IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v33y1997i2p201-208.html
   My bibliography  Save this article

Unifying the derivations for the Akaike and corrected Akaike information criteria

Author

Listed:
  • Cavanaugh, Joseph E.

Abstract

The Akaike (1973, 1974) information criterion, AIC, and the corrected Akaike information criterion (Hurvich and Tsai, 1989), AICc, were both designed as estimators of the expected Kullback-Leibler discrepancy between the model generating the data and a fitted candidate model. AIC is justified in a very general framework, and as a result, offers a crude estimator of the expected discrepancy: one which exhibits a potentially high degree of negative bias in small-sample applications (Hurvich and Tsai, 1989). AICc corrects for this bias, but is less broadly applicable than AIC since its justification depends upon the form of the candidate model (Hurvich and Tsai, 1989, 1993; Hurvich et al., 1990; Bedrick and Tsai, 1994). Although AIC and AICc share the same objective, the derivations of the criteria proceed along very different lines, making it difficult to reconcile how AICc improves upon the approximations leading to AIC. To address this issue, we present a derivation which unifies the justifications of AIC and AICc in the linear regression framework.

Suggested Citation

  • Cavanaugh, Joseph E., 1997. "Unifying the derivations for the Akaike and corrected Akaike information criteria," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 201-208, April.
    • Handle: RePEc:eee:stapro:v:33:y:1997:i:2:p:201-208
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(96)00128-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Clifford M. Hurvich & Chih‐Ling Tsai, 1993. "A Corrected Akaike Information Criterion For Vector Autoregressive Model Selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 271-279, May.
    2. J. M. Bernardo, 1976. "Psi (Digamma) Function," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(3), pages 315-317, November.
    Full references (including those not matched with items on IDEAS)

    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. François-Éric Racicot & Raymond Théoret, 2022. "Tracking market and non-traditional sources of risks in procyclical and countercyclical hedge fund strategies under extreme scenarios: a nonlinear VAR approach," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-56, December.
    2. Carlos A. Medel, 2015. "Probabilidad Clásica de Sobreajuste con Criterios de Información: Estimaciones con Series Macroeconómicas Chilenas," Revista de Analisis Economico – Economic Analysis Review, Universidad Alberto Hurtado/School of Economics and Business, vol. 30(1), pages 57-72, Abril.
    3. Daniel Grabowski & Anna Staszewska-Bystrova & Peter Winker, 2020. "Skewness-adjusted bootstrap confidence intervals and confidence bands for impulse response functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 5-32, March.
    4. Nan Li & Simon S. Kwok, 2021. "Jointly determining the state dimension and lag order for Markov‐switching vector autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 471-491, July.
    5. Daniel Fernández, 2011. "Suficiencia del capital y previsiones de la banca uruguaya por su exposición al sector industrial," Monetaria, CEMLA, vol. 0(4), pages 517-589, octubre-d.
    6. Meijer, Erik, 2004. "Computation of characteristics of value-of-time distributions and their standard errors," Research Report 04F09, University of Groningen, Research Institute SOM (Systems, Organisations and Management).
    7. Javier Pereda, 2011. "Estimación de la tasa natural de interés para Perú: un enfoque financiero," Monetaria, CEMLA, vol. 0(4), pages 429-459, octubre-d.
    8. Anna Staszewska-Bystrova, 2009. "Bootstrap Confidence Bands for Forecast Paths," Working Papers 024, COMISEF.
    9. Bengtsson, Thomas & Cavanaugh, Joseph E., 2006. "An improved Akaike information criterion for state-space model selection," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2635-2654, June.
    10. Boubacar Mainassara, Yacouba, 2010. "Selection of weak VARMA models by modified Akaike's information criteria," MPRA Paper 24981, University Library of Munich, Germany.
    11. Oscar Jorda, 2003. "Model-Free Impulse Responses," Working Papers 38, University of California, Davis, Department of Economics.
    12. Tamara Burdisso & Eduardo Ariel Corso, 2011. "Incertidumbre y dolarización de cartera: el caso argentino en el último medio siglo," Monetaria, CEMLA, vol. 0(4), pages 461-515, octubre-d.
    13. Marhuenda, Yolanda & Morales, Domingo & del Carmen Pardo, María, 2014. "Information criteria for Fay–Herriot model selection," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 268-280.
    14. Carlos Medel, 2012. "¿Akaike o Schwarz? ¿Cuál elegir para Predecir el PIB Chileno?," Working Papers Central Bank of Chile 658, Central Bank of Chile.
    15. M. El-Morshedy & Ziyad Ali Alhussain & Doaa Atta & Ehab M. Almetwally & M. S. Eliwa, 2020. "Bivariate Burr X Generator of Distributions: Properties and Estimation Methods with Applications to Complete and Type-II Censored Samples," Mathematics, MDPI, vol. 8(2), pages 1-31, February.
    16. Fulvia Pennoni & Francesco Bartolucci & Gianfranco Forte & Ferdinando Ametrano, 2022. "Exploring the dependencies among main cryptocurrency log‐returns: A hidden Markov model," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 51(1), February.
    17. Lee, Shyan-Yuan & Tsai, Chih-Ling, 1998. "Model selection for causal models: The global procedure with AICC and AICU," Global Finance Journal, Elsevier, vol. 9(2), pages 205-223.
    18. Racicot, François-Éric & Théoret, Raymond, 2018. "Multi-moment risk, hedging strategies, & the business cycle," International Review of Economics & Finance, Elsevier, vol. 58(C), pages 637-675.
    19. Shang, Junfeng & Cavanaugh, Joseph E., 2008. "Bootstrap variants of the Akaike information criterion for mixed model selection," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2004-2021, January.
    20. Òscar Jordà & Massimiliano Marcellino, 2010. "Path forecast evaluation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 635-662.

    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:eee:stapro:v:33:y:1997:i:2:p:201-208. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.