IDEAS home Printed from https://ideas.repec.org/p/nip/nipewp/07-2018.html
   My bibliography  Save this paper

Models with Multiplicative Decomposition of Conditional Variances and Correlations

Author

Listed:
  • Cristina Amado

    (University of Minho and NIPE, CREATES and Aarhus University)

  • Annastiina Silvennoinen

    (School of Economics and Finance, Queensland University of Technology)

  • Timo Ter¨asvirta

    (CREATES and Aarhus University, C.A.S.E., Humboldt-Universit¨at zu Berlin)

Abstract

Univariate and multivariate GARCH type models with multiplicative decomposition of the variance to short and long run components are surveyed. The latter component can be either deterministic or stochastic. Examples of both types are studied.

Suggested Citation

  • Cristina Amado & Annastiina Silvennoinen & Timo Ter¨asvirta, 2018. "Models with Multiplicative Decomposition of Conditional Variances and Correlations," NIPE Working Papers 07/2018, NIPE - Universidade do Minho.
    • Handle: RePEc:nip:nipewp:07/2018
    as

    Download full text from publisher

    File URL: http://www.nipe.eeg.uminho.pt/Uploads/WP_2018/NIPE_WP_7_2018.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Christian Conrad & Melanie Schienle, 2020. "Testing for an Omitted Multiplicative Long-Term Component in GARCH Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 229-242, April.
    2. Opschoor, Anne & van Dijk, Dick & van der Wel, Michel, 2014. "Predicting volatility and correlations with Financial Conditions Indexes," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 435-447.
    3. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," The Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
    4. Paul Catani & Timo Teräsvirta & Meiqun Yin, 2017. "A Lagrange multiplier test for testing the adequacy of constant conditional correlation GARCH model," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 599-621, October.
    5. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    6. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    7. Cristina Amado & Annastiina Silvennoinen & Timo Terasvirta, 2017. "Modelling and Forecasting WIG20 Daily Returns," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(3), pages 173-200, September.
    8. Connor, Gregory & Suurlaht, Anita, 2013. "Dynamic stock market covariances in the Eurozone," Journal of International Money and Finance, Elsevier, vol. 37(C), pages 353-370.
    9. repec:taf:jnlbes:v:30:y:2012:i:2:p:212-228 is not listed on IDEAS
    10. Feng, Yuanhua, 2006. "A local dynamic conditional correlation model," MPRA Paper 1592, University Library of Munich, Germany.
    11. Jacek Osiewalski & Anna Pajor, 2009. "Bayesian Analysis for Hybrid MSF-SBEKK Models of Multivariate Volatility," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 1(2), pages 179-202, November.
    12. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    13. Gallant, A. Ronald, 1981. "On the bias in flexible functional forms and an essentially unbiased form : The fourier flexible form," Journal of Econometrics, Elsevier, vol. 15(2), pages 211-245, February.
    14. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    15. Hafner, Christian M. & Linton, Oliver, 2010. "Efficient estimation of a multivariate multiplicative volatility model," Journal of Econometrics, Elsevier, vol. 159(1), pages 55-73, November.
    16. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    17. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
    18. Girardin, Eric & Joyeux, Roselyne, 2013. "Macro fundamentals as a source of stock market volatility in China: A GARCH-MIDAS approach," Economic Modelling, Elsevier, vol. 34(C), pages 59-68.
    19. Luc Bauwens & Christian M. Hafner & Diane Pierret, 2013. "Multivariate Volatility Modeling Of Electricity Futures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 743-761, August.
    20. Annastiina Silvennoinen & Timo Ter�svirta, 2015. "Modeling Conditional Correlations of Asset Returns: A Smooth Transition Approach," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 174-197, February.
    21. Cristina Amado & Timo Teräsvirta, 2017. "Specification and testing of multiplicative time-varying GARCH models with applications," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 421-446, April.
    22. Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155.
    23. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
    24. A. Ronald Gallant, 1984. "The Fourier Flexible Form," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 66(2), pages 204-208.
    25. Juan Rodríguez-Poo & Oliver Linton, 2001. "Nonparametric factor analysis of residual time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 161-182, June.
    26. Robert F. Engle & Eric Ghysels & Bumjean Sohn, 2013. "Stock Market Volatility and Macroeconomic Fundamentals," The Review of Economics and Statistics, MIT Press, vol. 95(3), pages 776-797, July.
    27. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    28. Christian T. Brownlees & Giampiero M. Gallo, 2010. "Comparison of Volatility Measures: a Risk Management Perspective," Journal of Financial Econometrics, Oxford University Press, vol. 8(1), pages 29-56, Winter.
    29. Christian Conrad & Karin Loch, 2015. "Anticipating Long‐Term Stock Market Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(7), pages 1090-1114, November.
    30. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    31. Francesco Audrino & Peter Bühlmann, 2009. "Splines for financial volatility," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 655-670, June.
    32. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    33. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    34. Blazej Mazur & Mateusz Pipien, 2012. "On the empirical importance of periodicity in the volatility of financial time series," NBP Working Papers 124, Narodowy Bank Polski.
    35. Berben, Robert-Paul & Jansen, W. Jos, 2005. "Comovement in international equity markets: A sectoral view," Journal of International Money and Finance, Elsevier, vol. 24(5), pages 832-857, September.
    36. repec:pdn:ciepap:104 is not listed on IDEAS
    37. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    38. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    39. Hossein Asgharian & Ai Jun Hou & Farrukh Javed, 2013. "The Importance of the Macroeconomic Variables in Forecasting Stock Return Variance: A GARCH‐MIDAS Approach," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 32(7), pages 600-612, November.
    40. Cristina Amado & Timo Teräsvirta, 2008. "Modelling Conditional and Unconditional Heteroskedasticity with Smoothly Time-Varying Structure," NIPE Working Papers 03/2008, NIPE - Universidade do Minho.
    41. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    42. Li, Dong & Zhang, Xingfa & Zhu, Ke & Ling, Shiqing, 2018. "The ZD-GARCH model: A new way to study heteroscedasticity," Journal of Econometrics, Elsevier, vol. 202(1), pages 1-17.
    43. Colacito, Riccardo & Engle, Robert F. & Ghysels, Eric, 2011. "A component model for dynamic correlations," Journal of Econometrics, Elsevier, vol. 164(1), pages 45-59, September.
    44. Feng, Yuanhua & McNeil, Alexander J., 2008. "Modelling of scale change, periodicity and conditional heteroskedasticity in return volatility," Economic Modelling, Elsevier, vol. 25(5), pages 850-867, September.
    45. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    46. Engle, Robert F. (ed.), 1995. "ARCH: Selected Readings," OUP Catalogue, Oxford University Press, number 9780198774327.
    47. Lundbergh, Stefan & Terasvirta, Timo, 2002. "Evaluating GARCH models," Journal of Econometrics, Elsevier, vol. 110(2), pages 417-435, October.
    48. Feng, Yuanhua, 2004. "Simultaneously Modeling Conditional Heteroskedasticity And Scale Change," Econometric Theory, Cambridge University Press, vol. 20(3), pages 563-596, June.
    49. Shiqing Ling & W. K. Li, 1997. "Diagnostic checking of nonlinear multivariate time series with multivariate arch errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(5), pages 447-464, September.
    50. Annastiina Silvennoinen & Timo Teräsvirta, 2017. "Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model," CREATES Research Papers 2017-28, Department of Economics and Business Economics, Aarhus University.
    51. Song, Peter X.K. & Fan, Yanqin & Kalbfleisch, John D., 2005. "Maximization by Parts in Likelihood Inference," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1145-1158, December.
    52. Chen, Wei-Peng & Choudhry, Taufiq & Wu, Chih-Chiang, 2013. "The extreme value in crude oil and US dollar markets," Journal of International Money and Finance, Elsevier, vol. 36(C), pages 191-210.
    53. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-234, April.
    54. repec:hal:journl:peer-00732539 is not listed on IDEAS
    55. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    56. Mishra, Santosh & Su, Liangjun & Ullah, Aman, 2010. "Semiparametric Estimator of Time Series Conditional Variance," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 256-274.
    57. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    58. Van Bellegem, Sebastien & von Sachs, Rainer, 2004. "Forecasting economic time series with unconditional time-varying variance," International Journal of Forecasting, Elsevier, vol. 20(4), pages 611-627.
    59. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    60. repec:bla:jfinan:v:53:y:1998:i:1:p:219-265 is not listed on IDEAS
    61. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-362, July.
    62. Wang, Fangfang & Ghysels, Eric, 2015. "Econometric Analysis Of Volatility Component Models," Econometric Theory, Cambridge University Press, vol. 31(2), pages 362-393, April.
    63. Conrad, Christian & Loch, Karin & Rittler, Daniel, 2014. "On the macroeconomic determinants of long-term volatilities and correlations in U.S. stock and crude oil markets," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 26-40.
    64. Błażej Mazur & Mateusz Pipień, 2012. "On the Empirical Importance of Periodicity in the Volatility of Financial Returns - Time Varying GARCH as a Second Order APC(2) Process," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 4(2), pages 95-116, June.
    65. 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 Conrad & Melanie Schienle, 2020. "Testing for an Omitted Multiplicative Long-Term Component in GARCH Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 229-242, April.
    2. Wu, Xinyu & Xie, Haibin, 2021. "A realized EGARCH-MIDAS model with higher moments," Finance Research Letters, Elsevier, vol. 38(C).
    3. Feng, Yuanhua & Härdle, Wolfgang Karl, 2020. "A data-driven P-spline smoother and the P-Spline-GARCH models," IRTG 1792 Discussion Papers 2020-016, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".

    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. Annastiina Silvennoinen & Timo Teräsvirta, 2017. "Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model," CREATES Research Papers 2017-28, Department of Economics and Business Economics, Aarhus University.
    2. Cristina Amado & Annastiina Silvennoinen & Timo Terasvirta, 2017. "Modelling and Forecasting WIG20 Daily Returns," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 9(3), pages 173-200, September.
    3. Jian Kang & Johan Stax Jakobsen & Annastiina Silvennoinen & Timo Teräsvirta & Glen Wade, 2022. "A Parsimonious Test of Constancy of a Positive Definite Correlation Matrix in a Multivariate Time-Varying GARCH Model," Econometrics, MDPI, vol. 10(3), pages 1-41, August.
    4. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Anthony D. Hall & Annastiina Silvennoinen & Timo Teräsvirta, 2021. "Four Australian Banks and the Multivariate Time-Varying Smooth Transition Correlation GARCH model," CREATES Research Papers 2021-13, Department of Economics and Business Economics, Aarhus University.
    6. Amado, Cristina & Teräsvirta, Timo, 2013. "Modelling volatility by variance decomposition," Journal of Econometrics, Elsevier, vol. 175(2), pages 142-153.
    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. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    9. Christian Conrad & Onno Kleen, 2020. "Two are better than one: Volatility forecasting using multiplicative component GARCH‐MIDAS models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(1), pages 19-45, January.
    10. Christian Conrad & Melanie Schienle, 2020. "Testing for an Omitted Multiplicative Long-Term Component in GARCH Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 229-242, April.
    11. Amado, Cristina & Teräsvirta, Timo, 2014. "Modelling changes in the unconditional variance of long stock return series," Journal of Empirical Finance, Elsevier, vol. 25(C), pages 15-35.
    12. Cristina Amado & Timo Teräsvirta, 2017. "Specification and testing of multiplicative time-varying GARCH models with applications," Econometric Reviews, Taylor & Francis Journals, vol. 36(4), pages 421-446, April.
    13. Amendola, Alessandra & Candila, Vincenzo & Gallo, Giampiero M., 2019. "On the asymmetric impact of macro–variables on volatility," Economic Modelling, Elsevier, vol. 76(C), pages 135-152.
    14. Campos-Martins, Susana & Amado, Cristina, 2022. "Financial market linkages and the sovereign debt crisis," Journal of International Money and Finance, Elsevier, vol. 123(C).
    15. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    16. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    17. Anthony D. Hall & Annastiina Silvennoinen & Timo Teräsvirta, 2023. "Building Multivariate Time-Varying Smooth Transition Correlation GARCH Models, with an Application to the Four Largest Australian Banks," Econometrics, MDPI, vol. 11(1), pages 1-37, February.
    18. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, September.
    19. Amendola, A. & Candila, V. & Cipollini, F. & Gallo, G.M., 2024. "Doubly multiplicative error models with long- and short-run components," Socio-Economic Planning Sciences, Elsevier, vol. 91(C).
    20. Yun-Shi Dai & Peng-Fei Dai & Wei-Xing Zhou, 2024. "The impact of geopolitical risk on the international agricultural market: Empirical analysis based on the GJR-GARCH-MIDAS model," Papers 2404.01641, arXiv.org.

    More about this item

    Keywords

    Conditional heteroskedasticity; Deterministically varying correlations; Multiplicative decomposition; Nonstationary volatility;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • 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:nip:nipewp:07/2018. 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: NIPE (email available below). General contact details of provider: https://edirc.repec.org/data/nipampt.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.