Time-series Modelling, Stationarity and Bayesian Nonparametric Methods
AbstractIn this paper we introduce two general non-parametric first-order stationary time-series models for which marginal (invariant) and transition distributions are expressed as infinite-dimensional mixtures. That feature makes them the first Bayesian stationary fully non-parametric models developed so far. We draw on the discussion of using stationary models in practice, as a motivation, and advocate the view that flexible (non-parametric) stationary models might be a source for reliable inferences and predictions. It will be noticed that our models adequately fit in the Bayesian inference framework due to a suitable representation theorem. A stationary scale-mixture model is developed as a particular case along with a computational strategy for posterior inference and predictions. The usefulness of that model is illustrated with the analysis of Euro/USD exchange rate log-returns.
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Bibliographic InfoPaper provided by Banco de México in its series Working Papers with number 2011-08.
Date of creation: Sep 2011
Date of revision:
Stationarity; Markov processes; Dynamic mixture models; Random probability measures; Conditional random probability measures; Latent processes.;
Find related papers by JEL classification:
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-10-15 (All new papers)
- NEP-ECM-2011-10-15 (Econometrics)
- NEP-ETS-2011-10-15 (Econometric Time Series)
- NEP-ORE-2011-10-15 (Operations Research)
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- Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-65, September.
- Lacour, Claire, 2008. "Nonparametric estimation of the stationary density and the transition density of a Markov chain," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 232-260, February.
- Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
- Barry, Christopher B. & Winkler, Robert L., 1976. "Nonstationarity and Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 11(02), pages 217-235, June.
- Giacomini, Raffaella & Gottschling, Andreas & Haefke, Christian & White, Halbert, 2007.
"Mixtures of t-distributions for Finance and Forecasting,"
216, Institute for Advanced Studies.
- Giacomini, Raffaella & Gottschling, Andreas & Haefke, Christian & White, Halbert, 2008. "Mixtures of t-distributions for finance and forecasting," Journal of Econometrics, Elsevier, vol. 144(1), pages 175-192, May.
- RodrÃguez, Abel & Dunson, David B & Gelfand, Alan E, 2008. "The Nested Dirichlet Process," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1131-1154.
- Rong Zhu & Harry Joe, 2006. "Modelling Count Data Time Series with Markov Processes Based on Binomial Thinning," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 725-738, 09.
- Clements Michael P. & Hendry David F., 2008. "Economic Forecasting in a Changing World," Capitalism and Society, De Gruyter, vol. 3(2), pages 1-20, October.
- Viviane Campos & Chang Dorea, 2005. "Kernel estimation for stationary density of Markov chains with general state space," Annals of the Institute of Statistical Mathematics, Springer, vol. 57(3), pages 443-453, September.
- Ramsés H. Mena & Stephen G. Walker, 2005. "Stationary Autoregressive Models via a Bayesian Nonparametric Approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 789-805, November.
- Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-84, March.
- Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 493-530.
- Luis E. Nieto-Barajas, 2002. "Markov Beta and Gamma Processes for Modelling Hazard Rates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 29(3), pages 413-424.
- Michael K. Pitt, 2002. "Constructing First Order Stationary Autoregressive Models via Latent Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 29(4), pages 657-663.
- Pitt, Michael K. & Walker, Stephen G., 2005. "Constructing Stationary Time Series Models Using Auxiliary Variables With Applications," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 554-564, June.
- Ramsés Mena & Stephen Walker, 2007. "On the Stationary Version of the Generalized Hyperbolic ARCH Model," Annals of the Institute of Statistical Mathematics, Springer, vol. 59(2), pages 325-348, June.
- Pitt, Michael K. & Walker, Stephen G., 2006. "Extended constructions of stationary autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 76(12), pages 1219-1224, July.
- Nadjib Bouzar & K. Jayakumar, 2008. "Time series with discrete semistable marginals," Statistical Papers, Springer, vol. 49(4), pages 619-635, October.
- Robert Engle, 2001. "GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 157-168, Fall.
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