IDEAS home Printed from https://ideas.repec.org/a/bpj/sndecm/v19y2015i3p339-353n2.html
   My bibliography  Save this article

Testing for co-nonlinearity

Author

Listed:
  • Hungnes Håvard

    (Research Department, Statistics Norway, P.O.B. 8131 Dep, N-0033 Oslo, Norway)

Abstract

This article introduces the concept of co-nonlinearity. Co-nonlinearity is an example of a common feature in time series [Engle, Robert F., and Sharon Kozicki. 1993. “Testing for Common Features.” Journal of Business & Economic Statistics 11 (4): 369–380] and an extension of the concept of common nonlinear components [Anderson, Heather M., and Farshid Vahid. 1998. “Testing Multiple Equation Systems for Common Nonlinear Components.” Journal of Econometrics 84 (1): 1–36]. If some time series follow a nonlinear process but where a linear relationship between the levels of these series removes the nonlinearity, such a relationship is defined as co-nonlinear. In this article I show how to determine the number of such co-nonlinear relationships. Furthermore, I show how to formulate hypothesis tests on the co-nonlinear relationships in a full maximum likelihood framework. The framework for identifying co-nonlinear relationships is illustrated in a system of Norwegian interest rates.

Suggested Citation

  • Hungnes Håvard, 2015. "Testing for co-nonlinearity," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(3), pages 339-353, June.
    • Handle: RePEc:bpj:sndecm:v:19:y:2015:i:3:p:339-353:n:2
    DOI: 10.1515/snde-2013-0092
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/snde-2013-0092
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.
    File URL: https://libkey.io/10.1515/snde-2013-0092?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. González Andrés & Teräsvirta Timo, 2008. "Modelling Autoregressive Processes with a Shifting Mean," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-28, March.
    2. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-360, Oct.-Dec..
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Engle, Robert F & Hylleberg, Svend, 1996. "Common Seasonal Features: Global Unemployment," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 615-630, November.
    5. Durbin, James & Koopman, Siem Jan, 2012. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, edition 2, number 9780199641178.
    6. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
    7. repec:bla:jecsur:v:13:y:1999:i:2:p:i is not listed on IDEAS
    8. H. Peter Boswijk & Jurgen A. Doornik, 2004. "Identifying, estimating and testing restricted cointegrated systems: An overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 440-465, November.
    9. Anderson, Heather M. & Victor Issler, Joao & Vahid, Farshid, 2006. "Common features," Journal of Econometrics, Elsevier, vol. 132(1), pages 1-5, May.
    10. Anderson, Heather M. & Vahid, Farshid, 1998. "Testing multiple equation systems for common nonlinear components," Journal of Econometrics, Elsevier, vol. 84(1), pages 1-36, May.
    11. Bierens, Herman J, 2000. "Nonparametric Nonlinear Cotrending Analysis, with an Application to Interest and Inflation in the United States," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 323-337, July.
    12. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155.
    13. H. Peter Boswijk & Jurgen A. Doornik, 2004. "Identifying, estimating and testing restricted cointegrated systems: An overview," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(4), pages 440-465.
    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. Boug, Pål & Brasch, Thomas von & Cappelen, Ådne & Hammersland, Roger & Hungnes, Håvard & Kolsrud, Dag & Skretting, Julia & Strøm, Birger & Vigtel, Trond C., 2023. "Fiscal policy, macroeconomic performance and industry structure in a small open economy," Journal of Macroeconomics, Elsevier, vol. 76(C).
    2. Kirstin Hubrich & Timo Teräsvirta, 2013. "Thresholds and Smooth Transitions in Vector Autoregressive Models," CREATES Research Papers 2013-18, Department of Economics and Business Economics, Aarhus University.

    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. Marco Centoni & Gianluca Cubadda, 2011. "Modelling comovements of economic time series: a selective survey," Statistica, Department of Statistics, University of Bologna, vol. 71(2), pages 267-294.
    2. Engle, Robert F. & Marcucci, Juri, 2006. "A long-run Pure Variance Common Features model for the common volatilities of the Dow Jones," Journal of Econometrics, Elsevier, vol. 132(1), pages 7-42, May.
    3. Harvey,Andrew C., 2013. "Dynamic Models for Volatility and Heavy Tails," Cambridge Books, Cambridge University Press, number 9781107034723, September.
    4. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, September.
    5. Fabio Araujo & Joao Victor Issler, 2005. "Estimating the Stochastic Discount Factor without a Utility Function," Computing in Economics and Finance 2005 202, Society for Computational Economics.
    6. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    7. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    8. Matthew T. Holt & Timo Teräsvirta, 2012. "Global Hemispheric Temperature Trends and Co–Shifting: A Shifting Mean Vector Autoregressive Analysis," CREATES Research Papers 2012-54, Department of Economics and Business Economics, Aarhus University.
    9. Athanasopoulos, George & de Carvalho Guillén, Osmani Teixeira & Issler, João Victor & Vahid, Farshid, 2011. "Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions," Journal of Econometrics, Elsevier, vol. 164(1), pages 116-129, September.
    10. Broto Carmen & Ruiz Esther, 2009. "Testing for Conditional Heteroscedasticity in the Components of Inflation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(2), pages 1-30, May.
    11. Joshua Chan & Arnaud Doucet & Roberto León-González & Rodney W. Strachan, 2018. "Multivariate Stochastic Volatility with Co-Heteroscedasticity," Working Paper series 18-38, Rimini Centre for Economic Analysis.
    12. Gorgi, P. & Koopman, S.J., 2023. "Beta observation-driven models with exogenous regressors: A joint analysis of realized correlation and leverage effects," Journal of Econometrics, Elsevier, vol. 237(2).
    13. Ben Tims & Ronald Mahieu, 2006. "A Range-Based Multivariate Stochastic Volatility Model for Exchange Rates," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 409-424.
    14. Chen, Li & Gao, Jiti & Vahid, Farshid, 2022. "Global temperatures and greenhouse gases: A common features approach," Journal of Econometrics, Elsevier, vol. 230(2), pages 240-254.
    15. Markku Lanne, 2006. "Nonlinear dynamics of interest rate and inflation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(8), pages 1157-1168, December.
    16. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
    17. Siem Jan Koopman & André Lucas & Marcel Scharth, 2016. "Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 97-110, March.
    18. Anil K. Bera & Philip Garcia & Jae-Sun Roh, 1997. "Estimation of Time-Varying Hedge Ratios for Corn and Soybeans: BGARCH and Random Coefficient Approaches," Finance 9712007, University Library of Munich, Germany.
    19. Koopman, Siem Jan & Jungbacker, Borus & Hol, Eugenie, 2005. "Forecasting daily variability of the S&P 100 stock index using historical, realised and implied volatility measurements," Journal of Empirical Finance, Elsevier, vol. 12(3), pages 445-475, June.
    20. Bernardi, Mauro & Catania, Leopoldo, 2018. "Portfolio optimisation under flexible dynamic dependence modelling," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 1-18.

    More about this item

    Keywords

    common features; nonlinearity; reduced-rank regression;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

    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:bpj:sndecm:v:19:y:2015:i:3:p:339-353:n:2. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.