desgn. Dfferent users tend to use dverse modelng approaches wthout followng the benchmark. Bured nose, and the complex dmensonalty of the nterest rate market, can also make t dffcult to learn or re-estmate the ANN parameters (6). Fnally, ANNs tend to suffer overfttng problems, reducng ther generalzaton ablty when they have been traned too long on the same dataset. Exstng gradent descent-based local search technques (e.g. error back-propagaton and modfcatons) are not effcent n fndng an adequate soluton n hghly mult-parametrc and mult-extreme search space of the network error functon. However, wth recent developments n the area of evolutonary computaton, new search/optmzaton algorthms, such as Dfferental Evoluton (DE) (7) and Partcle Swarm Optmzaton (PSO) (8), have been made avalable and are perfectly sutable to utlze as learnng tools for speedng up soluton of search

3 Davd Enke and Njat Mehdyev / Proceda Computer Scence 12 ( 2012 ) problems n contnuous numercal spaces. Alev, et al, (9) have suggested a Fuzzy Neural Network (FNN) wth a Dfferental Evoluton-based learnng algorthm for outperformng many exstng models and for solvng such problems as dentfcaton and control of dynamc systems and forecastng. The FNN can accept both crsp and fuzzy values as ts nput. Neuro-Fuzzy models allow researchers to use both quanttatve and qualtatve factors as nput varables Research Purpose The purpose of ths research s to develop a model to predct future nterest rates, n partcularly 3-month T-bll rates. The Root Mean Square Error (RMSE) s reported to measure model performance. In order to model the nterest rate markets, a Dfferental Evoluton-based Fuzzy Inference Neural Network s utlzed to elmnate the drawbacks of tradtonal artfcal neural networks and subsequently offer a superor predcton system to prevously mentoned conventonal statstcal technques. All exstng research n the nterest rate predcton area s based ether on techncal factors that refer to the past values of the nterest rates, or fundamental factors that mply that the varous economc and fnancal varables are determnants of the future returns. As dstngushed from the majorty of the work done n ths area, the authors also consder the conjuncton of the fundamental factors wth the hstorcal returns of the nterest rates (techncal factor) to get more precse results. The volatlty present n both the techncal and fundamental factors that nfluence the nterest rate markets and ther dynamc envronment requres a good grasp of whch varables have a stronger ablty to descrbe the tendences n nterest rates. Therefore, the proposed model s extended to nclude data preprocessng wth regresson analyss. 2. Proposed Model and Emprcal Results As mentoned n the ntroducton, ths paper ntroduces a new hybrd artfcal neural network model that ntegrates a Dfferental Evoluton Optmzaton-based (DE) Fuzzy Inference System wth Multple Regresson Analyss for predctng 3-month T-bll rates. As llustrated n Fgure 1, there are two stages of the proposed hybrd model. The frst stage reduces the varable sze by usng Multple Regresson Analyss (MRA) to select varables that are hghly correlated wth nterest rate returns and therefore should have strong predcton ablty. In the second stage of the proposed model, a Fuzzy Inference Neural Network, s utlzed for predctng future nterest rate returns usng the varables chosen from the frst stage. Fgure 1. Proposed Model 2.1. Multple Regresson Analyss Retanng hgh nformaton content, varable selecton s one of the most mportant ssues n stock market predcton. Stage 1 of the proposed model nvolves reducng the dmensonalty of the nput varable dataset by elmnatng varables wth weaker forecastng ablty. In the frst stage of the nterest rate predcton model, numerous varables can be chosen as nput to the hybrd model. For the proposed model, 20 dfferent fnancal and economc varables, ncludng leadng economc ndcators as well as non-lnear varants of hstorcal nterest rate returns, were ncluded to the regresson analyss. The quarterly data cover the perod from June 1960 to January 2011, for a total of 208 data ponts.

4 262 Davd Enke and Njat Mehdyev / Proceda Computer Scence 12 ( 2012 ) The results of the regresson analyss have kept the followng varables for the second stage: M2 (t-2) (Money Supply) GNP (t) (Gross Natonal Product) CPI (t-1) (Consumer Prce Index) FFR (t) (Federal Funds Rate) SP 500 (t-1) (Standard and Poor 500 Market Index) r² (t) (Squared 3-month T-bll rate of the current month) r³ (t) (Cubed 3-month T-bll rate of the current month) The combnaton of these varables ndcates hgh correlaton wth the 3-month T-bll rate of the next quarter, r (t+1). The sgnfcance level s much less than 0.05 (5% false-postve rate), whle R 2 = , mplyng that the model provdes a good ft (R = , adjusted R 2 = ) Fuzzy Inference Neural Network The Fuzzy Inference Neural Network that was mplemented n Stage 2 has fve layers, n addton to the varous nputs and the defuzzfed output (see Fgure 2). The frst layer of the model conssts of membershp functons that map nputs to the fuzzy terms used n the rules. The second layer comprses nodes representng these rules. Each rule node performs the Mn operaton on the outputs of the ncomng lnks from the prevous layer. The thrd layer conssts of output membershp functons. The fourth layer computes the fuzzy output sgnal for the output varables. Fnally, the ffth layer provdes an output usng the Center-of-Gravty (COG) defuzzfcaton technque. Fgure 2. Fuzzy Inference Neural Network The fuzzy nference process can be descrbed usng the followng steps: 1. For each rule level of valdty, defne the precondtons n mn[max( A ( x ) A ( x )) where A j ( x j ) j 1 X j are new ndependent values of nput varables 2. For each rule calculate the ndvdual outputs B ( y) j max( B ( y), B ( y),..., B 1 j 2 j j m ( y))

5 Davd Enke and Njat Mehdyev / Proceda Computer Scence 12 ( 2012 ) Calculate the aggregatve output: B ( y) mn(, B ( y)) The network was traned usng a data holdout procedure. A total of 138 of the avalable 208 data ponts were used for tranng the network. The remanng 70 data ponts were used for testng. The expermental results ndcate that the Fuzzy Inference Neural Network model wth Multple Regresson Analyss acheves a good performance wth RMSE = Fgure 3 llustrates both the real and predcted values of the 3-month T-bll rates r(t+1) 4 3 real forecast Date Fgure 3. Real Versus Predcted Values of the 3-month T-bll Rates 3. Concluson and Future Work For ths research, a hybrd Multple Regresson and Fuzzy Inference Neural Network model for nterest rate forecastng was proposed and developed. Durng the frst stage of the model, the number of the varables s reduced usng multple regresson analyss, keepng only those varables that have strong predcton ablty. One of the man dfferences to the exstng models s the combnaton of the techncal and fundamental factors. The followng fve fundamental and two techncal factors were selected as nput to the Fuzzy Inference Neural Network n order to predct the nterest rate returns for the followng perod: M2 (t-2) (Money Supply) GNP (t) (Gross Natonal Product) CPI (t-1) (Consumer Prce Index) FFR (t) (Federal Funds Rate) SP 500 (t-1) (Standard and Poor 500 Market Index) r² (t) (Squared 3-month T-bll rate of the current month) r³ (t) (Cubed 3-month T-bll rate of the current month) The model acheves a good performance wth an RMSE value of To extend the current research, dfferent data preprocessng technques other than regresson analyss can be selected and emprcally analyzed to determne whch model and/or technque may mprove the results. In addton, before predctng future nterest rate returns, the varable data from Stage 1 of the model can be clustered and the extracted rules from the clusters can be provded as nput to Stage 2. Implementaton of dverse types of neural networks, such as fuzzy type 2 neural networks, can also be tested n order to determne ther effect on mprovng the results of the model.

6 264 Davd Enke and Njat Mehdyev / Proceda Computer Scence 12 ( 2012 ) References 1. LeRoy, F. S., Effcent Captal Markets and Martngales, Journal of Economc Lterature, Vol. 27, No. 4 (1989): Larran, M., Testng Chaos and Nonlneartes n T-Bll Rates, Fnancal Analysts Journal, Vol. 47, No. 5 (1991): Dorfman, J.H. and C.S. McIntosh, Results of a prce forecastng competton, Amercan Journal of Agrcultural Economcs, Vol. 72 (1990): Kang, S., An Investgaton of the Use of Feed forward Neural Networks for Forecastng, Ph.D. Thess, Kent State Unversty, Khashe M., S.R. Hejaz, and M. Bjar A new hybrd artfcal neural networks and fuzzy regresson model for tme seres forecastng, Fuzzy Sets and Systems, Vol. 159 (2008): Km, K.J., and I. Han, Genetc algorthms approach to feature dscretzaton n artfcal neural networks for the predcton of stock prce ndex, Expert Systems wth Applcatons, 19 (2000): Thlo, F., M. Grauer, and C. Müller, Parallel Drect Search Methods for Optmzaton Servces n Grd Computng, Fronters Scence Seres, Unversal Academy Press, Vol. 1, No. 49 (2007): Thlo, F., M. Grauer, R. Menzel, and C. Müller, On Scalablty of Dstrbuted Smulaton and Optmzaton of Formng Processes, AIP Conference Proceedngs, Vol. 908, No. 2 (2007): Alev, R.A., B.G. Gurmov, B. Fazlollah, and R.R. Alev, Evolutonary algorthm-based learnng of fuzzy neural networks. Part 2: Recurrent fuzzy neural networks, Fuzzy Sets and Systems, Vol. 160, Issue 17 (2009):