Yıl 2013,
Cilt: 5 Sayı: 2, 53 - 69, 01.09.2013
### Öz

### Anahtar Kelimeler

### Kaynakça

ANN (Artificial Neural Network) models and Spline techniques have been applied to economic analysis, to handle economic problems, evaluate portfolio risk and stock performance, and to forecast stock exchange rates and gold prices. These techniques are improving nowadays and continue to serve as powerful predictive tools. In this study, we compare the performance of ANN models and Bayesian Spline models in forecasting economic datasets. We consider the most commonly used ANN models, which are Generalized Regression Neural Networks (GRNN), Multilayer Perceptron (MLP), and Radial Basis Function Neural Networks (RBFNN). We compare these models using BayesX and Statistica software with three important economic datasets: on the exchange rate of Turkish Liras (TL) to Euro, exchange rate of Turkish Liras (TL) to United States Dollars (USD), and Gold Price for Turkey. With these three economic datasets, we made a comparative study of these models, using the criterions MSE and MAPE to evaluate their forecasting performance. The results demonstrate that the penalized spline model performed best amongst the spline techniques and their Bayesian versions. Amongst the ANN models, the MLP model obtained the best performance criterion results.

Artificial Neural Networks Bayesian Spline Models Exchange Rates.

- Aladag, C.H., M.A. Basaran, E. Egrioglu, U. Yolcu and V.R. Uslu (2009). Forecasting in high order fuzzy times series by using neural networks to define fuzzy relations. Expert Systems with Applications, 36, 4228‒4231.
- Asma, S., A. Sezer and O. Ozdemir (2012). MLR and ANN models of significant wave height on the west coast of India. Computers & Geosciences, 49, 231‒237.
- Audrino, F. and P. Bühlmann (2009). Splines for financial volatility. Journal of the Royal Statistical Society. Series B, 71, 655‒670.
- Basci, S., A. Zaman and A. Kiraci (2010). Variance Estimates and Model Selection. International Econometric Review, 2 (2), 57‒72.
- BayesX (2011). http://www.stat.uni-muenchen.de/~bayesx/ (accessed January 20, 2011).
- Biller, C. (2000). Adaptive Bayesian Regression splines in semi parametric generalized linear models. Journal of Computational and Graphical Statistics, 9 (1), 122‒140.
- Bishop, C.M. (1995). Neural Networks for Pattern Recognition. Oxford: Oxford University Press.
- Craven, P. and G. Wahba (1979). Smoothing Noisy Data with Spline Functions. Numerische Mathematik, 31, 377-403.
- De Boor, C. (1978). A Practical Guide to Splines. New York: Springer-Verlag.
- Dierckx, P. (1993). Curve and Surface Fitting with Splines. Oxford: Clarendon Press.
- Egrioglu, E., C.H. Aladag, U. Yolcu, V.R. Uslu and M.A. Basaran (2009). A new approach based on artificial neural networks for high order multivariate fuzzy time-series. Expert Systems with Applications, 36, 10589‒10594.
- Eilers, P.H.C. and B.D. Marx (1996). Flexible smoothing using B-splines and penalized likelihood (with comments and rejoinders). Statistical Science, 11 (2), 89‒121.
- Eilers, P.H.C. and B.D. Marx (1998). Direct generalized additive modeling with penalized likelihood. Computational Statistics and Data Analysis, 28, 193‒209.
- Fahrmeir, L. and S. Lang (2001). Bayesian Inference for generalized additive mixed models based on Markov Random Field Priors. Journal of the Royal Statistical Society C (Applied Statistics), 50, 201‒220.
- Green, P.J. and B.M. Silverman (1994). Nonparametric regression and generalized linear models. London: Chapman and Hall.
- Greiner, A. and G. Kauermann (2007). Sustainability of U.S. Public Debt: Estimating smoothing spline regressions. Economic Modelling, 24 (2), 350‒364.
- Greiner, A. (2009). Estimating penalized spline regressions: theory and application to economics. Applied Economic Letters, 16 (28), 1831‒1835.
- Hastie, T.J. and R.J. Tibshirani (1990). Generalized Additive Models. Chapman & Hall/CRC.
- Haykin, S. (1999). Neural Networks: A Comprehensive Foundation. Prentice Hall, 1‒823.
- Hill, T. and P. Lewicki (2007). STATISTICS: Methods and Applications, StatSoft. Tulsa: OK.
- Hobert, J. and G. Casella (1996). The Effect of Improper priors on Gibbs Sampling in Hierarchical Linear Mixed Models. Journal of the American Statistical Association, 91, 1461‒1473.
- Jang, J.S.R. and C.T. Sun (1993). Functional Equivalence Between Radial Basis Function Networks and Fuzzy Inference Systems. IEEE Transactions on Neural Networks, 4 (1), 156‒159.
- Jang, J.S.R., C. T. Sun and E. Mizutani (1997). Neuro-Fuzzy and Soft Computing. New Jersey: Prentice-Hall.
- Lang, S. and A. Brezger (2001). Bayesian P-splines. Journal of Computational and Graphical Statistics, 13, 183‒212.
- Lee, M.-J. and Y.-K. Choi (2001). An Adaptive Control Method for Robot Manipulators using Radial Basis Function Networks. In Industrial Electronics, IEEE International Symposium, Pusan, South Korea, 3, 1827‒1832.
- Makridakis, S., S.C. Wheelwright and V.E. McGee (1983). Forecasting: Methods and Applications. 2nd ed. New York: John Wiley.
- Makridakis, S., C. Chatfield, M. Hibon, M. Lawrence, T. Mills, K. Ord and L.F. Simmons (1993). The M2-Competition: A real-time judgmentally based forecasting study. International Journal of Forecasting, 9, 5‒22.
- Mammone, R.J. and Y.Y. Zeevi (1991). Neural Networks: Theory and Applications. San Diego, CA: Academic, 1‒376.
- McCulloch, W.S. and W. Pitts (1943). A logical calculus of the ideas immanent in neurons activity. Bulletin of Mathematical Biophysics, 5, 115‒133.
- Moody, T. and C. Darken (1989). Fast learning in networks of locally tuned processing units. Neural Computation, 1, 281‒194.
- Mori, H. and A. Awata (2007). Data Mining of Electricity Price Forecasting with Regression Tree and Normalized Radial Basis Function Network. In IEEE Transactions on Systems, Man, and Cybernetics, IEEE International Conference, 3743‒3748.
- Mostafa, M.M. (2010). Forecasting stock exchange movements using neural networks: Empirical evidence from Kuwait. Expert Systems with Applications, 37 (9), 6302‒6309.
- Narendra, K.S. and K. Parthasarathy (1990). Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks, 1 (1), 4‒27.
- Nizamitdinov A., M. Memmedli and O. Ozdemir (2010a). Comparison Study of P-Spline and Univariate Additive Model (Cubic Smoothing Spline) in Time-Series Prediction. In 24th. Mini EURO Conference on Continuous Optimization and Information-Based Technologies in the Financial Sector (MEC EurOPT 2010), İzmir, TURKEY, Vilnius "Technika" 2010 (ISI proceedings), 34-39.
- Nizamitdinov A., M. Memmedli and O. Ozdemir (2010b). Time Series Forecasting Using Fuzzy Time Series Approach, Neural Network Models and Regression Splines. In 24th European Conference on Operational Research (EURO XXIV LISBON), Lisbon, Portugal, 257.
- Ord, K., M. Hibon and S. Makridakis (2000). The M3-Competition. International Journal of Forecasting, 16, 433‒436.
- Refenes, A.P.N. (1995). Neural Networks in the Capital Markets. New York: John Wiley & Sons.
- Renals, S. and R. Rohwer (1989). Phoneme classification experiments using radial basis functions. In Proceedings of International Joint Conference on Neural Networks, Washington, DC, 461‒467.
- Rumelhart, D.E. and J.L. McClelland (1986). Parallel Distributed Processing, Cambridge, MA: MIT Press.
- Rumelhart, D.E., G.E. Hinton and R. J. Williams (1986). Learning internal representations by error propagation. In Parallel distributed processing: explorations in the microstructure of cognition, ed. D.E. Rumelhart and J.L. McClelland. Cambridge, MA: MIT Press, 318–362.
- SFB386 (2011). http://www.stat.uni-muenchen.de/sfb386/ (accessed January 20, 2011).
- TCMB (2011). http://www.tcmb.gov.tr (accessed January 20, 2011).
- Trenn, S. (2008). Multilayer Perceptrons: Approximation Order and Necessary Number of Hidden Units, IEEE Transactions on Neural Networks, 19 (5), 836‒844.
- Vaughn, M.L. (1999). Derivation of the Multilayer Perceptron Weight Constraints for Direct Network Interpretation and Knowledge Discovery. Neural Networks, 12, 1259‒1271.
- Virili, F. and B. Freisleben (2000). Nonstationarity and data preprocessing for neural network predictions of an economic time-series. In IJCNN 2000, Proceedings of the IEEE-INNS- ENNS International Joint Conference on Neural Networks, 5, 129‒134.
- Wagener, T., H.S. Wheater and H.V. Gupta (2004). Rainfall-Runoff Modelling in Gauged and Ungauged Catchments. London: Imperial College Press.
- Wang, L.-X. (1994). Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Englewood Cliffs, NJ: Prentice-Hall.
- Wang, L.-X. (1996). Stable adaptive fuzzy controllers with application to inverted pendulum tracking. IEEE Transactions on Systems, Man, and Cybernetics- Part b: Cybernetics, 26 (5), 677‒691.
- Wasserman, P.D. (1993). Advanced Methods in Neural Computing. New York: Van Nostrand Reinhold.
- Weigend, A., B.A. Huberman and D.E. Rumelhart (1992). Predicting Sunspots and Exchange Rates with Connectionist Networks, Nonlinear Modelling and Forecasting. Redwood City, CA: Addison-Wesley.
- White, H. (1988). Economic Prediction Using Neural Networks: the Case of IBM Daily Stock Returns. In Proceedings of the 1988 IEEE International Conference on Neural Networks, 2, 451‒458.
- Wong, S.P. and T.-L. Lai (2004). Spline models in time-series analysis. In Abstract Book of International Conference on Threshold Models and New Developments in Time-series. Department of Statistics and Actuarial Science University of Hong Kong, 27.
- Wood, S.N. (2003). Thin plate regression splines. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65, 95‒114.
- Wood, S.N. (2006). Generalized additive models: an introduction with R. London: Chapman and Hall.
- Zhang, G., B.E. Patuwo and M.Y. Hu (1998). Forecasting with artificial neural networks: The state of art. International Journal of Forecasting, 14, 35‒62.
- Zhang, L. and B. Zhang (1999). A Geometrical Representation of McCulloch-Pitts Neural Model and Its Applications. IEEE Transactions on Neural Networks, 10 (4), 925‒929.
- Zhang, G.P. and M. Qi (2005). Neural network forecasting for seasonal and trend time-series. European Journal of Operational Research, 160 (2), 501‒514.

Yıl 2013,
Cilt: 5 Sayı: 2, 53 - 69, 01.09.2013
### Öz

### Kaynakça

- Aladag, C.H., M.A. Basaran, E. Egrioglu, U. Yolcu and V.R. Uslu (2009). Forecasting in high order fuzzy times series by using neural networks to define fuzzy relations. Expert Systems with Applications, 36, 4228‒4231.
- Asma, S., A. Sezer and O. Ozdemir (2012). MLR and ANN models of significant wave height on the west coast of India. Computers & Geosciences, 49, 231‒237.
- Audrino, F. and P. Bühlmann (2009). Splines for financial volatility. Journal of the Royal Statistical Society. Series B, 71, 655‒670.
- Basci, S., A. Zaman and A. Kiraci (2010). Variance Estimates and Model Selection. International Econometric Review, 2 (2), 57‒72.
- BayesX (2011). http://www.stat.uni-muenchen.de/~bayesx/ (accessed January 20, 2011).
- Biller, C. (2000). Adaptive Bayesian Regression splines in semi parametric generalized linear models. Journal of Computational and Graphical Statistics, 9 (1), 122‒140.
- Bishop, C.M. (1995). Neural Networks for Pattern Recognition. Oxford: Oxford University Press.
- Craven, P. and G. Wahba (1979). Smoothing Noisy Data with Spline Functions. Numerische Mathematik, 31, 377-403.
- De Boor, C. (1978). A Practical Guide to Splines. New York: Springer-Verlag.
- Dierckx, P. (1993). Curve and Surface Fitting with Splines. Oxford: Clarendon Press.
- Egrioglu, E., C.H. Aladag, U. Yolcu, V.R. Uslu and M.A. Basaran (2009). A new approach based on artificial neural networks for high order multivariate fuzzy time-series. Expert Systems with Applications, 36, 10589‒10594.
- Eilers, P.H.C. and B.D. Marx (1996). Flexible smoothing using B-splines and penalized likelihood (with comments and rejoinders). Statistical Science, 11 (2), 89‒121.
- Eilers, P.H.C. and B.D. Marx (1998). Direct generalized additive modeling with penalized likelihood. Computational Statistics and Data Analysis, 28, 193‒209.
- Fahrmeir, L. and S. Lang (2001). Bayesian Inference for generalized additive mixed models based on Markov Random Field Priors. Journal of the Royal Statistical Society C (Applied Statistics), 50, 201‒220.
- Green, P.J. and B.M. Silverman (1994). Nonparametric regression and generalized linear models. London: Chapman and Hall.
- Greiner, A. and G. Kauermann (2007). Sustainability of U.S. Public Debt: Estimating smoothing spline regressions. Economic Modelling, 24 (2), 350‒364.
- Greiner, A. (2009). Estimating penalized spline regressions: theory and application to economics. Applied Economic Letters, 16 (28), 1831‒1835.
- Hastie, T.J. and R.J. Tibshirani (1990). Generalized Additive Models. Chapman & Hall/CRC.
- Haykin, S. (1999). Neural Networks: A Comprehensive Foundation. Prentice Hall, 1‒823.
- Hill, T. and P. Lewicki (2007). STATISTICS: Methods and Applications, StatSoft. Tulsa: OK.
- Hobert, J. and G. Casella (1996). The Effect of Improper priors on Gibbs Sampling in Hierarchical Linear Mixed Models. Journal of the American Statistical Association, 91, 1461‒1473.
- Jang, J.S.R. and C.T. Sun (1993). Functional Equivalence Between Radial Basis Function Networks and Fuzzy Inference Systems. IEEE Transactions on Neural Networks, 4 (1), 156‒159.
- Jang, J.S.R., C. T. Sun and E. Mizutani (1997). Neuro-Fuzzy and Soft Computing. New Jersey: Prentice-Hall.
- Lang, S. and A. Brezger (2001). Bayesian P-splines. Journal of Computational and Graphical Statistics, 13, 183‒212.
- Lee, M.-J. and Y.-K. Choi (2001). An Adaptive Control Method for Robot Manipulators using Radial Basis Function Networks. In Industrial Electronics, IEEE International Symposium, Pusan, South Korea, 3, 1827‒1832.
- Makridakis, S., S.C. Wheelwright and V.E. McGee (1983). Forecasting: Methods and Applications. 2nd ed. New York: John Wiley.
- Makridakis, S., C. Chatfield, M. Hibon, M. Lawrence, T. Mills, K. Ord and L.F. Simmons (1993). The M2-Competition: A real-time judgmentally based forecasting study. International Journal of Forecasting, 9, 5‒22.
- Mammone, R.J. and Y.Y. Zeevi (1991). Neural Networks: Theory and Applications. San Diego, CA: Academic, 1‒376.
- McCulloch, W.S. and W. Pitts (1943). A logical calculus of the ideas immanent in neurons activity. Bulletin of Mathematical Biophysics, 5, 115‒133.
- Moody, T. and C. Darken (1989). Fast learning in networks of locally tuned processing units. Neural Computation, 1, 281‒194.
- Mori, H. and A. Awata (2007). Data Mining of Electricity Price Forecasting with Regression Tree and Normalized Radial Basis Function Network. In IEEE Transactions on Systems, Man, and Cybernetics, IEEE International Conference, 3743‒3748.
- Mostafa, M.M. (2010). Forecasting stock exchange movements using neural networks: Empirical evidence from Kuwait. Expert Systems with Applications, 37 (9), 6302‒6309.
- Narendra, K.S. and K. Parthasarathy (1990). Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks, 1 (1), 4‒27.
- Nizamitdinov A., M. Memmedli and O. Ozdemir (2010a). Comparison Study of P-Spline and Univariate Additive Model (Cubic Smoothing Spline) in Time-Series Prediction. In 24th. Mini EURO Conference on Continuous Optimization and Information-Based Technologies in the Financial Sector (MEC EurOPT 2010), İzmir, TURKEY, Vilnius "Technika" 2010 (ISI proceedings), 34-39.
- Nizamitdinov A., M. Memmedli and O. Ozdemir (2010b). Time Series Forecasting Using Fuzzy Time Series Approach, Neural Network Models and Regression Splines. In 24th European Conference on Operational Research (EURO XXIV LISBON), Lisbon, Portugal, 257.
- Ord, K., M. Hibon and S. Makridakis (2000). The M3-Competition. International Journal of Forecasting, 16, 433‒436.
- Refenes, A.P.N. (1995). Neural Networks in the Capital Markets. New York: John Wiley & Sons.
- Renals, S. and R. Rohwer (1989). Phoneme classification experiments using radial basis functions. In Proceedings of International Joint Conference on Neural Networks, Washington, DC, 461‒467.
- Rumelhart, D.E. and J.L. McClelland (1986). Parallel Distributed Processing, Cambridge, MA: MIT Press.
- Rumelhart, D.E., G.E. Hinton and R. J. Williams (1986). Learning internal representations by error propagation. In Parallel distributed processing: explorations in the microstructure of cognition, ed. D.E. Rumelhart and J.L. McClelland. Cambridge, MA: MIT Press, 318–362.
- SFB386 (2011). http://www.stat.uni-muenchen.de/sfb386/ (accessed January 20, 2011).
- TCMB (2011). http://www.tcmb.gov.tr (accessed January 20, 2011).
- Trenn, S. (2008). Multilayer Perceptrons: Approximation Order and Necessary Number of Hidden Units, IEEE Transactions on Neural Networks, 19 (5), 836‒844.
- Vaughn, M.L. (1999). Derivation of the Multilayer Perceptron Weight Constraints for Direct Network Interpretation and Knowledge Discovery. Neural Networks, 12, 1259‒1271.
- Virili, F. and B. Freisleben (2000). Nonstationarity and data preprocessing for neural network predictions of an economic time-series. In IJCNN 2000, Proceedings of the IEEE-INNS- ENNS International Joint Conference on Neural Networks, 5, 129‒134.
- Wagener, T., H.S. Wheater and H.V. Gupta (2004). Rainfall-Runoff Modelling in Gauged and Ungauged Catchments. London: Imperial College Press.
- Wang, L.-X. (1994). Adaptive Fuzzy Systems and Control: Design and Stability Analysis. Englewood Cliffs, NJ: Prentice-Hall.
- Wang, L.-X. (1996). Stable adaptive fuzzy controllers with application to inverted pendulum tracking. IEEE Transactions on Systems, Man, and Cybernetics- Part b: Cybernetics, 26 (5), 677‒691.
- Wasserman, P.D. (1993). Advanced Methods in Neural Computing. New York: Van Nostrand Reinhold.
- Weigend, A., B.A. Huberman and D.E. Rumelhart (1992). Predicting Sunspots and Exchange Rates with Connectionist Networks, Nonlinear Modelling and Forecasting. Redwood City, CA: Addison-Wesley.
- White, H. (1988). Economic Prediction Using Neural Networks: the Case of IBM Daily Stock Returns. In Proceedings of the 1988 IEEE International Conference on Neural Networks, 2, 451‒458.
- Wong, S.P. and T.-L. Lai (2004). Spline models in time-series analysis. In Abstract Book of International Conference on Threshold Models and New Developments in Time-series. Department of Statistics and Actuarial Science University of Hong Kong, 27.
- Wood, S.N. (2003). Thin plate regression splines. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65, 95‒114.
- Wood, S.N. (2006). Generalized additive models: an introduction with R. London: Chapman and Hall.
- Zhang, G., B.E. Patuwo and M.Y. Hu (1998). Forecasting with artificial neural networks: The state of art. International Journal of Forecasting, 14, 35‒62.
- Zhang, L. and B. Zhang (1999). A Geometrical Representation of McCulloch-Pitts Neural Model and Its Applications. IEEE Transactions on Neural Networks, 10 (4), 925‒929.
- Zhang, G.P. and M. Qi (2005). Neural network forecasting for seasonal and trend time-series. European Journal of Operational Research, 160 (2), 501‒514.

Toplam 57 adet kaynakça vardır.

Konular | İşletme |
---|---|

Diğer ID | JA22VK39VE |

Bölüm | Makaleler |

Yazarlar | |

Yayımlanma Tarihi | 1 Eylül 2013 |

Gönderilme Tarihi | 1 Eylül 2013 |

Yayımlandığı Sayı | Yıl 2013 Cilt: 5 Sayı: 2 |