IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this article

A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries

Listed author(s):
  • McAleer, Michael
  • Medeiros, Marcelo C.

In this paper we propose a flexible model to describe nonlinearities and long-range dependence in time series dynamics. The new model is a multiple regime smooth transition extension of the Heterogeneous Autoregressive (HAR) model, which is specifically designed to model the behavior of the volatility inherent in financial time series. The model is able to simultaneously approximate long memory behavior, as well as describe sign and size asymmetries. A sequence of tests is developed to determine the number of regimes, and an estimation and testing procedure is presented. Monte Carlo simulations evaluate the finite-sample properties of the proposed tests and estimation procedures. We apply the model to several Dow Jones Industrial Average index stocks using transaction level data from the Trades and Quotes database that covers ten years of data. We find strong support for long memory and both sign and size asymmetries. Furthermore, the new model, when combined with the linear HAR model, is viable and flexible for purposes of forecasting volatility.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(08)00128-0
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 147 (2008)
Issue (Month): 1 (November)
Pages: 104-119

as
in new window

Handle: RePEc:eee:econom:v:147:y:2008:i:1:p:104-119
Contact details of provider: Web page: http://www.elsevier.com/locate/jeconom

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Manabu Asai & Michael McAleer, 2005. "Asymmetric Multivariate Stochastic Volatility," DEA Working Papers 12, Universitat de les Illes Balears, Departament d'Economía Aplicada.
  2. Massimiliano Caporin & Michael McAleer, 2006. "Dynamic Asymmetric GARCH," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(3), pages 385-412.
  3. Meddahi, N., 2001. "A Theoretical Comparison Between Integrated and Realized Volatilies," Cahiers de recherche 2001-26, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(03), pages 722-729, June.
  5. Goetzmann, William N. & Ibbotson, Roger G. & Peng, Liang, 2001. "A new historical database for the NYSE 1815 to 1925: Performance and predictability," Journal of Financial Markets, Elsevier, vol. 4(1), pages 1-32, January.
  6. Pitarakis Jean-Yves, 2006. "Model Selection Uncertainty and Detection of Threshold Effects," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(1), pages 1-30, March.
  7. Offer Lieberman & Peter C. B. Phillips, 2006. "Refined Inference on Long Memory in Realized Volatility," Cowles Foundation Discussion Papers 1549, Cowles Foundation for Research in Economics, Yale University.
  8. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
  9. White,Halbert, 1994. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521252805, October.
  10. So, Mike K P & Lam, K & Li, W K, 1998. "A Stochastic Volatility Model with Markov Switching," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 244-253, April.
  11. Rohit Deo & Clifford Hurvich & Yi Lu, 2005. "Forecasting Realized Volatility Using a Long Memory Stochastic Volatility Model: Estimation, Prediction and Seasonal Adjustment," Econometrics 0501002, EconWPA.
  12. M. Angeles Carnero, 2004. "Persistence and Kurtosis in GARCH and Stochastic Volatility Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 319-342.
  13. Shiqing Ling & Michael McAleer, 2001. "Asymptotic Theory for a Vector ARMA-GARCH Model," ISER Discussion Paper 0549, Institute of Social and Economic Research, Osaka University.
  14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  15. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
  16. B. LeBaron, 2001. "Stochastic volatility as a simple generator of apparent financial power laws and long memory," Quantitative Finance, Taylor & Francis Journals, vol. 1(6), pages 621-631.
  17. Rech, Gianluigi & Teräsvirta, Timo & Tschernig, Rolf, 1999. "A simple variable selection technique for nonlinear models," SSE/EFI Working Paper Series in Economics and Finance 296, Stockholm School of Economics, revised 06 Apr 2000.
  18. Hillebrand, Eric, 2005. "Neglecting parameter changes in GARCH models," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 121-138.
  19. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
  20. Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Working Papers 13-2004, Singapore Management University, School of Economics.
  21. Davidson, James & Sibbertsen, Philipp, 2002. "Generating schemes for long memory processes: Regimes, aggregation and linearity," Technical Reports 2002,46, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  22. Ait-Sahalia, Yacine & Mykland, Per A. & Zhang, Lan, 2005. "Ultra high frequency volatility estimation with dependent microstructure noise," Discussion Paper Series 1: Economic Studies 2005,30, Deutsche Bundesbank, Research Centre.
  23. Medeiros, Marcelo & Veiga, Alvaro, 2000. "Diagnostic Checking in a Flexible Nonlinear Time Series Model," SSE/EFI Working Paper Series in Economics and Finance 386, Stockholm School of Economics, revised 15 Jan 2001.
  24. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
  25. Clifford M. Hurvich & Bonnie K. Ray, 2003. "The Local Whittle Estimator of Long-Memory Stochastic Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 1(3), pages 445-470.
  26. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
  27. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(01), pages 232-261, February.
  28. Hasbrouck, Joel, 1995. " One Security, Many Markets: Determining the Contributions to Price Discovery," Journal of Finance, American Finance Association, vol. 50(4), pages 1175-1199, September.
  29. Manabu Asai & Michael McAleer, 2005. "Dynamic Asymmetric Leverage in Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 24(3), pages 317-332.
  30. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
  31. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  32. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
  33. Esfandiar Maasoumi & Michael McAleer, 2006. "Multivariate Stochastic Volatility: An Overview," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 139-144.
  34. Granger, Clive W. J. & Terasvirta, Timo, 1999. "A simple nonlinear time series model with misleading linear properties," Economics Letters, Elsevier, vol. 62(2), pages 161-165, February.
  35. Blume, Marshall E & Goldstein, Michael A, 1997. " Quotes, Order Flow, and Price Discovery," Journal of Finance, American Finance Association, vol. 52(1), pages 221-244, March.
  36. Breidt, F. Jay & Crato, Nuno & de Lima, Pedro, 1998. "The detection and estimation of long memory in stochastic volatility," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 325-348.
  37. Eitrheim, Oyvind & Terasvirta, Timo, 1996. "Testing the adequacy of smooth transition autoregressive models," Journal of Econometrics, Elsevier, vol. 74(1), pages 59-75, September.
  38. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
  39. González-Rivera Gloria, 1998. "Smooth-Transition GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(2), pages 1-20, July.
  40. Medeiros, Marcelo C. & Teräsvirta, Timo & Rech, Gianluigi, 2002. "Building neural network models for time series: A statistical approach," SSE/EFI Working Paper Series in Economics and Finance 508, Stockholm School of Economics.
  41. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
  42. Mayte Suarez Farinãs & Carlos Eduardo Pedreira & Marcelo C. Medeiros, 2003. "Local-global neural networks: a new approach for nonlinear time series modelling," Textos para discussão 470, Department of Economics PUC-Rio (Brazil).
  43. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
  44. Hsu, Chih-Chiang, 2001. "Change point estimation in regressions with I(d) variables," Economics Letters, Elsevier, vol. 70(2), pages 147-155, February.
  45. Lobato, I.N. & Savin, N.E., 1996. "Real and Spurious Long Memory Properties of Stock Market Data," Working Papers 96-07, University of Iowa, Department of Economics.
  46. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
  47. Madhavan, Ananth, 2000. "Market microstructure: A survey," Journal of Financial Markets, Elsevier, vol. 3(3), pages 205-258, August.
  48. Nunzio Cappuccio & Diego Lubian & Davide Raggi, 2006. "Investigating asymmetry in US stock market indexes: evidence from a stochastic volatility model," Applied Financial Economics, Taylor & Francis Journals, vol. 16(6), pages 479-490.
  49. Nunes, Luis C. & Kuan, Chung-Ming & Newbold, Paul, 1995. "Spurious Break," Econometric Theory, Cambridge University Press, vol. 11(04), pages 736-749, August.
  50. Liudas Giraitis, 2004. "LARCH, Leverage, and Long Memory," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 177-210.
  51. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
  52. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
  53. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
  54. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
  55. 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.
  56. Stefan Lundbergh & Timo Teräsvirta, 1999. "Evaluating GARCH Models," Tinbergen Institute Discussion Papers 99-008/4, Tinbergen Institute.
  57. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
  58. van Dijk, Dick & Franses, Philip Hans & Paap, Richard, 2002. "A nonlinear long memory model, with an application to US unemployment," Journal of Econometrics, Elsevier, vol. 110(2), pages 135-165, October.
  59. 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.
  60. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-434, October.
  61. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
  62. Fornari, F. & Mele, A., 1995. "Sign- and Volatility -Switching ARCH Models: Theory and Applications to International Stock Markets," Papers 251, Banca Italia - Servizio di Studi.
  63. Schwert, G.W., 1989. "Stock Volatility And The Crash Of '87," Papers 89-01, Rochester, Business - General.
  64. Ole E. Barndorff-Nielsen & Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280.
  65. Smith, Aaron D., 2004. "Level Shifts and the Illusion of Long Memory in Economic Time Series," Working Papers 11974, University of California, Davis, Department of Agricultural and Resource Economics.
  66. Bai, Jushan, 1998. "A Note On Spurious Break," Econometric Theory, Cambridge University Press, vol. 14(05), pages 663-669, October.
  67. Manabu Asai & Michael McAleer, 2007. "Non-trading day effects in asymmetric conditional and stochastic volatility models," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 113-123, 03.
  68. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
  69. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
  70. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-263, July.
  71. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
  72. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  73. Biais, Bruno & Glosten, Larry & Spatt, Chester, 2004. "Market Microstructure: A Survey of Microfoundations, Empirical Results, and Policy Implications," IDEI Working Papers 253, Institut d'Économie Industrielle (IDEI), Toulouse.
  74. Zhou, Bin, 1996. "High-Frequency Data and Volatility in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(1), pages 45-52, January.
  75. So, Mike K P & Li, W K & Lam, K, 2002. "A Threshold Stochastic Volatility Model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 21(7), pages 473-500, November.
  76. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
  77. Mark J. Jensen, 2004. "Semiparametric Bayesian Inference of Long-Memory Stochastic Volatility Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(6), pages 895-922, November.
  78. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
  79. Marcel Scharth & Marcelo Cunha Medeiros, 2006. "Asymmetric effects and long memory in the volatility of Dow Jones stocks," Textos para discussão 532, Department of Economics PUC-Rio (Brazil).
  80. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
  81. Peter Hansen & Jeremy Large & Asger Lunde, 2008. "Moving Average-Based Estimators of Integrated Variance," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 79-111.
  82. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(01), pages 17-43, March.
  83. Malmsten, Hans & Teräsvirta, Timo, 2004. "Stylized Facts of Financial Time Series and Three Popular Models of Volatility," SSE/EFI Working Paper Series in Economics and Finance 563, Stockholm School of Economics, revised 03 Sep 2004.
  84. 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)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:147:y:2008:i:1:p:104-119. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.