Bootstrapping and Related Techniques pp 101-105 | Cite as
A Bootstrap Approach for Nonlinear Autoregressions Some Preliminary Results
Conference paper
Abstract
We consider non-linear autoregressions of order 1, i.e. discrete time processes generated by
where εt, - ∞ < t < ∞, are i.i.d. zero-mean real random variables with probability density fε and finite variance \( \sigma_{\varepsilon }^2 = {\rm var} \left( {\varepsilon {}_t} \right) \). Then, the transition probabilities P(x,.) of the Markov chain (1) are absolutely continuous with density fε (.- m(x)).
$$ {X_{{t + 1}}} = m\left( {{X_t}} \right) + {\varepsilon_{{t + 1}}}, - \infty \, < \,t\, < \,\infty, $$
(1)
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© Springer-Verlag Berlin Heidelberg 1992