Consistent bootstrap one-step prediction region for state-vector in state space model
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In this paper, we propose a bootstrap algorithm to construct non-parametric prediction region for a simplified state-space model and provide theoretical proof for its consistency. Besides, we introduce prediction problem under the situation that innovation depends on previous observations and extend definition in PAN20161 to a broader class of models. Numerical results show that performance of proposed bootstrap algorithm depends on smoothness of data and deviation of last observation and state variable. Results in this paper can be adjusted to other classical models, like stochastic volatility model, exogenous time series model and etc.
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