Linear and Nonlinear Processes

  • Christian Gouriéroux
Part of the Springer Series in Statistics book series (SSS)


The analysis of dynamics in economics is based on observations of relevant processes. Generally, the resulting time series shows that are some regularities that are present in explosive or cyclical components (see the evolution of unemployment in Fig 2.1 or comovements of different series (see Fig2.2 which displays the behavior of short and long term interest rates, where the two series have approximately the same trend and differ from one another in terms of their variabilities).


White Noise Gaussian White Noise Nonlinear Process Average Representation ARMA Model 
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  1. Ashley, R. and D. Patterson (1986) “A Nonparametric Distribution Free Test for Serial Dependence in Stock Returns”, Journal of Financial and Quantitative Analysis, 21, 221–227.CrossRefGoogle Scholar
  2. Ashley, R. and D. Patterson (1987) Linear Versus Nonlinear Macroeconomics: A Statistical Test, Discussion Paper. Blacksburg: Blacksburg University.Google Scholar
  3. Ashley, R., Patterson, D. and M. Hinich (1986) “A Diagnostic Test for Nonlinearity Serial Dependence in Time Series Fitting Errors”, Journal of Time Series Analysis, 7.Google Scholar
  4. Box, G. and G. Jenkins (1970) Time Series Analysis, Forecasting and Control, San Francisco: Holden—Day.Google Scholar
  5. Box, G. and D. Pierce (1970) “Distribution of Residual Autocorrelation in Autoregressive Integrated Moving Average Time Series Models”, Journal of the American Statistical Association, 70, 70–79.MathSciNetCrossRefGoogle Scholar
  6. Clark, P. (1973) “A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices”, Econometrica, 41, 135–155.MathSciNetzbMATHCrossRefGoogle Scholar
  7. Corrado, C. and J. Schatzberg (1990) “A Nonparametric Distribution Free Test for Serial Independence in Stock Returns: a Correction”, Jou nal rof Financial and Quantitative Analysis, 25, 411–416.CrossRefGoogle Scholar
  8. Dacarogna, M., Gauvreau, N., Muller, U., Olsen, R. and O. Piclet (1994) “Changing Time Scale for Short Term Forecasting in Financial Market”, Discussion Paper. Zurich: Olsen and Associates.Google Scholar
  9. Davies, N. and J. Petrucelli (1986) “Detecting Nonlinearity in Time Series”, The Statistician, 35, 271–280.CrossRefGoogle Scholar
  10. Engle, R. (1995) ARCH Selected Readings, Oxford: Oxford University Press.Google Scholar
  11. Garbade, K. (1977) “Two Methods for Examining the Stability of Regression Coefficients”, Journal of the American Statistical Association, 72, 54–63.zbMATHCrossRefGoogle Scholar
  12. Ghysels, E., Gouriéroux, C. and J. Jasiak (1995) “Trading Patterns, Time Deformation and Stochastic Volatility in Foreign Exchange Markets”, Discussion Paper 9542. Montréal: Centre interuniversitaire de recherche en analyse des organisations.Google Scholar
  13. Godfrey, L. (1978) “Testing Against General Autoregressive and Moving Average Error Models when the Regressors Include Lagged Dependent Variables”, Econometrica, 46, 1293–1302.MathSciNetzbMATHCrossRefGoogle Scholar
  14. Granger, C. and A. Andersen (1978) An Introduction to Bilinear Time Series Models, Göttingen: Vandenhoeck et Ruprecht.zbMATHGoogle Scholar
  15. Granger, G.W.J. and P. Newbold (1976) “Forecasting Transformed Series”, Journal of the Royal Statistical Society B, 38, 189–203.MathSciNetzbMATHGoogle Scholar
  16. Hasselman, K., Munk, W. and G. McDonald (1963) Bispectrum of Ocean Waves,Time Series Analysis (M. Rosenblatt, Ed.), New York: Wiley. pp. 125–139.Google Scholar
  17. Hinich, M.J. (1982) “Testing for Gaussianity and Linearity of a Stationary Time Series”, Journal of Time Series Analysis, 3, 169–176.MathSciNetzbMATHCrossRefGoogle Scholar
  18. Hinich, M. and D. Patterson (1985) “Evidence of Nonlinearity in Daily Stock Returns”, Journal of Business and Economic Statistics, 3, 69–77.Google Scholar
  19. Keenan, D.M. (1985) “A Tukey Nonadditivity-Type Test for Time Series Non Linearity”, Biometrika, 72, 39–44.MathSciNetzbMATHCrossRefGoogle Scholar
  20. Lawrance, A.J. and P.A. Lewis (1985) “Modelling and Residual Analysis of Nonlinear Autoregressive Time Series in Exponential Variables”, Journal of the Royal Statistical Society B, 47, 165–202.MathSciNetzbMATHGoogle Scholar
  21. Ljung, G.M. and G.E. Box (1978) “On a Measure of Lack of Fit in Time Series Models”, Biometrika 65, 297–303.zbMATHCrossRefGoogle Scholar
  22. Mc Leod, A.I. and W.K. Li (1983) “Diagnostic Checking ARMA Time Series Models Using Squared Residual Autocorrelations”, Journal of Time Series Analysis, 4, 269–273.MathSciNetCrossRefGoogle Scholar
  23. Maravall, A. (1983) “An Application of Nonlinear Time Series Forecasting”, Journal of Business and Economic Statistics, 1, 66–74.Google Scholar
  24. Nisio, M. (1960) “On Polynomial Approximation for Strictly Stationary Processes”, Journal of the Mathematical Society of Japan, 12, 207–226.MathSciNetzbMATHCrossRefGoogle Scholar
  25. Nisio, M. (1961) “Remarks on the Canonical Representation of Strictly Stationary Time Series”, American Statistician, 37, 323–324.Google Scholar
  26. Patterson, D. (1983) “BISPEC, A Program to Estimate the Bispectrum of a Stationary Time Series”, American Statistician, 37, 323–324.MathSciNetCrossRefGoogle Scholar
  27. Priestley, M. (1978) “Nonlinear Models in Time Series Analysis”, The Statistician, 27, 159–176.CrossRefGoogle Scholar
  28. Raftery, A.E. (1980) “Estimation efficace pour un processus autorégressif exponentiel à densité discontinue,” Publication de l’ Institute Statistique de l’Université de Paris, 25, 64–91.MathSciNetGoogle Scholar
  29. Raftery, A.E. (1981) “Un processus autorégressif... loi marginale exponentielle: propriétés asymptotiques et estimation du maximum de vraisemblance”, Annales Scientifiques de l’Université Clermont, 69, 149–160.MathSciNetGoogle Scholar
  30. Rosenblatt, M. and J.W. Van Ness (1964) Estimates of the Bispectrum of Stationary Random Processes, Discussion Paper. Providence, RI: Brown University.Google Scholar
  31. Stock, J. (1988) “Estimating Continuous Time Processes Subject to Time Deformation”, Journal of the American Statistical Association, 83, 877–884.Google Scholar
  32. Subba Rao, T. (1981) “On the Theory of Bilinear Models”, Journal of the Royal Statistical Society B, 43.Google Scholar
  33. Subba Rao, T. and M. Gabr (1980) An Introduction to Bispectral Analysis and Bilinear Time Series Models, New York: Springer-Verlag.Google Scholar
  34. Tong, M. and K. Lin (1980) “Threshold Autoregressions, Limit Cycles and Cyclical Data”, Journal of the Royal Statistical Society B, 42, 245–292.zbMATHGoogle Scholar
  35. Whittle, P. (1963) Prediction and Regulation, The English University Press.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Christian Gouriéroux
    • 1
  1. 1.Centre de Recherche en Economie et StatistiqueLaboratoire de Finance-AssuranceMalakoff CedexFrance

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