Constructing Non-linear Gaussian Time Series by Means of a Simplified State Space Representation
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Paolo Vidoni
State space models provide a useful stochastic description for dynamic phenomena, based on unobserved or latent variables. When the model rests on linear and Gaussian assumptions there exists a well-known iterative procedure, called the Kalman filter, which gives analytic updating recursion for the filtering, the prediction and the smoothing distributions. However, this is rare and a state space model does not usually admit such a filter. For this reason, instead of looking for analytic solutions, a number of papers aim to define alternative procedures, giving numerical or approximate solutions. This paper concerns a particular class of models based on the assumption that the mixed process, obtained by alternating states and observations, is a Markov process. The main features of this class of models, proposed for stochastic volatility description by Barndorff-Nielsen (1997), are emphasized. In this framework, some new non-linear Gaussian state space models, computationally tractable and of potential interest for applications, may be defined.
©2011 Walter de Gruyter GmbH & Co. KG, Berlin/Boston
Articles in the same Issue
- Article
- Introduction
- Extensions of the Forward Search to Time Series
- Analyzing Financial Time Series through Robust Estimators
- Clusters of Extreme Observations and Extremal Index Estimate in GARCH Processes
- Estimating Stochastic Volatility Models: A Comparison of Two Importance Samplers
- MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model
- GARCH-type Models with Generalized Secant Hyperbolic Innovations
- Mixture Processes for Financial Intradaily Durations
- Constructing Non-linear Gaussian Time Series by Means of a Simplified State Space Representation
- Statistical Tests for Lyapunov Exponents of Deterministic Systems
- Assessing Chaos in Time Series: Statistical Aspects and Perspectives
- On the Stationarity of First-order Nonlinear Time Series Models: Some Developments
- Experimental Design for Time-Dependent Models with Correlated Observations
- Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation
- Stability and Consistency of Seasonally Adjusted Aggregates and Their Component Patterns
- Seasonal Specific Structural Time Series
- Relationship between Local and Global Nonparametric Estimators Measures of Fitting and Smoothing
Articles in the same Issue
- Article
- Introduction
- Extensions of the Forward Search to Time Series
- Analyzing Financial Time Series through Robust Estimators
- Clusters of Extreme Observations and Extremal Index Estimate in GARCH Processes
- Estimating Stochastic Volatility Models: A Comparison of Two Importance Samplers
- MCMC Bayesian Estimation of a Skew-GED Stochastic Volatility Model
- GARCH-type Models with Generalized Secant Hyperbolic Innovations
- Mixture Processes for Financial Intradaily Durations
- Constructing Non-linear Gaussian Time Series by Means of a Simplified State Space Representation
- Statistical Tests for Lyapunov Exponents of Deterministic Systems
- Assessing Chaos in Time Series: Statistical Aspects and Perspectives
- On the Stationarity of First-order Nonlinear Time Series Models: Some Developments
- Experimental Design for Time-Dependent Models with Correlated Observations
- Inference and Forecasting for ARFIMA Models With an Application to US and UK Inflation
- Stability and Consistency of Seasonally Adjusted Aggregates and Their Component Patterns
- Seasonal Specific Structural Time Series
- Relationship between Local and Global Nonparametric Estimators Measures of Fitting and Smoothing
