IDEAS home Printed from https://ideas.repec.org/p/cte/wsrepe/10576.html
   My bibliography  Save this paper

Missing observations in ARIMA models: skipping strategy versus additive outlier approach

Author

Listed:
  • Gómez, Víctor
  • Maravall, Agustín
  • Peña, Daniel

Abstract

Optimal estimation of missing values in ARMA models is typically performed by using the Kalman Filter for likelihood evaluation, "skipping" in the computations the missing observations, obtaining the maximum likelihood (ML) estimators of the model parameters, and using some smoothing algorithm. The same type of procedure has been extended to nonstationary ARIMA models in G6mez Maravall (1994). An alternative procedure suggests filling in the holes in the series with arbitrary values and then performing ML estimation of the ARIMA model with Additive Outliers (AO). When the model parameters are not known the two methods differ, since the AO likelihood is affected by the arbitrary values. We develop the proper likelihood for the AO approach in the general non-stationary case and show the equivalence of this and the skipping method. Computationally efficient ways to apply both procedures, based on an Augmented Kalman Filter, are detailed. Finally, the two methods are compared through simulation, and their relative advantages assessed; the comparison also includes the AO method with the uncorrected likelihood.

Suggested Citation

  • Gómez, Víctor & Maravall, Agustín & Peña, Daniel, 1997. "Missing observations in ARIMA models: skipping strategy versus additive outlier approach," DES - Working Papers. Statistics and Econometrics. WS 10576, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:10576
    as

    Download full text from publisher

    File URL: https://e-archivo.uc3m.es/bitstream/handle/10016/10576/ws9715.pdf?sequence=1
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. S. R. Brubacher & G. Tunnicliffe Wilson, 1976. "Interpolating Time Series with Application to the Estimation of Holiday Effects on Electricity Demand," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(2), pages 107-116, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Barry, Boubacar-Sid & Wodon, Quentin, 2007. "Conflict, Growth, and Poverty in Guinea-Bissau," MPRA Paper 11112, University Library of Munich, Germany.
    2. Humberto Lopez & Quentin Wodon & Ian Bannon, 2004. "Rwanda : The Impact of Conflict on Growth and Poverty," World Bank Publications - Reports 11268, The World Bank Group.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alonso, Andres M. & Sipols, Ana E., 2008. "A time series bootstrap procedure for interpolation intervals," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 1792-1805, January.
    2. Comincioli, Nicola & Vergalli, Sergio, 2020. "Effects of Carbon Tax on Electricity Price Volatility: Empirical Evidences from the Australian Market," 2030 Agenda 305205, Fondazione Eni Enrico Mattei (FEEM).
    3. Álvarez, Luis J. & Delrieu, Juan C. & Espasa, Antoni, 1992. "Aproximación lineal por tramos a comportamientos no lineales: estimación de señales de nivel y crecimiento," DES - Documentos de Trabajo. Estadística y Econometría. DS 2940, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Victor M. Guerrero & Daniel Peña, 1995. "Linear Combination of Information in Time Series Analysis," Working Papers 9507, Centro de Investigacion Economica, ITAM.
    5. Maravall, Agustín & Peña, Daniel, 1992. "Missing observations and additive outliers in time series models," UC3M Working papers. Economics 2888, Universidad Carlos III de Madrid. Departamento de Economía.
    6. Gomez, Victor & Maravall, Agustin & Pena, Daniel, 1998. "Missing observations in ARIMA models: Skipping approach versus additive outlier approach," Journal of Econometrics, Elsevier, vol. 88(2), pages 341-363, November.
    7. Justel, Ana & Peña, Daniel & Sánchez, María Jesús, 1994. "Grupos atípicos en modelos econométricos," DES - Documentos de Trabajo. Estadística y Econometría. DS 10755, Universidad Carlos III de Madrid. Departamento de Estadística.
    8. Gómez, Víctor & Maravall, Agustín & Peña, Daniel, 1993. "Computing missing values in time series," DES - Working Papers. Statistics and Econometrics. WS 3737, Universidad Carlos III de Madrid. Departamento de Estadística.
    9. Cheng, R. & Pourahmadi, M., 1997. "Prediction with incomplete past and interpolation of missing values," Statistics & Probability Letters, Elsevier, vol. 33(4), pages 341-346, May.
    10. Pascal Bondon, 2005. "Influence of Missing Values on the Prediction of a Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 519-525, July.
    11. Pedro Delicado & Ana Justel, 1997. "Forecasting with missing data: Application to a real case," Economics Working Papers 213, Department of Economics and Business, Universitat Pompeu Fabra.
    12. Kasahara, Yukio & Pourahmadi, Mohsen & Inoue, Akihiko, 2009. "Duals of random vectors and processes with applications to prediction problems with missing values," Statistics & Probability Letters, Elsevier, vol. 79(14), pages 1637-1646, July.
    13. Delicado, Pedro, 1995. "Predicción con datos faltantes: aplicación a un caso real," DES - Documentos de Trabajo. Estadística y Econometría. DS 3583, Universidad Carlos III de Madrid. Departamento de Estadística.
    14. Zudi Lu & Y. Hui, 2003. "L 1 linear interpolator for missing values in time series," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(1), pages 197-216, March.

    More about this item

    Keywords

    Time series;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cte:wsrepe:10576. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Ana Poveda (email available below). General contact details of provider: http://portal.uc3m.es/portal/page/portal/dpto_estadistica .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.