IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v205y2018i1p280-301.html
   My bibliography  Save this article

Estimating stable latent factor models by indirect inference

Author

Listed:
  • Calzolari, Giorgio
  • Halbleib, Roxana

Abstract

Cross-sections of financial returns are characterized by common underlying factors and exhibit fat tails that may be captured by α-stable distributions. This paper focuses on estimating factor models with independent latent factors and idiosyncratic noises featuring a multivariate α-stable distribution constant over time (static factor models) or a time-varying conditional multivariate α-stable distribution (GARCH factor models). Although the simulation of such a distribution is straightforward, the estimation of its parameters encounters difficulties. These difficulties are overcome in this paper by implementing the indirect inference estimation method with the multivariate Student’s t as the auxiliary distribution.

Suggested Citation

  • Calzolari, Giorgio & Halbleib, Roxana, 2018. "Estimating stable latent factor models by indirect inference," Journal of Econometrics, Elsevier, vol. 205(1), pages 280-301.
    • Handle: RePEc:eee:econom:v:205:y:2018:i:1:p:280-301
    DOI: 10.1016/j.jeconom.2018.03.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407618300538
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2018.03.014?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. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. Sentana, Enrique & Calzolari, Giorgio & Fiorentini, Gabriele, 2008. "Indirect estimation of large conditionally heteroskedastic factor models, with an application to the Dow 30 stocks," Journal of Econometrics, Elsevier, vol. 146(1), pages 10-25, September.
    3. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    4. James H. Stock & Mark W. Watson, 2005. "Implications of Dynamic Factor Models for VAR Analysis," NBER Working Papers 11467, National Bureau of Economic Research, Inc.
    5. Geweke, John & Zhou, Guofu, 1996. "Measuring the Pricing Error of the Arbitrage Pricing Theory," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 557-587.
    6. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2002. "Stationarity of stable power-GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 97-107, January.
    7. Stephen A. Ross, 2005. "Mutual Fund Separation in Financial Theory—The Separating Distributions," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 10, pages 309-356, World Scientific Publishing Co. Pte. Ltd..
    8. Calzolari, Giorgio & Halbleib, Roxana & Parrini, Alessandro, 2014. "Estimating GARCH-type models with symmetric stable innovations: Indirect inference versus maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 158-171.
    9. Bawa, Vijay S & Elton, Edwin J & Gruber, Martin J, 1979. "Simple Rules for Optimal Portfolio Selection in Stable Paretian Markets," Journal of Finance, American Finance Association, vol. 34(4), pages 1041-1047, September.
    10. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    11. Aguilar, Omar & West, Mike, 2000. "Bayesian Dynamic Factor Models and Portfolio Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 338-357, July.
    12. McCulloch, J. Huston, 1985. "Interest-risk sensitive deposit insurance premia : Stable ACH estimates," Journal of Banking & Finance, Elsevier, vol. 9(1), pages 137-156, March.
    13. Svetlozar Rachev & Seonkoo Han, 2000. "Portfolio management with stable distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 341-352, April.
    14. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421-421.
    15. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.
    16. Rene Garcia & Eric Renault & David Veredas, 2011. "Estimation of stable distributions with indirect inference," ULB Institutional Repository 2013/136186, ULB -- Universite Libre de Bruxelles.
    17. Garcia, René & Renault, Eric & Veredas, David, 2011. "Estimation of stable distributions by indirect inference," Journal of Econometrics, Elsevier, vol. 161(2), pages 325-337, April.
    18. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
    19. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    20. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549.
    21. Ogata, Hiroaki, 2013. "Estimation for multivariate stable distributions with generalized empirical likelihood," Journal of Econometrics, Elsevier, vol. 172(2), pages 248-254.
    22. Mittnik, Stefan & Paolella, Marc S., 2003. "Prediction of Financial Downside-Risk with Heavy-Tailed Conditional Distributions," CFS Working Paper Series 2003/04, Center for Financial Studies (CFS).
    23. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
    24. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    25. repec:nys:sunysb:93-02 is not listed on IDEAS
    26. Toker Doganoglu & Christoph Hartz & Stefan Mittnik, 2007. "Portfolio optimization when risk factors are conditionally varying and heavy tailed," Computational Economics, Springer;Society for Computational Economics, vol. 29(3), pages 333-354, May.
    27. B. N. Cheng & S. T. Rachev, 1995. "Multivariate Stable Futures Prices," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 133-153, April.
    28. Smith, A A, Jr, 1993. "Estimating Nonlinear Time-Series Models Using Simulated Vector Autoregressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 63-84, Suppl. De.
    29. repec:ulb:ulbeco:2013/136280 is not listed on IDEAS
    30. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
    31. Marco J. Lombardi & Giorgio Calzolari, 2008. "Indirect Estimation of α-Stable Distributions and Processes," Econometrics Journal, Royal Economic Society, vol. 11(1), pages 193-208, March.
    32. Kyoung-Kuk Kim & Sojung Kim, 2016. "Simulation of Tempered Stable Lévy Bridges and Its Applications," Operations Research, INFORMS, vol. 64(2), pages 495-509, April.
    33. Dominicy, Yves & Veredas, David, 2013. "The method of simulated quantiles," Journal of Econometrics, Elsevier, vol. 172(2), pages 235-247.
    34. Connor, Gregory, 1984. "A unified beta pricing theory," Journal of Economic Theory, Elsevier, vol. 34(1), pages 13-31, October.
    35. Harvey, Andrew C & Koopman, Siem Jan, 1992. "Diagnostic Checking of Unobserved-Components Time Series Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 377-389, October.
    36. 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..
    37. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(3), pages 318-334, September.
    38. Liu, Shi-Miin & Brorsen, B Wade, 1995. "GARCH-Stable as a Model of Futures Price Movements," Review of Quantitative Finance and Accounting, Springer, vol. 5(2), pages 155-167, June.
    39. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(4), pages 945-973.
    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. Shuquan Yang & Nengxiang Ling & Yulin Gong, 2022. "Robust estimation of the number of factors for the pair-elliptical factor models," Computational Statistics, Springer, vol. 37(3), pages 1495-1522, July.
    2. Cosimo Magazzino & Marco Mele, 2022. "A Dynamic Factor and Neural Networks Analysis of the Co-movement of Public Revenues in the EMU," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 8(2), pages 289-338, July.
    3. Giorgio Calzolari & Roxana Halbleib & Christian Mucher, 2023. "Sequential Estimation of Multivariate Factor Stochastic Volatility Models," Papers 2302.07052, arXiv.org.
    4. Yu, Long & He, Yong & Zhang, Xinsheng, 2019. "Robust factor number specification for large-dimensional elliptical factor model," Journal of Multivariate Analysis, Elsevier, vol. 174(C).

    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. Calzolari, Giorgio & Halbleib, Roxana & Parrini, Alessandro, 2014. "Estimating GARCH-type models with symmetric stable innovations: Indirect inference versus maximum likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 158-171.
    2. Lombardi, Marco J. & Veredas, David, 2009. "Indirect estimation of elliptical stable distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2309-2324, April.
    3. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    4. Parrini, Alessandro, 2012. "Indirect estimation of GARCH models with alpha-stable innovations," MPRA Paper 38544, University Library of Munich, Germany.
    5. 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.
    6. Broda, Simon A. & Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Stable mixture GARCH models," Journal of Econometrics, Elsevier, vol. 172(2), pages 292-306.
    7. Marc S. Paolella, 2016. "Stable-GARCH Models for Financial Returns: Fast Estimation and Tests for Stability," Econometrics, MDPI, vol. 4(2), pages 1-28, May.
    8. Barigozzi, Matteo & Hallin, Marc, 2017. "Generalized dynamic factor models and volatilities: estimation and forecasting," Journal of Econometrics, Elsevier, vol. 201(2), pages 307-321.
    9. Gabriele Fiorentini & Enrique Sentana, 2009. "Dynamic Specification Tests for Static Factor Models," Working Papers wp2009_0912, CEMFI.
    10. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    11. Garcia, René & Renault, Eric & Veredas, David, 2011. "Estimation of stable distributions by indirect inference," Journal of Econometrics, Elsevier, vol. 161(2), pages 325-337, April.
    12. Matteo Barigozzi & Roxana Halbleib & David Veredas, 2012. "Which model to match?," Working Papers 1229, Banco de España.
    13. Sentana, Enrique & Calzolari, Giorgio & Fiorentini, Gabriele, 2008. "Indirect estimation of large conditionally heteroskedastic factor models, with an application to the Dow 30 stocks," Journal of Econometrics, Elsevier, vol. 146(1), pages 10-25, September.
    14. Matteo Barigozzi & Marc Hallin, 2016. "Generalized dynamic factor models and volatilities: recovering the market volatility shocks," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 33-60, February.
    15. Carlos Trucíos & João H. G. Mazzeu & Marc Hallin & Luiz K. Hotta & Pedro L. Valls Pereira & Mauricio Zevallos, 2022. "Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: A General Dynamic Factor Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 40-52, December.
    16. Gabriele Fiorentini & Enrique Sentana, 2012. "Tests for Serial Dependence in Static, Non-Gaussian Factor Models," Working Papers wp2012_1211, CEMFI.
    17. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    18. Broto, Carmen & Ruiz Ortega, Esther, 2006. "Using auxiliary residuals to detect conditional heteroscedasticity in inflation," DES - Working Papers. Statistics and Econometrics. WS ws060402, Universidad Carlos III de Madrid. Departamento de Estadística.
    19. Stelios Arvanitis, 2013. "On the Existence of Strongly Consistent Indirect Estimators When the Binding Function Is Compact Valued," Journal of Mathematics, Hindawi, vol. 2013, pages 1-14, November.
    20. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.

    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:econom:v:205:y:2018:i:1:p:280-301. 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/jeconom .

    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.