IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v180y2023ics0167947322002626.html
   My bibliography  Save this article

Dimension reduction in time series under the presence of conditional heteroscedasticity

Author

Listed:
  • da Silva, Murilo
  • Sriram, T.N.
  • Ke, Yuan

Abstract

Consider a time series, where the conditional mean is assumed to be an unknown function of linear combinations of past p observations and the conditional variance is assumed to be an unknown function of linear combinations of past q squared residuals. The linear combinations are assumed to contain all the necessary information about the time series that is available through the conditional mean and conditional variance, respectively. Nadaraya-Watson kernel smoother is used to estimate the unknown mean and variance function and an iterative approach is proposed to estimate the parameter matrices associated with the linear combinations. The estimators are shown to be consistent. To overcome computational challenges and provide numerical stability, a novel angular representation of parameter matrices is introduced. The numerical performance of the proposed method on forecasting the conditional mean is assessed by simulations studies. A real data of Brazilian Real (BRL)/U.S. Dollar Exchange Rate is analyzed. For the BRL/USD series, the estimated linear combinations yield a better time series model than an AR-ARCH model in terms of out-of-sample forecasts.

Suggested Citation

  • da Silva, Murilo & Sriram, T.N. & Ke, Yuan, 2023. "Dimension reduction in time series under the presence of conditional heteroscedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002626
    DOI: 10.1016/j.csda.2022.107682
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947322002626
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2022.107682?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    2. Ye Z. & Weiss R.E., 2003. "Using the Bootstrap to Select One of a New Class of Dimension Reduction Methods," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 968-979, January.
    3. Hong, Seok Young & Linton, Oliver, 2020. "Nonparametric estimation of infinite order regression and its application to the risk-return tradeoff," Journal of Econometrics, Elsevier, vol. 219(2), pages 389-424.
    4. Jin‐Hong Park & T. N. Sriram, 2017. "Robust estimation of conditional variance of time series using density power divergences," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(6), pages 703-717, September.
    5. Shaojun Guo & John Leigh Box & Wenyang Zhang, 2017. "A Dynamic Structure for High-Dimensional Covariance Matrices and Its Application in Portfolio Allocation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 235-253, January.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    7. Yingcun Xia & Howell Tong & W. K. Li & Li‐Xing Zhu, 2002. "An adaptive estimation of dimension reduction space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 363-410, August.
    8. Jin‐Hong Park & S. Yaser Samadi, 2020. "Dimension reduction for the conditional mean and variance functions in time series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(1), pages 134-155, March.
    9. Xiangrong Yin & R. Dennis Cook, 2005. "Direction estimation in single-index regressions," Biometrika, Biometrika Trust, vol. 92(2), pages 371-384, June.
    10. Robert Engle, 2001. "GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 157-168, Fall.
    11. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    12. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    13. 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)

    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. Linton, Oliver & Mammen, Enno, 2003. "Estimating semiparametric ARCH (8) models by kernel smoothing methods," LSE Research Online Documents on Economics 2187, London School of Economics and Political Science, LSE Library.
    2. S. Yaser Samadi & Tharindu P. De Alwis, 2023. "Fourier Methods for Sufficient Dimension Reduction in Time Series," Papers 2312.02110, arXiv.org.
    3. O. Linton & E. Mammen, 2005. "Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods," Econometrica, Econometric Society, vol. 73(3), pages 771-836, May.
    4. Wilson Ye Chen & Richard H. Gerlach, 2017. "Semiparametric GARCH via Bayesian model averaging," Papers 1708.07587, arXiv.org.
    5. Chen, Gongmeng & Choi, Yoon K. & Zhou, Yong, 2005. "Nonparametric estimation of structural change points in volatility models for time series," Journal of Econometrics, Elsevier, vol. 126(1), pages 79-114, May.
    6. Panagiotis Avramidis, 2016. "Adaptive likelihood estimator of conditional variance function," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 132-151, March.
    7. Heejoon Han & Shen Zhang, 2012. "Non‐stationary non‐parametric volatility model," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 204-225, June.
    8. Zhang, Hongfan, 2018. "Quasi-likelihood estimation of the single index conditional variance model," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 58-72.
    9. Siddiqi, Hammad, 2007. "Rational Interacting Agents and Volatility Clustering: A New Approach," MPRA Paper 2984, University Library of Munich, Germany.
    10. Yin, Xiangrong & Li, Bing & Cook, R. Dennis, 2008. "Successive direction extraction for estimating the central subspace in a multiple-index regression," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1733-1757, September.
    11. Allen, David E. & Amram, Ron & McAleer, Michael, 2013. "Volatility spillovers from the Chinese stock market to economic neighbours," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 238-257.
    12. Shehu Usman Rano, Aliyu, 2010. "Does inflation has an Impact on Stock Returns and Volatility? Evidence from Nigeria and Ghana," MPRA Paper 30091, University Library of Munich, Germany, revised 19 Mar 2011.
    13. Ñíguez, Trino-Manuel & Perote, Javier, 2017. "Moments expansion densities for quantifying financial risk," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 53-69.
    14. Suripto & Supriyanto, 2021. "The Effect of the COVID-19 Pandemic on Stock Prices with the Event Window Approach: A Case Study of State Gas Companies, in the Energy Sector," International Journal of Energy Economics and Policy, Econjournals, vol. 11(3), pages 155-162.
    15. Abdmoulah, Walid, 2010. "Testing the evolving efficiency of Arab stock markets," International Review of Financial Analysis, Elsevier, vol. 19(1), pages 25-34, January.
    16. Bernardi, Mauro & Costola, Michele, 2019. "High-dimensional sparse financial networks through a regularised regression model," SAFE Working Paper Series 244, Leibniz Institute for Financial Research SAFE.
    17. Buczyński Mateusz & Chlebus Marcin, 2018. "Comparison of Semi-Parametric and Benchmark Value-At-Risk Models in Several Time Periods with Different Volatility Levels," Financial Internet Quarterly (formerly e-Finanse), Sciendo, vol. 14(2), pages 67-82, June.
    18. León Beleña & Ernesto Curbelo & Luca Martino & Valero Laparra, 2024. "Second-Moment/Order Approximations by Kernel Smoothers with Application to Volatility Estimation," Mathematics, MDPI, vol. 12(9), pages 1-15, May.
    19. Doyle, John R. & Chen, Catherine Huirong, 2009. "The wandering weekday effect in major stock markets," Journal of Banking & Finance, Elsevier, vol. 33(8), pages 1388-1399, August.
    20. Tjøstheim, Dag & Hufthammer, Karl Ove, 2013. "Local Gaussian correlation: A new measure of dependence," Journal of Econometrics, Elsevier, vol. 172(1), pages 33-48.

    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:eee:csdana:v:180:y:2023:i:c:s0167947322002626. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.