A semiparametric state space model
AbstractThis paper considers the problem of estimating a linear univariate Time Series State Space model for which the shape of the distribution of the observation noise is not specified a priori. Although somewhat challenging computationally, the simultaneous estimation of the parameters of the model and the unknown observation noise density is made feasible through a combination of Gaussian-sum Filtering and Smoothing algorithms and Kernel Density Estimation methods. The bottleneck in these calculations consists in avoiding the geometric increase, with time, of the number of simultaneous Kalman filter components. It is the aim of this paper to show that this can be achieved by the use of standard techniques from Cluster Analysis and unsupervised Classification. An empirical illustration of this new methodology is included; this consists in the application of a semiparametric version of the Local Level model to the analysis of the wellknown river Nile data series.
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Bibliographic InfoPaper provided by Universidad Carlos III, Departamento de Estadística y Econometría in its series Statistics and Econometrics Working Papers with number ws103418.
Date of creation: Sep 2010
Date of revision:
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More information through EDIRC
Clustering; Gaussian-Sum; Kernel methods; Signal extraction; State space models;
Find related papers by JEL classification:
- C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
- 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 &bull Diffusion Processes
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-10-30 (All new papers)
- NEP-ECM-2010-10-30 (Econometrics)
- NEP-ETS-2010-10-30 (Econometric Time Series)
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- Jason Ng & Catherine S. Forbes & Gael M. Martin & Brendan P.M. McCabe, 2011.
"Non-Parametric Estimation of Forecast Distributions in Non-Gaussian, Non-linear State Space Models,"
Monash Econometrics and Business Statistics Working Papers
11/11, Monash University, Department of Econometrics and Business Statistics.
- 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.
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