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Local Linear Forecasts Using Cubic Smoothing Splines

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  • Rob J Hyndman

    ()

  • Maxwell L. King

    ()

  • Ivet Pitrun
  • Baki Billah

Abstract

We show how cubic smoothing splines fitted to univariate time series data can be used to obtain local linear forecasts. Our approach is based on a stochastic state space model which allows the use of a likelihood approach for estimating the smoothing parameter, and which enables easy construction of prediction intervals. We show that our model is a special case of an ARIMA(0,2,2) model and we provide a simple upper bound for the smoothing parameter to ensure an invertible model. We also show that the spline model is not a special case of Holt's local linear trend method. Finally we compare the spline forecasts with Holt's forecasts and those obtained from the full ARIMA(0,2,2) model, showing that the restricted parameter space does not impair forecast performance.

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File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2002/wp10-02.pdf
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Bibliographic Info

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 10/02.

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Length: 19 pages
Date of creation: Aug 2002
Date of revision:
Handle: RePEc:msh:ebswps:2002-10

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Related research

Keywords: ARIMA models; exponential smoothing; Holt's local linear forecasts; maximum likelihood estimation; nonparametric regression; smoothing splines; state space model; stochastic trends.;

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References

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  1. Hyndman, Rob J. & Koehler, Anne B. & Snyder, Ralph D. & Grose, Simone, 2002. "A state space framework for automatic forecasting using exponential smoothing methods," International Journal of Forecasting, Elsevier, vol. 18(3), pages 439-454.
  2. Assimakopoulos, V. & Nikolopoulos, K., 2000. "The theta model: a decomposition approach to forecasting," International Journal of Forecasting, Elsevier, vol. 16(4), pages 521-530.
  3. Harvey, A.C. & Koopman, S.J.M., 1999. "Signal Extraction and the Formulation of Unobserved Components Models," Discussion Paper 1999-44, Tilburg University, Center for Economic Research.
  4. Hyndman, R.J. & Billah, B., 2001. "Unmasking the Theta Method," Monash Econometrics and Business Statistics Working Papers 5/01, Monash University, Department of Econometrics and Business Statistics.
  5. Piet Jong & Sonia Mazzi, 2001. "Modeling and Smoothing Unequally Spaced Sequence Data," Statistical Inference for Stochastic Processes, Springer, vol. 4(1), pages 53-71, January.
  6. Hyndman, R.J. & Koehler, A.B. & Ord, J.K. & Snyder, R.D., 2001. "Prediction Intervals for Exponential Smoothing State Space Models," Monash Econometrics and Business Statistics Working Papers 11/01, Monash University, Department of Econometrics and Business Statistics.
  7. Beran, Jan & Feng, Yuanhua, 2002. "SEMIFAR models--a semiparametric approach to modelling trends, long-range dependence and nonstationarity," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 393-419, August.
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Cited by:
  1. Rob J. Hyndman & Yeasmin Khandakar, 2007. "Automatic time series forecasting: the forecast package for R," Monash Econometrics and Business Statistics Working Papers 6/07, Monash University, Department of Econometrics and Business Statistics.
  2. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.

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