Nonlinear Econometric Modelling: A Selective Review

  • Norman R. Swanson
  • Philip Hans Franses
Part of the Dynamic Modeling and Econometrics in Economics and Finance book series (DMEF, volume 1)

Abstract

In recent years nonlinear econometric modelling has received increasing attention in econometrics. This is not to say, however, that nonlinear phenomena have not been considered an important aspect of economics for many decades. Rather, as statistical and econometric methodology has developed, our ability to formulate, and more importantly, estimate nonlinear models have increased. However, as with all sciences and social sciences, nonlinear theories and models have been around virtually from the beginning. Although many examples can be brought to bear in support of this notion, one need really simply consider business cycles, which have long been known to exhibit various seasonal and cyclical nonlinearities (for example, see Burns and Mitchell (1946)).

Keywords

Covariance Income Autocorrelation Radon 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bishop, C. M. (1995). Neural Networks for Pattern Recognition. Oxford: Claredon Press.Google Scholar
  2. Boswijk, H. P. and P. H. Franses (1997). “Common Persistence in Nonlinear Autoregressive Models,” Econometric Institute Report 9702, Erasmus University.Google Scholar
  3. Brandt, A. (1986). “The Stochastic Equation with Stationary Coefficients,” Advances In Applied Probability, 18, 211–220.CrossRefGoogle Scholar
  4. Brock, W. A., W. D. Dechert, J. A. Scheinkman, and B. Le Baron (1996). “A Test for Independence Based on the Correlation Dimension,” Econometric Reviews, 15, 197–235.CrossRefGoogle Scholar
  5. Brock, W. A., D. A. Hsieh, and B. Le Baron (1991). Nonlinear Dynamics, Chaos, and Instability. Cambridge: MIT Press.Google Scholar
  6. Burns, A. F. and W. C. Mitchell (1946). Measuring Business Cycles. New York: Columbia University Press.Google Scholar
  7. Carroll, S. M. and B. W. Dickinson (1989). “Construction of Neural Nets Using the Radon Transform,” in Proceedings of the International Joint Conference on Neural Networks. Washington DC. New York: IEEE Press, 607–611.CrossRefGoogle Scholar
  8. Chen, X. and N. R. Swanson (1997). “Semiparametic ARX Neural Network Models With an Application to Forecasting Inflation,” working paper, Department of Economics, Pennsylvania State University.Google Scholar
  9. Corradi, V., N. R. Swanson, and H. White (1997). “Testing for Stationarity Ergodicity and for Comovement Between Nonlinear Discrete Time Markov Processes,” working paper, Department of Economics, Pennsylvania State University.Google Scholar
  10. Croushore, D. (1993). “Introducing: The Survey of Professional Forecasters,” The Federal Reserve Bank of Philadelphia Business Review, November-December, 3-15.Google Scholar
  11. Cybenko, G. (1989). “Approximation by Superpositions of a Sigmoid Function,” Mathematics of Control Signals and Systems, 2, 303–314.CrossRefGoogle Scholar
  12. Diebold, F. X. and R. S. Mariano (1995). “Comparing Predictive Accuracy,” Journal of Business and Economic Statistics, 13, 253–263.Google Scholar
  13. Diebold, F. X. and J. A. Nason (1990). “Nonparametric Exchange Rate Prediction,” Journal of International Economics, 28, 315–332.CrossRefGoogle Scholar
  14. Dorsey, R. E., J. D. Johnson, and M. V. van Boening (1994). “The Use of Artificial Neural Networks for Estimation of Decision Surfaces in First Price Sealed Bid Auctions,” in Cooper, W. W. and A. Whinston, (eds.) New Directions in Computational Economics. Boston: Kluwer, 19–40.CrossRefGoogle Scholar
  15. Dropsy, V. (1992). “Exchange Rates and Neural Networks,” working paper No. 1-92, Department of Economics, California State University Fullerton.Google Scholar
  16. Dutta, S. and S. Shekhar (1989). “Bond Rating: A Non-Conservative Application of Neural Networks,” in Proceedings of the IEEE International Conference on Neural Networks, San Diego. New York: IEEE Press, 443–450.Google Scholar
  17. Engle, R. F. (1982). “Autoregressive Conditional Heteroskedasticity With Estimates of the Variance of U.K. Inflation,” Econometrica, 50, 987–1008.CrossRefGoogle Scholar
  18. Engle, R. F. and S. J. Brown (1986). “Model Selection for Forecasting,” Applied Mathematics and Compulation, 20, 313–327.CrossRefGoogle Scholar
  19. Fair, R. C. and R. J. Shiller (1990). “Comparing Information in Forecasts from Econometric Models,” American Economic Review, 80, 375–389.Google Scholar
  20. Franses, P. H. (1996). Periodicity and Stochastic Trends in Economic Time Series. Oxford: Oxford University Press.Google Scholar
  21. Franses, P. H. and D. Van Dijk (1997). “Do We Often Find ARCH Because of Neglected Outliers?” Economic Institute Report 9706, Erasmus University.Google Scholar
  22. Franses, P. H. and R. Paap (1996). “Does Seasonal Adjustment Change Inference from Markov Switching Models?” Econometric Institute Report 9615, Erasmus University.Google Scholar
  23. Franses, P. H. and G. Draisma (1997). “Recognizing Changing Seasonal Patterns Using Artificial Neural Networks,” Journal of Econometrics, forthcoming.Google Scholar
  24. Franses, P. H. and P. Van Homelen (1997). “On Forecasting Exchange Rates Using Neural Networks,” Applied Financial Economics, forthcoming.Google Scholar
  25. Funahashi, K. (1989). “On the Approximate Realization of Continuous Mappings by Neural Networks,” Neural Networks, 2, 183–192.CrossRefGoogle Scholar
  26. Ghysels, E., C. W. J. Granger, and P. L. Siklos (1996). “Is Seasonal Adjustment a Linear or Nonlinear Data Filtering Process?” Journal of Business and Economic Statistics, 14, 374–386.Google Scholar
  27. Granger, C. W. J. (1993). “Strategies for Modeling Nonlinear Time Series Relationships,” The Economic Record, 69, 233–238.CrossRefGoogle Scholar
  28. Granger, C. W. J. and A. P. Andersen (1978). An Introduction to Bilinear Time Series Models. Göttingen: Vandenhoeck and Ruprecht.Google Scholar
  29. Granger, C. W. J. and N. R. Swanson (1996). “Further Developments in the Study of Cointegrated Variables,” Oxford Bulletin of Economics and Statistics, 58, 537–553.CrossRefGoogle Scholar
  30. Granger, C. W. J. and N. R. Swanson (1997). “An Introduction to Stochastic Unit Root Processes,” Journal of Econometrics, 80, 35–62.CrossRefGoogle Scholar
  31. Granger, C. W. J. and T. Teräsvirta (1993). Modelling Nonlinear Relationships. New York: Oxford University Press.Google Scholar
  32. Guyton, D. A.,N.-F. Zhang and R. V. Foutz (1986). “A Random Parameter Process for Modeling and Forecasting Time Series,” Journal of Time Series Analysis, 7, 105–115.CrossRefGoogle Scholar
  33. Hall, R. E. (1978). “Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence,” Journal of Political Economy, 96, 971–987.CrossRefGoogle Scholar
  34. Hamilton, J. D. (1989). “A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle,” Econometrica, 57, 357–384.CrossRefGoogle Scholar
  35. Hamilton, J. D. (1994). Time Series Analysis. New Jersey: Princeton University Press.Google Scholar
  36. Henriksson, R. D. and R. C. Merton (1981). “On Market Timing and Investment Performance. H. Statistical Procedures for Evaluating Forecasting Skills, ” Journal of Business, 54, 513–533.CrossRefGoogle Scholar
  37. Hornik, K., M. Stinchcombe, and H. White (1989). “Multilayer Feedforward Networks are Universal Approximators,” Neural Networks, 2, 359–366.CrossRefGoogle Scholar
  38. Hornik, K., M. Stinchcombe, and H. White (1990). “Universal Approximation of an Unknown Mapping and its Derivatives Using Multilayer Feedforward Networks,” Neural Networks, 3, 551–560.CrossRefGoogle Scholar
  39. Journal of Applied Econometrics (1992). “Special Issue on Nonlinear Dynamics and Econometrics,” 7, December, New York: Wiley.Google Scholar
  40. Keane, M. P. and D. E. Runkle (1990). “Testing the Rationality of Price Forecasts,” American Economic Review, 80, 714–735.Google Scholar
  41. Koopmans, L. H. (1974). The Spectral Analysis of Time Series. New York: Academic Press.Google Scholar
  42. Kuan, C.-M. and T. Liu (1995). “Forecasting Exchange Rates Using Feedforward and Recurrent Neural Networks,” Journal of Applied Econometrics, 10, 347–364.CrossRefGoogle Scholar
  43. Kuan, C.-M. and H. White (1994). “Artificial Neural Networks: An Econometric Perspective,” Econometric Reviews, 13, 1–91.CrossRefGoogle Scholar
  44. Laroque, G. and B. Salanie (1994). “Estimating the Canonical Disequilibrium Model: Asymptotic Theory and Finite Sample Properties,” Journal of Econometrics, 62, 165–210.CrossRefGoogle Scholar
  45. Lee, T.-H., H. White, and C. W. J. Granger (1993). “Testing for Neglected Nonlinearity in Time Series Models: A Comparison of Neural Network Methods and Alternative Tests,” Journal of Econometrics, 56, 269–290.CrossRefGoogle Scholar
  46. Leitch, G. and J. E. Tanner (1991). “Economic Forecast Evaluation: Profits Versus the Conventional Error Measures,” American Economic Review, 81, 580–590.Google Scholar
  47. Leybourne, S. J., B. P. M. McCabe, and A. R. Tremayne (1994). “Can Economic Time Series be Differenced to Stationarity?” working paper, University of Nottingham.Google Scholar
  48. Luukkonen, R., P. Saikkonen, and T. Teräsvirta (1988a). “Testing Linearity Against Smooth Transition Autoregressive Models,” Biometrika, 75, 491–499.CrossRefGoogle Scholar
  49. Luukkonen, R., P. Saikkonen, and T. Teräsvirta (1988b). “Testing Linearity in Univariate Time Series Models,” Scandinavian Journal of Statistics, 15, 161–175.Google Scholar
  50. Mishkin, F. S. (1988). “The Information in the Term Structure: Some Further Results,” Journal of Applied Econometrics, 3, 307–314.CrossRefGoogle Scholar
  51. Mizrach, B. (1992). “Multivariate Nearest-Neighbor Forecasts of EMS Exchange Rates,” Journal of Applied Economics, 7, 151–164.CrossRefGoogle Scholar
  52. Moody, J. and J. Utans (1991). “Principled Architecture Selection for Neural Networks: Applications to Corporate Bond Rating Predictions,” in J. E. Moody, S. J. Hanson, and R. P. Lippmann, (eds.) Advances in Neural Information Processing Systems 4. San Mateo: Morgan Kaufman, 638–690.Google Scholar
  53. Neftci, S. N. (1984). “Are Economic Time Series Asymmetric. Over the Business Cycles?” Journal of Political Economy, 92, 306–328.CrossRefGoogle Scholar
  54. Pesaran, M. H. and A. G. Timmerman (1992). “A Simple Nonparametric Test of Predictive Performance, Journal of Business and Economic Statistics, 10, 461–465.Google Scholar
  55. Pesaran, M. H. and A. G. Timmerman (1994a). “The Use of Recursive Model Selection Strategies in Forecasting Stock Returns,” working paper, Department of Economics, University of Cambridge.Google Scholar
  56. Pesaran, M. H. and A. G. Timmerman (1994b). “A Generalization of the Non-Parametric Henriksson-Merton Test of Market Timing,” Economic Letters, 44, 1–7.CrossRefGoogle Scholar
  57. Potter, S. M. (1995). “ANonlinear Approach to US GNP,” Journal of Applied Econometrics, 10, 109–125.CrossRefGoogle Scholar
  58. Pourahmadi, M. (1986). “On Stationarity of the Solution of a Doubly Stochastic Model,” Journal Of Time Series Analysis, 7, 123–131.CrossRefGoogle Scholar
  59. Pourahmadi, M. (1988). “Stationarity of the Solution of and Analysis of Non-Gaussian Dependent Random Variables,” Journal of Time Series Analysis, 9, 225–230.CrossRefGoogle Scholar
  60. Ripley, B. D. (1994). “Neural Networks and Related Methods for Classification,” Journal of the Royal Statistical Society Series B, 56, 409–456.Google Scholar
  61. Rothman, P. (1992). “The Comparative Power of the TR Test Against Simple Threshold Models,” Journal of Applied Econometrics, 7, 187–195.CrossRefGoogle Scholar
  62. Rumelhart, D. E. and J. L. McClelland (1986). Parallel Distributed Processing: Explorations in the Microstructures of Cognition. Cambridge: MIT Press.Google Scholar
  63. Steckler, H. O. (1991). “Macroeconomic Forecast Evaluation Techniques,” International Journal of Forecasting, 7, 375–384.CrossRefGoogle Scholar
  64. Steckler, H. O. (1994). “Are Economic Forecasts Valuable?” Journal of Forecasting, 13, 495–505.CrossRefGoogle Scholar
  65. Swanson, N. R. (1996). “Forecasting Using First Available Versus Fully Revised Economic Time Series Data,” Studies in Nonlinear Dynamics and Econometrics, 1, 47–64.Google Scholar
  66. Swanson, N. R. and H. White (1995). “A Model Selection Approach to Assessing the Information in the Term Structure Using Linear Models and Artificial Neural Networks,” Journal of Business and Economic Statistics, 13, 265–275.Google Scholar
  67. Swanson, N. R. and H. White (1997). “A Model Selection Approach to Real Time Macroeconomic Forecasting Using Linear Models and Artificial Neural Networks, Review of Economics and Statistics, 79, 540–550.CrossRefGoogle Scholar
  68. Teräsvirta, T. and H. M. Anderson (1992). “Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models,” Journal of Applied Econometrics, 7, 119–136.CrossRefGoogle Scholar
  69. TjØstheim, T. (1986). “Some Doubly Stochastic Time Series Models,” Journal of Time Series Analysis, 7, 51–72.CrossRefGoogle Scholar
  70. Tong, H. (1983). Threshold Models in Non-Linear Time Series Analysis. New York: Springer-Verlag.CrossRefGoogle Scholar
  71. Tong, H. (1990). Non-Linear Time Series: A Dynamical System Approach. Oxford: Oxford University Press.Google Scholar
  72. Trippi, R. and E. Turbau (1993). Neural Networks in Finance and Investing. Chicago: Probus Publishing Company.Google Scholar
  73. Van Dijk, D., P. H. Franses, and A. Lucas (1996a). “Testing for Smooth Transition Autoregression in the Presence of Outliers,” Econometric Institute Report 9622, Erasmus University.Google Scholar
  74. Van Dijk, D., P. H. Franses, and A. Lucas (1996b). “Testing for ARCH in the Presence of Additive Outliers,” Econometric Institute Report 9659, Erasmus University.Google Scholar
  75. Weiss, A. A. (1996). “Estimating Time Series Models Using the Relevant Cost Function,” Journal of Applied Econometrics, 11, 539–560.CrossRefGoogle Scholar
  76. White, H. (1988). “Economic Prediction Using Neural Networks: The Case of IBM Daily Stock Returns,” in Proceedings of the IEEE International Conference on Neural Networks, San Diego. New York: IEEE Press, 451–458.CrossRefGoogle Scholar
  77. White, H. (1989). “Learning in Artificial Neural Networks: A Statistical Perspective,” Neural Computation, 1, 425–464.CrossRefGoogle Scholar
  78. White, H. (1990). “Connectionist Nonparametric Regression: Multilayer Feedforward Networks Can Learn Arbitrary Mappings,” Neural Networks, 3, 535–549.CrossRefGoogle Scholar
  79. Zamowitz, V. and P. Braun (1992). “Twenty-Two Years of the NBER-ASA Quarterly Economic Outlook Surveys: Aspects and Comparisons of Forecasting Performance,” NBER working paper No. 3965.Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Norman R. Swanson
    • 1
  • Philip Hans Franses
    • 2
  1. 1.Pennsylvania State UniversityUSA
  2. 2.Erasmus UniversityRotterdamUSA

Personalised recommendations