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ARCH Models and Financial Applications pp 5–27Cite as

Linear and Nonlinear Processes

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Abstract

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).

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References

  • 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.

    Article  Google Scholar 

  • Ashley, R. and D. Patterson (1987) Linear Versus Nonlinear Macroeconomics: A Statistical Test, Discussion Paper. Blacksburg: Blacksburg University.

    Google Scholar 

  • 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 

  • Box, G. and G. Jenkins (1970) Time Series Analysis, Forecasting and Control, San Francisco: Holden—Day.

    Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Clark, P. (1973) “A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices”, Econometrica, 41, 135–155.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Davies, N. and J. Petrucelli (1986) “Detecting Nonlinearity in Time Series”, The Statistician, 35, 271–280.

    Article  Google Scholar 

  • Engle, R. (1995) ARCH Selected Readings, Oxford: Oxford University Press.

    Google Scholar 

  • Garbade, K. (1977) “Two Methods for Examining the Stability of Regression Coefficients”, Journal of the American Statistical Association, 72, 54–63.

    Article  MATH  Google Scholar 

  • 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 

  • Godfrey, L. (1978) “Testing Against General Autoregressive and Moving Average Error Models when the Regressors Include Lagged Dependent Variables”, Econometrica, 46, 1293–1302.

    Article  MathSciNet  MATH  Google Scholar 

  • Granger, C. and A. Andersen (1978) An Introduction to Bilinear Time Series Models, Göttingen: Vandenhoeck et Ruprecht.

    MATH  Google Scholar 

  • Granger, G.W.J. and P. Newbold (1976) “Forecasting Transformed Series”, Journal of the Royal Statistical Society B, 38, 189–203.

    MathSciNet  MATH  Google Scholar 

  • 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 

  • Hinich, M.J. (1982) “Testing for Gaussianity and Linearity of a Stationary Time Series”, Journal of Time Series Analysis, 3, 169–176.

    Article  MathSciNet  MATH  Google Scholar 

  • Hinich, M. and D. Patterson (1985) “Evidence of Nonlinearity in Daily Stock Returns”, Journal of Business and Economic Statistics, 3, 69–77.

    Google Scholar 

  • Keenan, D.M. (1985) “A Tukey Nonadditivity-Type Test for Time Series Non Linearity”, Biometrika, 72, 39–44.

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    MathSciNet  MATH  Google Scholar 

  • Ljung, G.M. and G.E. Box (1978) “On a Measure of Lack of Fit in Time Series Models”, Biometrika 65, 297–303.

    Article  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Maravall, A. (1983) “An Application of Nonlinear Time Series Forecasting”, Journal of Business and Economic Statistics, 1, 66–74.

    Google Scholar 

  • Nisio, M. (1960) “On Polynomial Approximation for Strictly Stationary Processes”, Journal of the Mathematical Society of Japan, 12, 207–226.

    Article  MathSciNet  MATH  Google Scholar 

  • Nisio, M. (1961) “Remarks on the Canonical Representation of Strictly Stationary Time Series”, American Statistician, 37, 323–324.

    Google Scholar 

  • Patterson, D. (1983) “BISPEC, A Program to Estimate the Bispectrum of a Stationary Time Series”, American Statistician, 37, 323–324.

    Article  MathSciNet  Google Scholar 

  • Priestley, M. (1978) “Nonlinear Models in Time Series Analysis”, The Statistician, 27, 159–176.

    Article  Google Scholar 

  • 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.

    MathSciNet  Google Scholar 

  • 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.

    MathSciNet  Google Scholar 

  • Rosenblatt, M. and J.W. Van Ness (1964) Estimates of the Bispectrum of Stationary Random Processes, Discussion Paper. Providence, RI: Brown University.

    Google Scholar 

  • Stock, J. (1988) “Estimating Continuous Time Processes Subject to Time Deformation”, Journal of the American Statistical Association, 83, 877–884.

    Google Scholar 

  • Subba Rao, T. (1981) “On the Theory of Bilinear Models”, Journal of the Royal Statistical Society B, 43.

    Google Scholar 

  • Subba Rao, T. and M. Gabr (1980) An Introduction to Bispectral Analysis and Bilinear Time Series Models, New York: Springer-Verlag.

    Google Scholar 

  • Tong, M. and K. Lin (1980) “Threshold Autoregressions, Limit Cycles and Cyclical Data”, Journal of the Royal Statistical Society B, 42, 245–292.

    MATH  Google Scholar 

  • Whittle, P. (1963) Prediction and Regulation, The English University Press.

    Google Scholar 

Download references

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Authors and Affiliations

  1. Centre de Recherche en Economie et Statistique, Laboratoire de Finance-Assurance, Bâtiment Malakoff 2-Timbre J320, 15 Boulevard Gabriel Péri, Malakoff Cedex, 92245, France

    Christian Gouriéroux

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  1. Christian Gouriéroux
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© 1997 Springer Science+Business Media New York

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Gouriéroux, C. (1997). Linear and Nonlinear Processes. In: ARCH Models and Financial Applications. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1860-9_2

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  • DOI: https://doi.org/10.1007/978-1-4612-1860-9_2

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7314-1

  • Online ISBN: 978-1-4612-1860-9

  • eBook Packages: Springer Book Archive

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