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Non-parametric estimation of forecast distributions in non-Gaussian, non-linear state space models

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  • Ng, Jason
  • Forbes, Catherine S.
  • Martin, Gael M.
  • McCabe, Brendan P.M.

Abstract

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 filtered 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.

Suggested Citation

  • Ng, Jason & Forbes, Catherine S. & Martin, Gael M. & McCabe, Brendan P.M., 2013. "Non-parametric estimation of forecast distributions in non-Gaussian, non-linear state space models," International Journal of Forecasting, Elsevier, vol. 29(3), pages 411-430.
  • Handle: RePEc:eee:intfor:v:29:y:2013:i:3:p:411-430
    DOI: 10.1016/j.ijforecast.2012.10.005
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    as
    1. 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.
    2. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    3. 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.
    4. 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, April.
    5. 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.
    6. 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.
    7. Alejandro Rodriguez & Esther Ruiz, 2009. "Bootstrap prediction intervals in state-space models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(2), pages 167-178, March.
    8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    9. 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.
    10. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    11. Tilmann Gneiting, 2008. "Editorial: Probabilistic forecasting," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(2), pages 319-321.
    12. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2005. "Bootstrap prediction intervals for power-transformed time series," International Journal of Forecasting, Elsevier, vol. 21(2), pages 219-235.
    13. Pascual, Lorenzo & Romo, Juan & Ruiz, Esther, 2001. "Effects of parameter estimation on prediction densities: a bootstrap approach," International Journal of Forecasting, Elsevier, vol. 17(1), pages 83-103.
    14. De Rossi, Giuliano & Harvey, Andrew, 2009. "Quantiles, expectiles and splines," Journal of Econometrics, Elsevier, vol. 152(2), pages 179-185, October.
    15. Anthony Tay & Kenneth F. Wallis, 2000. "Density Forecasting: A Survey," Econometric Society World Congress 2000 Contributed Papers 0370, Econometric Society.
    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. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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.
    23. Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
    24. 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.
    25. V. L. Martin & G. M. Martin & G. C. Lim, 2005. "Parametric pricing of higher order moments in S&P500 options," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 20(3), pages 377-404.
    26. Bauwens, Luc & Giot, Pierre & Grammig, Joachim & Veredas, David, 2004. "A comparison of financial duration models via density forecasts," International Journal of Forecasting, Elsevier, vol. 20(4), pages 589-609.
    27. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    28. 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.
    29. 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.
    30. 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, March.
    31. 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.
    32. 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 863-883, November.
    33. Amisano, Gianni & Giacomini, Raffaella, 2007. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 177-190, April.
    34. 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.
    35. Maneesoonthorn, Worapree & Martin, Gael M. & Forbes, Catherine S. & Grose, Simone D., 2012. "Probabilistic forecasts of volatility and its risk premia," Journal of Econometrics, Elsevier, vol. 171(2), pages 217-236.
    36. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
    37. 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.
    38. 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.
    39. Rodríguez, Alejandro & Ruiz, Esther, 2012. "Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 62-74, January.
    40. 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, July.
    41. 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, June.
    42. 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.
    43. 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.
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    Cited by:

    1. Gael M. Martin & Brendan P.M. McCabe & David T. Frazier & Worapree Maneesoonthorn & Christian P. Robert, 2016. "Auxiliary Likelihood-Based Approximate Bayesian Computation in State Space Models," Monash Econometrics and Business Statistics Working Papers 09/16, Monash University, Department of Econometrics and Business Statistics.
    2. Patrick Leung & Catherine S. Forbes & Gael M. Martin & Brendan McCabe, 2016. "Data-driven particle Filters for particle Markov Chain Monte Carlo," Monash Econometrics and Business Statistics Working Papers 17/16, Monash University, Department of Econometrics and Business Statistics.
    3. Gael M. Martin & Brendan P.M. McCabe & Worapree Maneesoonthorn & Christian P. Robert, 2014. "Approximate Bayesian Computation in State Space Models," Monash Econometrics and Business Statistics Working Papers 20/14, Monash University, Department of Econometrics and Business Statistics.
    4. Pauwels, Laurent L. & Vasnev, Andrey L., 2016. "A note on the estimation of optimal weights for density forecast combinations," International Journal of Forecasting, Elsevier, vol. 32(2), pages 391-397.

    More about this item

    Keywords

    Probabilistic forecasting; Non-Gaussian time series; Grid-based filtering; Penalized likelihood; Subsampling; Realized volatility;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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