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Original Articles

Spline confidence bands for variance functions in nonparametric time series regressive models

, &
Pages 699-714 | Received 16 Aug 2011, Accepted 06 May 2012, Published online: 26 Jun 2012

References

  • Audrino , F. and Bühlmann , P. 2009 . Splines for Financial Volatility . Journal of the Royal Statistical Society, Series B , 71 : 655 – 670 .
  • de Boor , C. 2001 . A Practical Guide to Splines , New York : Springer .
  • Bosq , D. 1998 . Nonparametric Statistics for Stochastic Processes , New York : Springer .
  • Demko , S. 1977 . Inverse of Band Matrices and Local Convergence of Spline Projections . SIAM Journal on Numerical Analysis , 4 : 616 – 619 .
  • DeVore , R. A. and Lorentz , G. G. 1993 . Constructive Approximation , New York : Springer .
  • Engle , R. F. 1982 . Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation . Econometrica , 50 : 987 – 1007 .
  • Engle, R.F., and Rangel, J.G. (2005), ‘The Spline GARCH Model for Unconditional Volatility and Its Global Macroeconomic Causes’, Czech National Bank Working Paper Series #13. http://www.cnb.cz/en/research/research_publications/cnb_wp/download/cnbwp_2005_13.pdf.
  • Fan , J. and Gijbels , I. 1996 . Local Polynomial Modelling and its Applications , London : Chapman & Hall .
  • Fan , J. and Yao , Q. 1998 . Efficient Estimation of Conditional Variance Functions in Stochatic Regression . Biometrika , 85 : 645 – 660 .
  • Fan , J. and Yao , Q. 2003 . Nonlinear Time Series: Nonparametric and Parametric Methods , New York : Springer .
  • Hall , P. and Carroll , R. J. 1989 . Variance Function Estimation in Regression: The Effect of Estimating the Mean . Journal of the Royal Statistical Society, Series B , 51 : 3 – 14 .
  • Härdle , W. and Tsybakov , A. 1997 . Local Polynomial Estimators of the Volatility Function in Nonparametric Autoregression . Journal of Econometrics , 81 : 223 – 242 .
  • Huang , J. Z. 2003 . Local Asymptotics for Polynomial Spline Regression . The Annals of Statistics , 31 : 1600 – 1635 .
  • Huang , J. Z. and Yang , L. 2004 . Identification of Non-Linear Additive Autoregressive Models . Journal of the Royal Statistical Society, Series B , 66 : 463 – 477 .
  • Silverman , B. W. 1986 . Density Estimation for Statistics and Data Analysis , London : Chapman & Hall .
  • Song , Q. and Yang , L. 2009 . Spline Confidence Bands for Variance Function . Journal of Nonparametric Statistics , 21 : 589 – 609 .
  • Stone , C. J. 1985 . Additive Regression and Other Nonparametric Models . The Annals of Statistics , 13 : 689 – 705 .
  • Wang , L. and Yang , L. 2007 . Spline-Backfitted Kernel Smoothing of Nonlinear Additive Autoregression Model . The Annals of Statistics , 35 : 2474 – 2503 .
  • Wang , J. and Yang , L. 2009 . Polynomial Spline Confidence Bands for Regression Curves . Statistca Sinica , 19 : 325 – 342 .
  • Wang , L. and Yang , L. 2010 . Simultaneous Confidence Bands for Time-Series Prediction Function . Journal of Nonparametric Statistics , 22 : 999 – 1018 .
  • Wu , X. , Tian , Z. and Wang , H. 2009 . Polynomial Spline Estimation for Nonparametric (Auto-)Regressive Models . Studia Scientiarum Mathematicarum Hungarica , 46 : 515 – 538 .
  • Xue , L. and Yang , L. 2006 . Additive Coefficient Modeling Via Polynomial Spline . Statistica Sinica , 16 : 1423 – 1446 .
  • Zhao , Z. B. and Wu , W. B. 2008 . Confidence Bands in Nonparametric Time Series Regression . The Annals of Statistics , 36 : 1854 – 1878 .

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