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Time series smoothing by penalized least squares

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  • Guerrero, Victor M.

Abstract

The time series smoothing problem is approached in a slightly more general form than usual. The proposed statistical solution involves an implicit adjustment to the observations at both extremes of the time series. The resulting estimated trend becomes more statistically grounded and an estimate of its sampling variability is provided. An index of smoothness is derived and proposed as a tool for choosing the smoothing constant.

Suggested Citation

  • Guerrero, Victor M., 2007. "Time series smoothing by penalized least squares," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1225-1234, July.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:12:p:1225-1234
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    References listed on IDEAS

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    1. Jewson Stephen & Penzer Jeremy, 2006. "Estimating Trends in Weather Series: Consequences for Pricing Derivatives," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(3), pages 1-17, September.
    2. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231.
    3. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    4. Guerrero, Víctor M. & Juárez, Rodrigo & Poncela, Pilar, 2001. "Data graduation based on statistical time series methods," Statistics & Probability Letters, Elsevier, vol. 52(2), pages 169-175, April.
    5. Reeves Jonathan J. & Blyth Conrad A. & Triggs Christopher M. & Small John P., 2000. "The Hodrick-Prescott Filter, a Generalization, and a New Procedure for Extracting an Empirical Cycle from a Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 4(1), pages 1-17, April.
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    1. Eliud Silva & Víctor M. Guerrero, 2017. "Penalized least squares smoothing of two-dimensional mortality tables with imposed smoothness," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(9), pages 1662-1679, July.
    2. Víctor M. Guerrero & Daniela Cortés Toto & Hortensia J. Reyes Cervantes, 2018. "Effect of autocorrelation when estimating the trend of a time series via penalized least squares with controlled smoothness," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 109-130, March.
    3. A. ISLAS & Víctor M. GUERRERO & Eliud SILVA, 2019. "Forecasting Remittances to Mexico with a Multi-State Markov-Switching Model Applied to the Trend with Controlled Smoothness," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 38-56, March.
    4. Víctor M. Guerrero & Adriana Galicia‐Vázquez, 2010. "Trend estimation of financial time series," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 205-223, May.
    5. Víctor M. Guerrero & Juan A. Mendoza, 2019. "On measuring economic growth from outer space: a single country approach," Empirical Economics, Springer, vol. 57(3), pages 971-990, September.

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