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

Non-Parametric Estimation of Forecast Distributions in Non-Gaussian, Non-linear State Space Models

  • Jason Ng

    ()

  • Catherine S. Forbes

    ()

  • Gael M. Martin

    ()

  • Brendan P.M. McCabe

The object of this paper is to produce non-parametric maximum likelihood estimates of forecast distributions in a general non-Gaussian, non-linear state space setting. The transition densities that define the evolution of the dynamic state process are represented in parametric form, but the conditional distribution of the non-Gaussian variable is estimated non-parametrically. The filtering and prediction distributions are estimated via a computationally efficient algorithm that exploits the functional relationship between the observed variable, the state variable and a measurement error with an invariant distribution. Simulation experiments are used to document the accuracy of the non-parametric method relative to both correctly and incorrectly specified parametric alternatives. In an empirical illustration, the method is used to produce sequential estimates of the forecast distribution of realized volatility on the S&P500 stock index during the recent financial crisis. A resampling technique for measuring sampling variation in the estimated forecast distributions is also demonstrated.

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://business.monash.edu/econometrics-and-business-statistics/research/publications/ebs/wp11-11.pdf
Download Restriction: no

Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 11/11.

as
in new window

Length: 37 pages
Date of creation: 31 Aug 2011
Date of revision:
Handle: RePEc:msh:ebswps:2011-11
Contact details of provider: Postal:
PO Box 11E, Monash University, Victoria 3800, Australia

Phone: +61 3 99052489
Fax: +61 3 99055474
Web page: http://business.monash.edu/econometrics-and-business-statistics
Email:


More information through EDIRC

Order Information: Web: http://business.monash.edu/econometrics-and-business-statistics Email:


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. Ruiz, Esther & Romo, Juan & Pascual, L., 1999. "Effects of parameter estimation on prediction densities a bootstrap approach," DES - Working Papers. Statistics and Econometrics. WS 6304, Universidad Carlos III de Madrid. Departamento de Estadística.
  2. Raffaella Giacomini & Ivana Komunjer, 2003. "Evaluation and Combination of Conditional Quantile Forecasts," Boston College Working Papers in Economics 571, Boston College Department of Economics.
  3. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
  4. Bauwens, Luc & Veredas, David, 2004. "The stochastic conditional duration model: a latent variable model for the analysis of financial durations," Journal of Econometrics, Elsevier, vol. 119(2), pages 381-412, April.
  5. Ruiz, Esther & Rodríguez, Alejandro, 2008. "Bootstrap prediction intervals in State Space models," DES - Working Papers. Statistics and Econometrics. WS ws081104, Universidad Carlos III de Madrid. Departamento de Estadística.
  6. DeRossi, G. & Harvey, A., 2007. "Quantiles, Expectiles and Splines," Cambridge Working Papers in Economics 0660, Faculty of Economics, University of Cambridge.
  7. Strickland, Chris M. & Forbes, Catherine S. & Martin, Gael M., 2006. "Bayesian analysis of the stochastic conditional duration model," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2247-2267, May.
  8. Joyce E. Berg & John Geweke & Thomas A. Rietz, 2010. "Memoirs of an indifferent trader: Estimating forecast distributions from prediction markets," Quantitative Economics, Econometric Society, vol. 1(1), pages 163-186, 07.
  9. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(2), pages 174-196, Spring.
  10. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
  11. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
  12. Gianni Amisano & Raffaella Giacomini, 2005. "Comparing Density Forecsts via Weighted Likelihood Ratio Tests," Working Papers ubs0504, University of Brescia, Department of Economics.
  13. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
  14. Worapree Maneesoonthorn & Gael M. Martin & Catherine S. Forbes & Simone Grose, 2010. "Probabilistic Forecasts of Volatility and its Risk Premia," Monash Econometrics and Business Statistics Working Papers 22/10, Monash University, Department of Econometrics and Business Statistics.
  15. Ruiz, Esther & Romo, Juan & Pascual, Lorenzo, 2001. "Bootstrap prediction intervals for power-transformed time series," DES - Working Papers. Statistics and Econometrics. WS ws010503, Universidad Carlos III de Madrid. Departamento de Estadística.
  16. Durham, Garland B., 2007. "SV mixture models with application to S&P 500 index returns," Journal of Financial Economics, Elsevier, vol. 85(3), pages 822-856, September.
  17. Bu, Ruijun & McCabe, Brendan, 2008. "Model selection, estimation and forecasting in INAR(p) models: A likelihood-based Markov Chain approach," International Journal of Forecasting, Elsevier, vol. 24(1), pages 151-162.
  18. Boero, Gianna & Smith, Jeremy & Wallis, Kenneth F., 2011. "Scoring rules and survey density forecasts," International Journal of Forecasting, Elsevier, vol. 27(2), pages 379-393.
  19. Brownlees, C.T. & Gallo, G.M., 2006. "Financial econometric analysis at ultra-high frequency: Data handling concerns," Computational Statistics & Data Analysis, Elsevier, vol. 51(4), pages 2232-2245, December.
  20. Gael M. Martin & Andrew Reidy & Jill Wright, 2009. "Does the option market produce superior forecasts of noise-corrected volatility measures?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 77-104.
  21. Brendan P. M. McCabe & Gael M. Martin & David Harris, 2011. "Efficient probabilistic forecasts for counts," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(2), pages 253-272, 03.
  22. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-74, October.
  23. Tilmann Gneiting & Fadoua Balabdaoui & Adrian E. Raftery, 2007. "Probabilistic forecasts, calibration and sharpness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 243-268.
  24. Tilmann Gneiting, 2008. "Editorial: Probabilistic forecasting," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(2), pages 319-321.
  25. G.C. Lim & G.M. Martin & V.L. Martin, 2002. "Parametric Pricing of Higher Order Moments in S&P500 Options," Monash Econometrics and Business Statistics Working Papers 1/02, Monash University, Department of Econometrics and Business Statistics.
  26. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  27. BAUWENS , Luc & GIOT, Pierre & GRAMMIG, Joachim & VEREDAS, David, 2000. "A comparison of financial duration models via density forecasts," CORE Discussion Papers 2000060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  28. Ruiz, Esther & Rodríguez, Alejandro, 2010. "Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters," DES - Working Papers. Statistics and Econometrics. WS ws100301, Universidad Carlos III de Madrid. Departamento de Estadística.
  29. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  30. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, 04.
  31. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
  32. Monteiro, André A., 2010. "A semiparametric state space model," DES - Working Papers. Statistics and Econometrics. WS ws103418, Universidad Carlos III de Madrid. Departamento de Estadística.
  33. Durham, Garland B., 2006. "Monte Carlo methods for estimating, smoothing, and filtering one- and two-factor stochastic volatility models," Journal of Econometrics, Elsevier, vol. 133(1), pages 273-305, July.
  34. McCabe, B.P.M. & Martin, G.M., 2005. "Bayesian predictions of low count time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 315-330.
  35. C. Yau & O. Papaspiliopoulos & G. O. Roberts & C. Holmes, 2011. "Bayesian non‐parametric hidden Markov models with applications in genomics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 37-57, January.
  36. Geweke, John & Amisano, Gianni, 2010. "Comparing and evaluating Bayesian predictive distributions of asset returns," International Journal of Forecasting, Elsevier, vol. 26(2), pages 216-230, April.
  37. Freeland, R. K. & McCabe, B. P. M., 2004. "Forecasting discrete valued low count time series," International Journal of Forecasting, Elsevier, vol. 20(3), pages 427-434.
  38. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
  39. Genshiro Kitagawa, 1994. "The two-filter formula for smoothing and an implementation of the Gaussian-sum smoother," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 605-623, December.
  40. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
  41. 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.
  42. Adam Clements & Stan Hurn & Scott White, 2006. "Estimating Stochastic Volatility Models Using a Discrete Non-linear Filter. Working paper #3," NCER Working Paper Series 3, National Centre for Econometric Research.
  43. Mark Broadie & Mikhail Chernov & Michael Johannes, 2007. "Model Specification and Risk Premia: Evidence from Futures Options," Journal of Finance, American Finance Association, vol. 62(3), pages 1453-1490, 06.
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:msh:ebswps:2011-11. 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: (Dr Xibin Zhang)

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.