IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2008-05.html
   My bibliography  Save this paper

Barlett’s Formula for Non Linear Processes

Author

Listed:
  • Christian Francq

    (Crest)

  • Jean-Michel Zakoïan

    (Crest)

Abstract

A Bartlett-type formula is proposed for the asymptotic distribution of the sample autocorrelations ofnonlinear processes. The asymptotic covariances between sample autocorrelations are expressed as thesum of two terms. The first term corresponds to the standard Bartlett’s formula for linear processes,involving only the autocorrelation function of the observed process. The second term, which is specificto nonlinear processes, involves the autocorrelation function of the observed process, the kurtosis of thelinear innovation process and the autocorrelation function of its square. This formula is obtained under asymmetry assumption on the linear innovation process. An application to GARCH models is proposed.

Suggested Citation

  • Christian Francq & Jean-Michel Zakoïan, 2008. "Barlett’s Formula for Non Linear Processes," Working Papers 2008-05, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2008-05
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2008-05.pdf
    File Function: Crest working paper version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(3), pages 722-729, June.
    2. Alain Berlinet & Christian Francq, 1997. "On Bartlett’s Formula for Non‐linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(6), pages 535-552, November.
    3. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521547871, September.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Lütkepohl,Helmut & Krätzig,Markus (ed.), 2004. "Applied Time Series Econometrics," Cambridge Books, Cambridge University Press, number 9780521839198, September.
    6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    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. Christian Francq & Jean‐Michel Zakoïan, 2009. "Bartlett's formula for a general class of nonlinear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 449-465, July.
    2. Christian Francq & Roch Roy & Abdessamad Saidi, 2011. "Asymptotic Properties of Weighted Least Squares Estimation in Weak PARMA Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 32(6), pages 699-723, November.

    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. Christian Francq & Jean‐Michel Zakoïan, 2009. "Bartlett's formula for a general class of nonlinear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 449-465, July.
    2. Efimova, Olga & Serletis, Apostolos, 2014. "Energy markets volatility modelling using GARCH," Energy Economics, Elsevier, vol. 43(C), pages 264-273.
    3. Sahminan, 2005. "Interest Rates And The Role Of Exchange Rate Regimes In Major Southeast Asian Countries," Bulletin of Monetary Economics and Banking, Bank Indonesia, vol. 8(2), pages 181-198, September.
    4. Brümmer, Bernhard, 2021. "Preisvolatilität auf Agrarmärkten," IAMO Discussion Papers 310089, Institute of Agricultural Development in Transition Economies (IAMO).
    5. Fresoli, Diego E. & Ruiz, Esther, 2016. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 170-185.
    6. repec:zbw:iamodp:310089 is not listed on IDEAS
    7. Pami Dua & Divya Tuteja, 2013. "Interdependence Of International Financial Market-- The Case Of India And U.S," Working papers 223, Centre for Development Economics, Delhi School of Economics.
    8. Hollander, Hilke & Prokop, Jörg, 2015. "Stock price effects of asset securitization: The case of liquidity facility providers," The Quarterly Review of Economics and Finance, Elsevier, vol. 57(C), pages 147-160.
    9. Amendola, Alessandra & Christian, Francq, 2009. "Concepts and tools for nonlinear time series modelling," MPRA Paper 15140, University Library of Munich, Germany.
    10. Chang, Chia-Lin, 2015. "Modelling a latent daily Tourism Financial Conditions Index," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 113-126.
    11. Massimiliano Caporin & Michael McAleer, 2011. "Thresholds, news impact surfaces and dynamic asymmetric multivariate GARCH," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(2), pages 125-163, May.
    12. Chan, Felix & Marinova, Dora & McAleer, Michael, 2004. "Modelling the asymmetric volatility of electronics patents in the USA," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(1), pages 169-184.
    13. CHIA-LIN CHANG & MICHAEL McALEER & ROENGCHAI TANSUCHAT, 2012. "Modelling Long Memory Volatility In Agricultural Commodity Futures Returns," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 1-27.
    14. Chia-Lin Chang & Michael Mcaleer, 2009. "Daily Tourist Arrivals, Exchange Rates and Voatility for Korea and Taiwan," Korean Economic Review, Korean Economic Association, vol. 25, pages 241-267.
    15. Wan, Xiaoli & Yan, Yuruo & Zeng, Zhixiong, 2020. "Exchange rate regimes and market integration: evidence from the dynamic relations between renminbi onshore and offshore markets," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    16. Michael McAleer, 2009. "The Ten Commandments For Optimizing Value‐At‐Risk And Daily Capital Charges," Journal of Economic Surveys, Wiley Blackwell, vol. 23(5), pages 831-849, December.
    17. McAleer, M.J. & Jiménez-Martín, J.A. & Pérez-Amaral, T., 2008. "A decision rule to minimize daily capital charges in forecasting value-at-risk," Econometric Institute Research Papers EI 2008-34, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    18. Chia-Lin Chang & Michael McAleer & Christine Lim, 2010. "Modelling the Volatility in Short and Long Haul Japanese Tourist Arrivals to New Zealand and Taiwan," Working Papers in Economics 10/40, University of Canterbury, Department of Economics and Finance.
    19. Huang, Biing-Wen & Chen, Meng-Gu & Chang, Chia-Lin & McAleer, Michael, 2009. "Modelling risk in agricultural finance: Application to the poultry industry in Taiwan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(5), pages 1472-1487.
    20. Chang, Chia-Lin & González-Serrano, Lydia & Jimenez-Martin, Juan-Angel, 2013. "Currency hedging strategies using dynamic multivariate GARCH," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 164-182.
    21. Chang, Chia-Lin & Jimenez-Martin, Juan-Angel & McAleer, Michael & Amaral, Teodosio Perez, 2013. "The rise and fall of S&P500 variance futures," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 151-167.

    More about this item

    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:crs:wpaper:2008-05. 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: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    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.