IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/81033.html
   My bibliography  Save this paper

Residual-based diagnostic tests for noninvertible ARMA models

Author

Listed:
  • Nyholm, Juho

Abstract

This paper proposes two residual-based diagnostic tests for noninvertible ARMA models. The tests are analogous to the portmanteau tests developed by Box and Pierce (1970), Ljung and Box (1978) and McLeod and Li (1983) in the conventional invertible case. We derive the asymptotic chi-squared distribution for the tests and study the size and power properties in a Monte Carlo simulation study. An empirical application employing financial time series data points out the usefulness of noninvertible ARMA model in analyzing stock returns and the use of the proposed test statistics.

Suggested Citation

  • Nyholm, Juho, 2017. "Residual-based diagnostic tests for noninvertible ARMA models," MPRA Paper 81033, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:81033
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/81033/1/MPRA_paper_81033.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jesús Fernández-Villaverde & Juan F. Rubio-Ramírez & Thomas J. Sargent & Mark W. Watson, 2007. "ABCs (and Ds) of Understanding VARs," American Economic Review, American Economic Association, vol. 97(3), pages 1021-1026, June.
    2. Kenneth Kasa & Todd B. Walker & Charles H. Whiteman, 2014. "Heterogeneous Beliefs and Tests of Present Value Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(3), pages 1137-1163.
    3. Lucia Alessi & Matteo Barigozzi & Marco Capasso, 2011. "Non‐Fundamentalness in Structural Econometric Models: A Review," International Statistical Review, International Statistical Institute, vol. 79(1), pages 16-47, April.
    4. Meitz, Mika & Saikkonen, Pentti, 2013. "Maximum likelihood estimation of a noninvertible ARMA model with autoregressive conditional heteroskedasticity," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 227-255.
    5. Lof Matthijs, 2013. "Noncausality and asset pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(2), pages 211-220, April.
    6. Andrews, Beth & Davis, Richard A. & Jay Breidt, F., 2006. "Maximum likelihood estimation for all-pass time series models," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1638-1659, August.
    7. Markku Lanne & Mika Meitz & Pentti Saikkonen, 2013. "Testing for Linear and Nonlinear Predictability of Stock Returns," Journal of Financial Econometrics, Oxford University Press, vol. 11(4), pages 682-705, September.
    8. Eric M. Leeper & Todd B. Walker & Shu‐Chun Susan Yang, 2013. "Fiscal Foresight and Information Flows," Econometrica, Econometric Society, vol. 81(3), pages 1115-1145, May.
    9. Poterba, James M. & Summers, Lawrence H., 1988. "Mean reversion in stock prices : Evidence and Implications," Journal of Financial Economics, Elsevier, vol. 22(1), pages 27-59, October.
    10. Forni, Mario & Gambetti, Luca, 2014. "Sufficient information in structural VARs," Journal of Monetary Economics, Elsevier, vol. 66(C), pages 124-136.
    11. Lars Peter Hansen & Thomas J. Sargent, 1981. "Exact linear rational expectations models: specification and estimation," Staff Report 71, Federal Reserve Bank of Minneapolis.
    12. Rongning Wu & Richard A. Davis, 2010. "Least absolute deviation estimation for general autoregressive moving average time‐series models," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(2), pages 98-112, March.
    13. A. I. McLeod & W. K. Li, 1983. "Diagnostic Checking Arma Time Series Models Using Squared‐Residual Autocorrelations," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 269-273, July.
    14. Henri Nyberg & Markku Lanne & Erkka Saarinen, 2012. "Does noncausality help in forecasting economic time series?," Economics Bulletin, AccessEcon, vol. 32(4), pages 2849-2859.
    15. Taylor, Stephen J., 1982. "Tests of the Random Walk Hypothesis Against a Price-Trend Hypothesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(1), pages 37-61, March.
    16. Jian Huang & Yudi Pawitan, 2000. "Quasi‐likelihood Estimation of Non‐invertible Moving Average Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 689-702, December.
    17. Olivier Blanchard & Roberto Perotti, 2002. "An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(4), pages 1329-1368.
    18. Kian‐Ping Lim & Robert Brooks, 2011. "The Evolution Of Stock Market Efficiency Over Time: A Survey Of The Empirical Literature," Journal of Economic Surveys, Wiley Blackwell, vol. 25(1), pages 69-108, February.
    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. Hamidi Sahneh, Mehdi, 2015. "Are the shocks obtained from SVAR fundamental?," MPRA Paper 65126, University Library of Munich, Germany.
    2. Frédérique Bec & Heino Bohn Nielsen & Sarra Saïdi, 2020. "Mixed Causal–Noncausal Autoregressions: Bimodality Issues in Estimation and Unit Root Testing," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1413-1428, December.
    3. Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2012. "Testing for predictability in a noninvertible ARMA model," MPRA Paper 37151, University Library of Munich, Germany.
    4. Jean-Baptiste MICHAU, 2019. "Helicopter Drops of Money under Secular Stagnation," Working Papers 2019-10, Center for Research in Economics and Statistics.
    5. Hecq, A.W. & Lieb, L.M. & Telg, J.M.A., 2015. "Identification of Mixed Causal-Noncausal Models : How Fat Should We Go?," Research Memorandum 035, Maastricht University, Graduate School of Business and Economics (GSBE).
    6. Pentti Saikkonen & Rickard Sandberg, 2016. "Testing for a Unit Root in Noncausal Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 99-125, January.
    7. Soccorsi, Stefano, 2016. "Measuring nonfundamentalness for structural VARs," Journal of Economic Dynamics and Control, Elsevier, vol. 71(C), pages 86-101.
    8. Ellahie, Atif & Ricco, Giovanni, 2017. "Government purchases reloaded: Informational insufficiency and heterogeneity in fiscal VARs," Journal of Monetary Economics, Elsevier, vol. 90(C), pages 13-27.
    9. Lof, Matthijs & Nyberg, Henri, 2017. "Noncausality and the commodity currency hypothesis," Energy Economics, Elsevier, vol. 65(C), pages 424-433.
    10. Bin Chen & Jinho Choi & Juan Carlos Escanciano, 2017. "Testing for fundamental vector moving average representations," Quantitative Economics, Econometric Society, vol. 8(1), pages 149-180, March.
    11. Alain Hecq & Daniel Velasquez-Gaviria, 2023. "Spectral identification and estimation of mixed causal-noncausal invertible-noninvertible models," Papers 2310.19543, arXiv.org.
    12. Iskrev, Nikolay, 2019. "On the sources of information about latent variables in DSGE models," European Economic Review, Elsevier, vol. 119(C), pages 318-332.
    13. Hecq, Alain & Issler, João Victor & Telg, Sean, 2017. "Mixed Causal-Noncausal Autoregressions with Strictly Exogenous Regressors," MPRA Paper 80767, University Library of Munich, Germany.
    14. Nelimarkka, Jaakko, 2017. "The effects of government spending under anticipation: the noncausal VAR approach," MPRA Paper 81303, University Library of Munich, Germany.
    15. Nadav Ben Zeev, 2019. "Is There A Single Shock That Drives The Majority Of Business Cycle Fluctuations?," Working Papers 1906, Ben-Gurion University of the Negev, Department of Economics.
    16. Nelimarkka, Jaakko, 2017. "Evidence on News Shocks under Information Deficiency," MPRA Paper 80850, University Library of Munich, Germany.
    17. Ben Zeev, Nadav, 2018. "What can we learn about news shocks from the late 1990s and early 2000s boom-bust period?," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 94-105.
    18. Ramey, V.A., 2016. "Macroeconomic Shocks and Their Propagation," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 71-162, Elsevier.
    19. Daniela Fantozzi & Alessio Muscarnera, 2021. "A News-based Policy Index for Italy: Expectations and Fiscal Policy," CEIS Research Paper 509, Tor Vergata University, CEIS, revised 11 Mar 2021.
    20. Nikolay Gospodinov & Serena Ng, 2015. "Minimum Distance Estimation of Possibly Noninvertible Moving Average Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(3), pages 403-417, July.

    More about this item

    Keywords

    Non-Gaussian time series; noninvertible ARMA model; model selection;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:81033. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.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.