Projections of Inflation Dynamics for Pakistan: GMDH Approach

Shahid IQBAL, Maqbool H. SIAL

Abstract


Abstract. This study is focused on identifying, based on various forecast accuracy criteria, best inflation forecasting model for Pakistan using the in sample projections for Pakistan inflation from 2006II to 2009II. To resolve the important issue of degree of contribution in forecasting performance of the two monetary aggregates in forecasting inflation, three main predictors: real GDP, interest rate and one out of the two monetary aggregate have been used, thus constructing two models; one with Divisia Monetary Index (DMI) and other with Simple sum monetary aggregate (SSMA). It is revealed that, though both of the monetary aggregates are important predictors in forecasting inflation, but DMAs provide better fit and improved forecasts as compared to their simple sum counterpart. Hence, the evidence is established that monetary aggregates still play a dominant role in predicting inflation for Pakistan economy. The study recommends the construction, publication, and use of high frequency DMAs by the State Bank of Pakistan (SBP) for forecasting inflation in Pakistan instead of SSMAs. Finally, to identify the improvement in forecast accuracy w.r.t. different forecasts combination, these forecasts have been combined and compared. It is revealed that when the structure of an empirically observed underlying series has complex nonlinear structure then forecasts based on single nonlinear model may fail to capture these diverse complexities. The best strategy is then to use various nonlinear models and combine these forecasts. Further the study concluded that if the complex nonlinear structure of an observed series is, a priory, unknown then universal approximators like Group Method of Data Handling (GMDH)- Polynomial Neural Networks (PNNs) and GMDH-Combinatorially Optimized (CO)  could provide outstandingly accurate forecasts yet avoiding ‘overfitting’ even for small sample size. Specifically, it recommends the use of nonlinear non-parametric universal approximators for forecasting inflation in Pakistan by the SBP.

Keywords. Monetary aggregate, Nonparametric nonlinear models, Universal approximators, Forecasting performance, Forecasts combination.

JEL. E31, E47, E51, E52.

Keywords


monetary aggregate, nonparametric nonlinear models, universal approximators, forecasting performance, forecasts combination.

Full Text:


References


Abdullah, M., & Kalim, R. (2009). Determinants of food price inflation in Pakistan. Paper presented in the conference of University of Management Sciences, 1-21.

Abidemi, O.I., & Malik, S.A.A. (2010). Analysis of Inflation and its determinant in Nigeria. Pakistan Journal of Social Sciences, 7(2), 97-100. doi. 10.3923/pjssci.2010.97.100

Ahangar, R.G., Yahyazadehfar, M., & Pournaghshband, H. (2010). The comparison of methods artificial neural network with linear regression using specific variables for prediction stock price in Tehran stock exchange, International Journal of Computer Science and Information Security, 7(2), 38-46.

Ang, A., Bekaert, G., & Wei, M. (2007). Do macro variables, asset markets, or surveys forecast inflation better? Journal of Monetary Economics, 54(4), 1163-1212. doi. 10.1016/j.jmoneco.2006.04.006

Bahuguna, G.N., & Chandrahas, (1992). Models for forecasting aphid pest of mustard crop. IASRI Publication.

Bashir, F., Nawaz, S., Yasin, K., Khursheed, U., Khan, J., & Qureshi, M.J. (2011). Determinants of inflation in Pakistan: An econometric analysis using johansen co-integration approach. Australian Journal of Business and Management Research, 1(5), 71-82.

Bates, J.M. & Granger C.W.J. (1969). Combination of forecasts. Operational Research Quarterly, 20(4), 451-468. doi. 10.2307/3008764

Berger, H., & Österholm, P. (2011). Does money growth granger cause inflation in the Euro area? Evidence from out-of-sample forecasts using Bayesian VARs. Economic Record, 87(276), 45-60. doi. 10.1111/j.1475-4932.2010.00657.x

Binner, J.M., Gazely, A.M., Chen, S.H. & Chie, B.T. (2004). Financial innovation and Divisia money in Taiwan: comparative evidence from neural networks and vector error correction forecasting models, Contemporary Economic Policy, 22(2), 213-24. doi. 10.1093/cep/byh015

Binner, J., Tino, P., Tepper, J., Andersen, R., Jones, B., & Kendall, G. (2010). Does money matter in inflation forecasting? Physica A:Statistical Mechanics and its Applications, 389(21), 4793-4808. doi. 10.1016/j.physa.2010.06.015

BLS, (1997) US bureau of labor statistics: Measurement issues in the consumer price index. [Retrieved from].

Bokil, M., & Schimmelpfennig, A. (2005), Three attempts at Inflation Forecasting in Pakistan, IMF Working Paper, No. 05/105.

Canova, F. (2007). G-7 Inflation forecasts: Random walk, Phillips curve, or what else? Macroeconomic Dynamics, 11(1), 1-30. doi. 10.1017/S136510050705033X

Castle, J.L., & Hendry, D.F. (2006). Extending the boundaries of PcGets: Nonlinear models, Working Paper, Department of Economics, Oxford University.

Castle, J.L., & Hendry, D.F. (2010). A low-dimension portmanteau test for non-linearity, Journal of Econometrics, 158(2), 231-245. doi. 10.1016/j.jeconom.2010.01.006

Chaudhary, M.A., & Chaudhary M.A.S. (2006). Why the state bank of Pakistan should not adopt inflation targeting. SBP Research Bulletin, 2(1), 195-209.

Chaudhuri, R. (2012). A combinatorial GMDH approach to identification, modelling and prediction of money market state variables, International Conference on Technology and Business Management, March 26-28.

Clark, T.E., & McCracken, M.W. (2010). Averaging forecasts from VARs with uncertain instabilities. Journal of Applied Econometrics, 25(1), 5-29. doi. 10.1002/jae.1127

Clemen, R.T. (1989). Combining forecasts: A review and annotated bibliography. International Journal of Forecasting, 5(4), 559-583. doi. 10.1016/0169-2070(89)90012-5

Diebold, F.X. & Lopez, J.A. (1996). Forecast evaluation and combination. in Maddala & Rao, eds., Handbook of Statistics, Elsevier: Amsterdam.

Dorsey, R. (2000). Neural networks with Divisia money: better forecasts of future inflation? in Divisia Monetary Aggregates; Theory and Practice, edited by M.T. Belongia, & J.M. Binner. Basingstoke, pp. 28-43. UK: Palgrave Publishers.

Drake, L. & Mills, T. (2005). A new empirically weighted monetary aggregate for the United States. Economic Enquiry, 43(1), 138-157. doi. 10.1093/ei/cbi010

ECB, (2003). The European Central Bank (ECB) ECB’s monetary policy strategy after the evaluation and clarification of May 2003. Speech by Jean-Claude Trichet, 20 November.

Elger, C.T., Jones, B.E., & Nilsson, B. (2006). Forecasting with monetary aggregates: Recent evidence for the United States. Journal of Economics and Business, 58(5-6), 428-446. doi. 10.1016/j.jeconbus.2006.06.004

Haider, A. & Hanif, M.N. (2009). Inflation forecasting in Pakistan using artificial neural networks. Pakistan Economic and Social Review, 47(1), 123-138.

Hale, G., & Jorda, O. (2007). Do monetary aggregates help forecast inflation? FRBSF Economic Letter No. 2007-10.

Hashem, S., Yih, Y., & Schmeiser B. (1993). An efficient model for product allocation using optimal combinations of neural networks. In Intelligent Engineering Systems through Artificial Neural Networks, C. Dagli, L.I. Burke, B.R. Fernandez, & J. Ghosh, (eds.), 3:669-674, ASME Press.

Hashem, S. (1997). Optimal linear combinations of neural networks. Neural Networks, 10(4), 599–614. doi. 10.1016/S0893-6080(96)00098-6

Hendry, D.F. & Clements, M.P. (2004), Pooling of forecasts, Econometrics Journal, 7(1), 1–31. doi. 10.1111/j.1368-423X.2004.00119.x

Inoue, A. & Kilian, L. (2008). How useful is bagging in forecasting economic time Series? A case study of U.S. CPI inflation. Journal of the American Statistical Association, 103(482), 511-522. doi. 10.1198/016214507000000473

Iqbal. S., Sial, M.H., & ul Hassan, N. (2015). Inflation welfare cost analysis for Pakistan: An ARDL approach, Pakistan Journal of Commerce and Social Sciences Johar Educational, 9(2), 380-417.

Ivakhnenko, A.G. (1968). The group method of data handling - a rival of the method of stochastic approximation. Soviet Automatic Control c/c of Avtomatika, 1(3), 43-55.

Ivakhnenko, A.G. (1988). Sorting methods for modelling and clusterization (survey of the GMDH papers for the years 1983-1988). The present stage of GMDH development. Soviet Journal of Automation and Information Sciences c/c of Avtomatika. 21(4), 1-13.

Ivakhnenko, A.G. & Kocherga, Y.L. (1983). Theory of two-level GMDH algorithms for long-range quantitative prediction. Soviet Automatic Contr ol c/c of Avtomatika 16(6), 7-12.

Jaditz, T., Riddick, L.A., & Sayers, L. (1998). Multivariate nonlinear forecasting. Macroeconomic Dynamics, 2(3), 369-382.

Kock, A.B. (2009). Forecasting with universal approximators and a learning algorithm, Working paper, CREATES, Aarhus University.

Kock, A.B., & Terasvirta, T. (2011). Forecasting with nonlinear time series models, in M. P. Clements & D. F. Hendry (eds), Oxford Handbook of Economic Forecasting, Oxford University Press, Oxford, pp. 61-87.

Kovanen, A. (2011). Does Money Matter for Inflation in Ghana? IMF Working Papers 11/274.

Krolzig, H.-M. & Hendry, D.F. (2001). Computer automation of general-to-specific model selection procedures. Journal of Economic Dynamics and Control 25(6-7), 831-866. doi. 10.1016/S0165-1889(00)00058-0

Leung, M.T., Chen, A.S. & Daouk, H. (2000). Forecasting exchange rates using general regression neural networks, Computers and Operations Research, 27(11), 1093-1110. doi. 10.1016/S0305-0548(99)00144-6

Marcellino, M. (2002). Instability and non-linearity in the EMU, Discussion Paper No. 3312, Centre for Economic Policy Research.

Marcellino, M. (2004). Forecasting EMU macroeconomic variables, International Journal of Forecasting, 20(2), 359-372. doi. 10.1016/j.ijforecast.2003.09.003

Muller, J.A., & Ivakhnenko, I.G. (1996). Self-organizing modelling in analysis and prediction of stock market. In Proceedings of the Second International Conference on Application of Fuzzy Systems and Soft Computing – ICAFS’96, Siegen, Germany, pp.491-500.

Samsudin, R., Saad, P., & Shabri, A. (2011). River flow time series using least squares support vector machines. Hydroogy and Earth System Sciences, 15, 1835–1852. doi. 10.5194/hess-15-1835-2011

SBP, (2010). Handbook of Statistics on Pakistan Economy 2010.The State Bank of Pakistan..

SBP-MSB, (2011). Monthly Statistical Bulletin. SBP, Karachi January, and various previous Issues.

Schunk, D.L. (2001). The Relative Forecasting Performance of the Divisia and Simple Sum Monetary Aggregates. Journal of Money, Credit and Banking, 33(2), 272-83. doi. 10.2307/2673885

Stepashko, V.S., & Yurachkovskiy, Y.P. (1986). The present state of the theory of the group method of data handling. Soviet Journal of Automation and Information Sciences c/c of Avtomatika, 19(4), 36-46.

Stock, J.H.. & Watson, M.W. (1999). Forecasting inflation. Journal of Monetary Economics, 44(2), 293-335. doi. 10.1016/S0304-3932(99)00027-6

Stock, J.H. & Watson M.W. (2003). Has the Business Cycle Changed and Why? NBER Working Paper No. 9127. doi. 10.3386/w9127

Terasvirta, T., Dijk, D.V., & Medeiros, M.C. (2005). Smooth transition autoregressions, neural networks, and linear models in forecasting macroeconomic time series: A re-examination. International Journal of Forecasting, 21(4), 755-774. doi. 10.1016/j.ijforecast.2005.04.010

Timmermann, A. (2006). Forecast combination. In Elliott, G., Granger, C.W.J. & Timmermann, A. (eds), Handbook of Economic Forecasts, Amsterdam: Elsevier.

Urwatul-Wutsqa, D., Subanar, Guritno, S., & Sujuti, Z. (2006). Forecasting Performance of VAR-NN and VARMA Models. Proceedings of the 2nd IMT-GT Regional Conference on Mathematics, Statistics and Their Applications School of Mathematical Sciences, Universiti Sains Malaysia, Penang, June 13-15.

Valle e Azevedo, J., & Pereira, A. (2010a). Forecasting Inflation with Monetary Aggregates, Economic Bulletin and Financial Stability. Report Articles, issue (Autumn): 151-168.

Varahrami, V. (2012). Good Prediction of Gas Price between MLFF and GMDH Neural Network.International Journal of Finance and Accounting, 1(3), 23-27. doi. 10.5923/j.ijfa.20120103.01

Weierstrass’s, K. (1885). Über die analytische Darstellbarkeit sogenannter willkürlicher Funktionen einer reellen Veränderlichen, Sitzungsberichte der Akademie zu Berlin, 1885: 633-639 and 789-805.

White, H. (2006). Approximate nonlinear forecasting methods, in G. Elliott, C. W. J. Granger & A. Timmermann (eds), Handbook of Economic Forecasting, Elsevier, Amsterdam, 1: 459-512.

Yang, X.H., Wang, F.M., Huang, J.F., Wang, J.W., Wang, R..C., Shen, Z.Q. & Wang, X.Z. (2009). Comparison between radial basis function neural network and regression model for estimation of rice biophysical parameters using remote sensing. Pedosphere. 19(2), 176–188. doi. 10.1016/S1002-0160(09)60107-7

Yao, Y., & Ni, Q. (2009). Oil price forecasting based on self-organizing data mining. In Conference on Grey Systems and Intelligent Services, 10-12 Nov. 2009. GSIS 2009. IEEE International, 1386-1390.

Zheng, A., Liu, W., & Zhao, F. (2010). Double trends time series forecasting using a combined ARIMA and GMDH model. In Control and Decision Conference (CCDC), 26-28 May, 2010 Chinese: 1820-1824.




DOI: http://dx.doi.org/10.1453/jepe.v3i3.904

Refbacks

  • There are currently no refbacks.


Bookmark and Share


.......................................................................................................................................................................................................................................................................................................................................

Journal of Economics and Political Economy - J. Econ. Pol. Econ. - JEPE - www.kspjournals.org

ISSN: 2148-8347

Editor: [email protected]   Secretarial: [email protected]   Istanbul - Turkey.

Copyright © KSP Library