122
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Smoothing a Time Series by Segments of the Data Range

&
Pages 4568-4585 | Received 30 Jul 2013, Accepted 26 Feb 2014, Published online: 11 Nov 2015

References

  • Box, G., Jenkins, G., Reinsel, G. (1994). Time Series Analysis. Forecasting and Control (3rd ed.). Englewood Cliffs, NJ: Prentice Hall.
  • Brown, P., de Jong, P. (2001). Nonparametric smoothing using state space techniques. Can. J. Stat. 29:37–50.
  • Cantoni, E., Hastie, T. (2002). Degrees of freedom tests for smoothing splines. Biometrika 89:251–263.
  • Carriere, J. (1992). Parametric models for life tables. Trans. Soc. Actuaries 44:77–99.
  • Chandler, R., Scott, M. (2011). Statistical Methods for Trend Detection and Analysis in the Environmental Sciences ( 1st ed.). London: Wiley.
  • Currie, I.D., Durban, M. (2002). Flexible smoothing with P-splines: A unified approach. Stat. Modell. 4:333–349.
  • Eilers, P., Marx, B. (1996). Flexible smoothing with B-splines and penalties. Stat. Sci. 11:89–121.
  • Fledelius, P., Guillen, M., Jens, P., Petersen, K. (2004). A comparative study of parametric and non-parametric estimators of old-age mortality in Sweden. J. Actuarial Pract. 11:101–126.
  • Guerrero, V.M. (2007). Time series smoothing by penalized least squares. Stat. Probab. Lett. 77:1225–1234.
  • Guerrero, V.M. (2008). Estimating trends with percentage of smoothness chosen by the user. Int. Stat. Rev. 76:187–202.
  • Guerrero, V.M., Silva, E. (2010). Non-parametric and structured graduation of mortality rates. Popul. Rev. 49:13–26.
  • Helligman, L., Pollard, J. (1980). The age pattern of mortality. J. Inst. Actuaries 107:49–80.
  • Hodrick, R., Prescott, E. (1997). Post-war U.S. business cycles: An empirical investigation. J. Money, Credit and Banking 29:1–16.
  • Lee, R., Carter, L. (1992). Modeling and forecasting U.S. mortality. J. Am. Stat. Assoc. 87:659–675.
  • Leser, C. (1961). A simple method of trend construction. J. R. Stat. Soc., Ser.B 23:91–107.
  • London, D. (1985). GRADUATION: The Revision of Estimates. Winsted, CT: ACTEX.
  • Hastie, T., Tibshirani, R. (1999). Generalized Additive Models. London: Chapman & Hall.
  • Hurvich, C., Simonoff, J.S., Tsai, C.L. (1998). Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. J. R. Stat. Soc. Ser.B 60:271–293.
  • Kaiser, R., Maravall, A. (2001). Measuring Business Cycles in Economic Time Series. Lecture Notes in Statistics 154. New York: Springer.
  • Kauermann, G. (2005). A note on smoothing parameter selection for penalized spline smoothing. J. Stat. Plann. Inference 127:53–69.
  • Kitagawa, G., Gersch, W. (1996). Smoothness Priors Analysis of Time Series. Lecture Notes in Statistics 116. New York: Springer.
  • Stockhammar, P., Öller, L.-E. (2012). A simple heteroscedasticity removing filter. Commun. Stat.– Theory and Methods 41:281–299.
  • Proietti, T. (2005). Forecasting and signal extraction with misspecified models. J. Forecasting 24:539–556.
  • Ripley, B. (2013). P-spline: Penalized Smoothing Splines [R package version 1.0-16] http://cran.r-project.org/web/packages/pspline/index.html.
  • Ruppert, D., Wand, M., Carroll, R. (2003). Semiparametric Regression. Cambridge: Cambridge University Press.
  • Theil, H. (1963). On the use of incomplete prior information in regression analysis. J. Am. Stat. Assoc. 58:401–414.
  • Thiele, P. (1871). On a mathematical formula to express the rate of mortality through the whole of life. J. Inst. Actuaries 16:313–329.
  • Tuljapurkar, S., Edwards, R. (2011). Variance in death and its implications for modeling and forecasting mortality. Demogr. Res. 21:497–526.
  • Wand, M. (1999). On the optimal amount of smoothing in penalised spline regression. Biometrika 86:936–940.
  • Whittaker, E. (1923). On a new method of graduation. Proc. Edinburgh Math. Soc. 41:63–75.
  • Whittaker, E. (1924). On the theory of graduation. Proc. R. Soc. Edinburgh 44:77–83.
  • Zhang, C. (2003). Calibrating the degrees of freedom for automatic data smoothing and effective curve checking. J. Am. Stat. Assoc. 98:609–628.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.