IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2206.00409.html
   My bibliography  Save this paper

Time-Varying Multivariate Causal Processes

Author

Listed:
  • Jiti Gao
  • Bin Peng
  • Wei Biao Wu
  • Yayi Yan

Abstract

In this paper, we consider a wide class of time-varying multivariate causal processes which nests many classic and new examples as special cases. We first prove the existence of a weakly dependent stationary approximation for our model which is the foundation to initiate the theoretical development. Afterwards, we consider the QMLE estimation approach, and provide both point-wise and simultaneous inferences on the coefficient functions. In addition, we demonstrate the theoretical findings through both simulated and real data examples. In particular, we show the empirical relevance of our study using an application to evaluate the conditional correlations between the stock markets of China and U.S. We find that the interdependence between the two stock markets is increasing over time.

Suggested Citation

  • Jiti Gao & Bin Peng & Wei Biao Wu & Yayi Yan, 2022. "Time-Varying Multivariate Causal Processes," Papers 2206.00409, arXiv.org.
    • Handle: RePEc:arx:papers:2206.00409
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2206.00409
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jushan Bai, 1997. "Estimation Of A Change Point In Multiple Regression Models," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 551-563, November.
    2. Jia Li & Zhipeng Liao & Mengsi Gao, 2020. "Uniform nonparametric inference for time series using Stata," Stata Journal, StataCorp LP, vol. 20(3), pages 706-720, September.
    3. Francis X. Diebold & Kamil Yilmaz, 2009. "Measuring Financial Asset Return and Volatility Spillovers, with Application to Global Equity Markets," Economic Journal, Royal Economic Society, vol. 119(534), pages 158-171, January.
    4. Silvia Miranda-Agrippino & Giovanni Ricco, 2021. "The Transmission of Monetary Policy Shocks," American Economic Journal: Macroeconomics, American Economic Association, vol. 13(3), pages 74-107, July.
    5. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    6. Diebold, Francis X. & Yılmaz, Kamil, 2014. "On the network topology of variance decompositions: Measuring the connectedness of financial firms," Journal of Econometrics, Elsevier, vol. 182(1), pages 119-134.
    7. Philip Preuss & Ruprecht Puchstein & Holger Dette, 2015. "Detection of Multiple Structural Breaks in Multivariate Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 654-668, June.
    8. Zhou Zhou & Wei Biao Wu, 2010. "Simultaneous inference of linear models with time varying coefficients," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 513-531, September.
    9. Inoue, Atsushi & Kilian, Lutz, 2022. "Joint Bayesian inference about impulse responses in VAR models," Journal of Econometrics, Elsevier, vol. 231(2), pages 457-476.
    10. Kilian,Lutz & Lütkepohl,Helmut, 2018. "Structural Vector Autoregressive Analysis," Cambridge Books, Cambridge University Press, number 9781107196575, October.
    11. Xiaohong Chen & Timothy M. Christensen, 2018. "Optimal sup‐norm rates and uniform inference on nonlinear functionals of nonparametric IV regression," Quantitative Economics, Econometric Society, vol. 9(1), pages 39-84, March.
    12. Baele, Lieven, 2005. "Volatility Spillover Effects in European Equity Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 40(2), pages 373-401, June.
    13. Zhang, Bing & Li, Xiao-Ming, 2014. "Has there been any change in the comovement between the Chinese and US stock markets?," International Review of Economics & Finance, Elsevier, vol. 29(C), pages 525-536.
    14. Athanasopoulos, George & Vahid, Farshid, 2008. "VARMA versus VAR for Macroeconomic Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 237-252, April.
    15. Frank Schorfheide & Dongho Song, 2015. "Real-Time Forecasting With a Mixed-Frequency VAR," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(3), pages 366-380, July.
    16. Ling S., 2003. "Adaptive Estimators and Tests of Stationary and Nonstationary Short- and Long-Memory ARFIMA-GARCH Models," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 955-967, January.
    17. 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.
    18. Massimiliano Caporin & Michael McAleer, 2013. "Ten Things you should know about DCC," Tinbergen Institute Discussion Papers 13-048/III, Tinbergen Institute.
    19. Phillips, Peter C.B. & Li, Degui & Gao, Jiti, 2017. "Estimating smooth structural change in cointegration models," Journal of Econometrics, Elsevier, vol. 196(1), pages 180-195.
    20. Beirne, John & Caporale, Guglielmo Maria & Schulze-Ghattas, Marianne & Spagnolo, Nicola, 2010. "Global and regional spillovers in emerging stock markets: A multivariate GARCH-in-mean analysis," Emerging Markets Review, Elsevier, vol. 11(3), pages 250-260, September.
    21. Massimiliano Caporin & Michael McAleer, 2013. "Ten Things You Should Know about the Dynamic Conditional Correlation Representation," Econometrics, MDPI, vol. 1(1), pages 1-12, June.
    22. Giampiero M. Gallo & Edoardo Otranto, 2012. "Realized Volatility and Change of Regimes," Econometrics Working Papers Archive 2012_02, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Jul 2012.
    23. BenSaïda, Ahmed, 2019. "Good and bad volatility spillovers: An asymmetric connectedness," Journal of Financial Markets, Elsevier, vol. 43(C), pages 78-95.
    24. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    25. Dette, Holger & Preuß, Philip & Vetter, Mathias, 2011. "A Measure of Stationarity in Locally Stationary Processes With Applications to Testing," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1113-1124.
    26. Augustyniak, Maciej & Badescu, Alexandru & Bégin, Jean-François, 2023. "A discrete-time hedging framework with multiple factors and fat tails: On what matters," Journal of Econometrics, Elsevier, vol. 232(2), pages 416-444.
    27. Lionel Truquet, 2017. "Parameter stability and semiparametric inference in time varying auto-regressive conditional heteroscedasticity models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1391-1414, November.
    28. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
    29. Andreou, Elena & Werker, Bas J.M., 2015. "Residual-based rank specification tests for AR–GARCH type models," Journal of Econometrics, Elsevier, vol. 185(2), pages 305-331.
    30. Pan, Qunxing & Mei, Xiaowen & Gao, Tianqing, 2022. "Modeling dynamic conditional correlations with leverage effects and volatility spillover effects: Evidence from the Chinese and US stock markets affected by the recent trade friction," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    31. Robert F. Engle & Emil N. Siriwardane, 2018. "Structural GARCH: The Volatility-Leverage Connection," The Review of Financial Studies, Society for Financial Studies, vol. 31(2), pages 449-492.
    32. 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.
    33. Geraci, Marco Valerio & Gnabo, Jean-Yves, 2018. "Measuring Interconnectedness between Financial Institutions with Bayesian Time-Varying Vector Autoregressions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(3), pages 1371-1390, June.
    34. Namgyoo K. Park, 2004. "A guide to using event study methods in multi‐country settings," Strategic Management Journal, Wiley Blackwell, vol. 25(7), pages 655-668, July.
    35. Berger, Tino & Morley, James & Wong, Benjamin, 2023. "Nowcasting the output gap," Journal of Econometrics, Elsevier, vol. 232(1), pages 18-34.
      • Tino Berger & James Morley & Benjamin Wong, 2020. "Nowcasting the output gap," CAMA Working Papers 2020-78, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    36. Jia Li & Zhipeng Liao & Wenyu Zhou, 2023. "Uniform nonparametric inference for spatially dependent panel data: The xtnpsreg command," Stata Journal, StataCorp LP, vol. 23(1), pages 243-264, March.
    37. Hong, Yongmiao, 2001. "A test for volatility spillover with application to exchange rates," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 183-224, July.
    38. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2020. "Multivariate leverage effects and realized semicovariance GARCH models," Journal of Econometrics, Elsevier, vol. 217(2), pages 411-430.
    39. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    40. Bin Chen & Yongmiao Hong, 2012. "Testing for Smooth Structural Changes in Time Series Models via Nonparametric Regression," Econometrica, Econometric Society, vol. 80(3), pages 1157-1183, May.
    41. Likai Chen & Weining Wang & Wei Biao Wu, 2022. "Inference of Breakpoints in High-dimensional Time Series," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(540), pages 1951-1963, October.
    42. Karmakar, Sayar & Richter, Stefan & Wu, Wei Biao, 2022. "Simultaneous inference for time-varying models," Journal of Econometrics, Elsevier, vol. 227(2), pages 408-428.
    43. Michael Vogt, 2012. "Nonparametric regression for locally stationary time series," CeMMAP working papers CWP22/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    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. Jiti Gao & Bin Peng & Wei Biao Wu & Yayi Yan, 2022. "Time-Varying Multivariate Causal Processes," Monash Econometrics and Business Statistics Working Papers 8/22, Monash University, Department of Econometrics and Business Statistics.
    2. Chia-Lin Chang & Yiying Li & Michael McAleer, 2018. "Volatility Spillovers between Energy and Agricultural Markets: A Critical Appraisal of Theory and Practice," Energies, MDPI, vol. 11(6), pages 1-19, June.
    3. Paolella, Marc S. & Polak, Paweł, 2015. "ALRIGHT: Asymmetric LaRge-scale (I)GARCH with Hetero-Tails," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 282-297.
    4. Chia-Lin Chang & Michael McAleer & Jiarong Tian, 2019. "Modeling and Testing Volatility Spillovers in Oil and Financial Markets for the USA, the UK, and China," Energies, MDPI, vol. 12(8), pages 1-24, April.
    5. Tomasz Woźniak, 2018. "Granger-causal analysis of GARCH models: A Bayesian approach," Econometric Reviews, Taylor & Francis Journals, vol. 37(4), pages 325-346, April.
    6. 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.
    7. Pan, Zhiyuan & Wang, Yudong & Yang, Li, 2014. "Hedging crude oil using refined product: A regime switching asymmetric DCC approach," Energy Economics, Elsevier, vol. 46(C), pages 472-484.
    8. Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers ECO2012/19, European University Institute.
    9. repec:wyi:journl:002141 is not listed on IDEAS
    10. Nadine McCloud & Yongmiao Hong, 2011. "Testing The Structure Of Conditional Correlations In Multivariate Garch Models: A Generalized Cross‐Spectrum Approach," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(4), pages 991-1037, November.
    11. Pedersen, Rasmus Søndergaard, 2016. "Targeting Estimation Of Ccc-Garch Models With Infinite Fourth Moments," Econometric Theory, Cambridge University Press, vol. 32(2), pages 498-531, April.
    12. Chia-Lin Chang & Tai-Lin Hsieh & Michael McAleer, 2016. "Connecting VIX and Stock Index ETF," Tinbergen Institute Discussion Papers 16-010/III, Tinbergen Institute, revised 23 Jan 2017.
    13. Imran Yousaf & Shoaib Ali & Wing-Keung Wong, 2020. "An Empirical Analysis of the Volatility Spillover Effect between World-Leading and the Asian Stock Markets: Implications for Portfolio Management," JRFM, MDPI, vol. 13(10), pages 1-28, September.
    14. 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.
    15. repec:bgu:wpaper:0608 is not listed on IDEAS
    16. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
    17. Hafner, Christian M. & Herwartz, Helmut & Maxand, Simone, 2022. "Identification of structural multivariate GARCH models," Journal of Econometrics, Elsevier, vol. 227(1), pages 212-227.
    18. 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.
    19. Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," CARF F-Series CARF-F-219, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    20. Paolella, Marc S. & Polak, Paweł & Walker, Patrick S., 2021. "A non-elliptical orthogonal GARCH model for portfolio selection under transaction costs," Journal of Banking & Finance, Elsevier, vol. 125(C).
    21. Tomoaki Nakatani & Timo Terasvirta, 2009. "Testing for volatility interactions in the Constant Conditional Correlation GARCH model," Econometrics Journal, Royal Economic Society, vol. 12(1), pages 147-163, March.
    22. 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.

    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: 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
    • G15 - Financial Economics - - General Financial Markets - - - International Financial Markets

    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:arx:papers:2206.00409. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.