Advanced Search
MyIDEAS: Login to save this paper or follow this series

Likelihood-based estimation of latent generalised ARCH structures

Contents:

Author Info

  • Gabriele Fiorentini
  • Enrique Sentana
  • Neil Shephard

Abstract

GARCH models are commonly used as latent processes in econometrics, financial economics and macroeconomics. Yet no exact likelihood analysis of these models has been provided so far. In this paper we outline the issues and suggest a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a Bayesian solution in O(T) computational operations, where T denotes the sample size. We assess the performance of our proposed algorithm in the context of both artificial examples and an empirical application to 26 UK sectorial stock returns, and compare it to existing approximate solutions.

Download Info

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.finance.ox.ac.uk/file_links/finecon_papers/2004fe02.pdf
Our checks indicate that this address may not be valid because: 404 Not Found. If this is indeed the case, please notify (Maxine Collett)
Download Restriction: no

Bibliographic Info

Paper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2004fe02.

as in new window
Length:
Date of creation: 2004
Date of revision:
Handle: RePEc:sbs:wpsefe:2004fe02

Contact details of provider:
Email:
Web page: http://www.finance.ox.ac.uk
More information through EDIRC

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

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. Eichengreen, Barry & Watson, Mark W & Grossman, Richard S, 1985. "Bank Rate Policy under the Interwar Gold Standard: A Dynamic Probit Model," Economic Journal, Royal Economic Society, Royal Economic Society, vol. 95(379), pages 725-45, September.
  2. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 74(1), pages 3-30, September.
  3. Michael Dueker, 1998. "Conditional heteroskedasticity in qualitative response models of time series: a Gibbs sampling approach to the bank prime rate," Working Papers 1998-011, Federal Reserve Bank of St. Louis.
  4. Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
  5. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, Elsevier, vol. 49(3), pages 305-341, September.
  6. Brennan, Michael J., 1986. "A theory of price limits in futures markets," Journal of Financial Economics, Elsevier, Elsevier, vol. 16(2), pages 213-233, June.
  7. GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, Econometric Society, vol. 57(6), pages 1317-39, November.
  9. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, Econometric Society, vol. 51(5), pages 1281-304, September.
  10. Francis X. Diebold & Til Schuermann, 1996. "Exact Maximum Likelihood Estimation of Observation-Driven Econometric Models," NBER Technical Working Papers 0194, National Bureau of Economic Research, Inc.
  11. repec:fth:inseep:9107 is not listed on IDEAS
  12. Shephard, Neil, 1993. "Fitting Nonlinear Time-Series Models with Applications to Stochastic Variance Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 8(S), pages S135-52, Suppl. De.
  13. 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 557-87.
  14. Sentana, Enrique, 2004. "Factor representing portfolios in large asset markets," Journal of Econometrics, Elsevier, Elsevier, vol. 119(2), pages 257-289, April.
  15. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, Elsevier, vol. 31(3), pages 307-327, April.
  16. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, Elsevier, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038 Elsevier.
  17. Bauwens, L. & Lubrano, M., 1996. "Bayesian Inference on GARCH Models Using the Gibbs Sampler," G.R.E.Q.A.M., Universite Aix-Marseille III 96a21, Universite Aix-Marseille III.
  18. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  19. Vassilis A. Hajivassiliou & Daniel L. McFadden, 1998. "The Method of Simulated Scores for the Estimation of LDV Models," Econometrica, Econometric Society, Econometric Society, vol. 66(4), pages 863-896, July.
  20. Morten B. Jensen & Asger Lunde, 2001. "The NIG-S&ARCH model: a fat-tailed, stochastic, and autoregressive conditional heteroskedastic volatility model," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 10.
  21. Anthony D. Hall & Paul Kofman & Steve Manaster, 2001. "Migration of Price Discovery With Constrained Futures Markets," Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney 70, Quantitative Finance Research Centre, University of Technology, Sydney.
  22. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, Elsevier, vol. 52(1-2), pages 129-157.
  23. Neil Shephard & Siddhartha Chib, 1999. "Analysis of High Dimensional Multivariate Stochastic Volatility Models," Economics Series Working Papers 1999-W18, University of Oxford, Department of Economics.
  24. Ray Chou & Robert F. Engle & Alex Kane, 1991. "Measuring Risk Aversion From Excess Returns on a Stock Index," NBER Working Papers 3643, National Bureau of Economic Research, Inc.
  25. Wei, Steven X., 2002. "A censored-GARCH model of asset returns with price limits," Journal of Empirical Finance, Elsevier, Elsevier, vol. 9(2), pages 197-223, March.
  26. Mardi Dungey & Vance L Martin & Adrian R Pagan, 2000. "A multivariate latent factor decomposition of international bond yield spreads," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 15(6), pages 697-715.
  27. Thomas H. McCurdy & Ieuan G. Morgan, 1986. "Tests of the Martingale Hypothesis for Foreign Currency Futures with Time-Varying Volatility," Working Papers, Queen's University, Department of Economics 663, Queen's University, Department of Economics.
  28. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De.
  29. Francis X. Diebold & Marc Nerlove, 1986. "The dynamics of exchange rate volatility: a multivariate latent factor ARCH model," Special Studies Papers 205, Board of Governors of the Federal Reserve System (U.S.).
  30. Nakatsuma, Teruo, 2000. "Bayesian analysis of ARMA-GARCH models: A Markov chain sampling approach," Journal of Econometrics, Elsevier, Elsevier, vol. 95(1), pages 57-69, March.
  31. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
  32. Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, Elsevier, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649 Elsevier.
  33. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, Elsevier, vol. 64(1-2), pages 183-206.
  34. Lee, Lung-fei, 1999. "Estimation of dynamic and ARCH Tobit models," Journal of Econometrics, Elsevier, Elsevier, vol. 92(2), pages 355-390, October.
  35. Nielsen, Soren Feodor, 2000. "On simulated EM algorithms," Journal of Econometrics, Elsevier, Elsevier, vol. 96(2), pages 267-292, June.
  36. Enrique Sentana & Giorgio Calzolari & Gabriele Fiorentini, 2004. "Indirect Estimation Of Conditionally Heteroskedastic Factor Models," Working Papers, CEMFI wp2004_0409, CEMFI.
  37. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
  38. Mervyn King & Enrique Sentana & Sushil Wadhwani, 1990. "Volatiltiy and Links Between National Stock Markets," NBER Working Papers 3357, National Bureau of Economic Research, Inc.
  39. Demos, A & Sentana, E, 1996. "An EM Algorithm for Conditionally Heteroskedastic Factor Models," Papers, Centro de Estudios Monetarios Y Financieros- 9615, Centro de Estudios Monetarios Y Financieros-.
  40. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, December.
  41. Sentana,E., 1995. "Quadratic Arch Models," Papers, Centro de Estudios Monetarios Y Financieros- 9517, Centro de Estudios Monetarios Y Financieros-.
  42. 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 542-47, August.
  43. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 11(1), pages 1-15, January.
  44. Joel Hasbrouck, 1999. "The Dynamics of Discrete Bid and Ask Quotes," Journal of Finance, American Finance Association, American Finance Association, vol. 54(6), pages 2109-2142, December.
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 in new window

Cited by:
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.

Lists

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

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:sbs:wpsefe:2004fe02. 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: (Maxine Collett).

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.