Locally time homogeneous time series modeling

  • Danilo Mercurio


An adaptive estimation algorithm for time series is presented in this chapter. The basic idea is the following: given a time series and a linear model, we select on-line the largest sample of the most recent observations, such that the model is not rejected. Assume for example that the data can be well fitted by a regression, an autoregression or even by a constant in an unknown interval. The main problem is then to detect the time interval where the model approximately holds. We call such an interval: interval of time homogeneity.


Exchange Rate Interest Rate Kalman Filter Investment Horizon Adaptive Estimation 
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  1. Bollerslev, T. (1995). Generalised autoregressive conditional heteroskedasticity, in Engle (1995).Google Scholar
  2. Carroll, R. and Ruppert, D. (1988). Transformation and Weighting in Regression, Chapman and Hall, New York.MATHGoogle Scholar
  3. Christoffersen, P. and Giorgianni, L. (2000). Interest rate in currency basket: Forecasting weights and measuring risk, Journal of Business and Economic Statistics 18: 321–335.Google Scholar
  4. Chui, C. and Chen, G. (1998). Kaiman Filtering, Information Sciences, third edn, Springer-Verlag, Berlin.Google Scholar
  5. Clements, M. P. and Hendry, D. F. (1998). Forecastng Economic Time Series, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
  6. Cooley, T. F. and Prescott, E. C. (1973). An adaptive regression model, International Economic Review 14: 364–371.MathSciNetCrossRefGoogle Scholar
  7. Eichengreen, B., Masson, P., Savastano, M. and Sharma, S. (1999). Transition Strategies and Nominal Anchors on the Road to Greater Exchange Rate Flexibility, number 213 in Essays in International Finance, Princeton University Press.Google Scholar
  8. Elliot, R. J., Aggoun, L. and Moore, J. B. (1995). Hidden Markov Models, Springer-Verlag, Berlin.Google Scholar
  9. Engie, R. F. (ed.) (1995). ARCH, selected readings, Oxford University Press, Oxford.Google Scholar
  10. Franke, J., Härdle, W. and Hafner, C. (2001). Einführung in die Statistik der Finanzmärkte, Springer, Berlin.Google Scholar
  11. Härdle, W., Herwartz, H. and Spokoiny, V. (2001). Time inhomogeous multiple volatility modelling. Discussion Paper 7, Sonderforschungsbereich 373, Humboldt-Universität zu Berlin. To appear in Financial Econometrics. Google Scholar
  12. Härdle, W., Spokoiny, V. and Teyssière, G. (2000). Adaptive estimation for a time inhomogeneouse stochastic volatility model. Discussion Paper 6, Sonderforschungsbereich 373, Humboldt-Universität zu Berlin.Google Scholar
  13. Harvey, A., Ruiz, E. and Shephard, N. (1995). Multivariate stochastic variance models, in Engle (1995).Google Scholar
  14. Lepski, O. (1990). One problem of adaptive estimation in gaussian white noise, Theory Probab. Appl. 35: 459–470.MathSciNetCrossRefGoogle Scholar
  15. Lepski, O. and Spokoiny, V. (1997). Optimal pointwise adaptive methods in nonparametric estimation, Annals of Statistics 25: 2512–2546.MathSciNetMATHCrossRefGoogle Scholar
  16. Liptser, R. and Spokoiny, V. (1999). Deviation probability bound for martingales with applications to statistical estimation, Stat. & Prob. Letter 46: 347–357.MathSciNetCrossRefGoogle Scholar
  17. Mercurio, D. and Spokoiny, V. (2000). Statistical inference for time-inhomogeneous volatility models. Discussion Paper 583, Weierstrass Institute for Applied Analysis and Stochastic, Berlin.Google Scholar
  18. Mercurio, D. and Torricelli, C. (2001). Estimation and arbitrage opportunities for exchange rate baskets. Discussion Paper 37, Sonderforschungsbereich 373, Humboldt-Universität zu Berlin.Google Scholar
  19. Musiela, M. and Rutkowski, M. (1997). Martingale Methods in Financial Modelling, number 36 in Application of Mathemathics. Stochastic Modelling and Applied Probability, Springer, New York.CrossRefGoogle Scholar
  20. Spokoiny, V. (1998). Estimation of a function with discontinuities via local polynomial fit with an adaptive window choice, Annals of Statistics 26: 1356–1378.MathSciNetMATHCrossRefGoogle Scholar
  21. Taylor, S. J. (1986). Modelling Financial Time Series, Wiley, Chichester.MATHGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2002

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  • Danilo Mercurio

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