Abstract
In this chapter we discuss versatile generalizations of the basic time series models in Sect. 10.1, collectively known under the name state space models. These models not only can capture the serial dependence of the observations (i.e., the dependence across time), but also can describe the persistence and volatility of the measurements. That is, they can model continued periods of high or low measurements and time-varying amounts of random fluctuation. In contrast, the AR(p) model, for example, cannot capture these features, as the model parameters do not depend on time. Throughout this chapter we shall use Bayesian notation when specifying (conditional) densities, even when working in a non-Bayesian setting.
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References
Bishop, C. M. 2006. Pattern Recognition and Machine Learning. Springer-Verlag New York, Inc., Secaucus, NJ.
Botev, Z. I., J. F. Grotowski, & D. P. Kroese 2010. Kernel density estimation via diffusion. Annals of Statistics, 38(5):2916–2957.
Chib, S. 1995. Marginal Likelihood from the Gibbs Output. Journal of the American Statistical Association, 90:1313–1321.
Chib, S., & I. Jeliazkov 2001. Marginal Likelihood from the Metropolis-Hastings Output. Journal of the American Statistical Association, 96:270–281.
Fair, R. C. 1978. A Theory of Extramarital Affairs. Journal of Political Economy, 86:45–61.
Feller, W. 1970. An Introduction to Probability Theory and Its Applications, volume I. John Wiley & Sons, New York, second edition.
Gelfand, A. E., S. Hills, A. Racine-Poon, & A. F. M. Smith 1990. Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling. Journal of American Statistical Association, 85:972–985.
Kim, S., N. Shepherd, & S. Chib 1998. Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models. Review of Economic Studies, 65(3):361–393.
Koop, G., D. J. Poirier, J. L., & Tobias 2007. Bayesian Econometric Methods. Cambridge University Press.
Kroese, D. P., T. Taimre, & Z. I. Botev 2011. Handbook of Monte Carlo Methods. John Wiley & Sons, New York.
L’Ecuyer, P. 1999. Good Parameters and Implementations for Combined Multiple Recursive Random Number Generators. Operations Research, 47(1):159 – 164.
Marsaglia, G., & W. Tsang 2000. A Simple Method for Generating Gamma Variables. ACM Transactions on Mathematical Software, 26(3):363–372.
McLachlan, G. J., & T. Krishnan 2008. The EM Algorithm and Extensions. John Wiley & Sons, Hoboken, NJ, second edition.
Metropolis, M., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, & E. Teller 1953. Equations of state calculations by fast computing machines. J. of Chemical Physics, 21:1087–1092.
Verdinelli, I., & L. Wasserman 1995. Computing Bayes Factors Using a Generalization of the Savage-Dickey Density Ratio. Journal of the American Statistical Association, 90(430): 614–618.
Williams, D. 1991. Probability with Martingales. Cambridge University Press, Cambridge.
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Kroese, D.P., Chan, J.C.C. (2014). State Space Models. In: Statistical Modeling and Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8775-3_11
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DOI: https://doi.org/10.1007/978-1-4614-8775-3_11
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