Nonparametric estimation in a nonlinear cointegration type model
Nonparametric estimation in a nonlinear cointegration type model
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DOI：
10.1214/009053606000001181
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发表时间：
2007-02
影响因子：
4.5
通讯作者：
H. A. Karlsen;Terje Myklebust;D. Tjøstheim
中科院分区：
文献类型：
--
作者：
H. A. Karlsen;Terje Myklebust;D. Tjøstheim
本文给出了非线性传递函数模型Z（t）= f（Xt）+ Wt的非参数估计的渐近理论，其中{Xt}和{Zt}是可观测的非平稳过程，{Wt}是平稳过程.在计量经济学中，这可以被解释为非线性协整类型的关系，但我们相信我们的结果有更广泛的兴趣。允许{Xt}的非平稳过程类是零递归类的子类。马尔可夫链这个子类包含随机游走模型和单位根过程。在两组不同的假设下，我们得到了f（z）的非参数估计的渐近性：i）{Wt}是线性过程，ii）{Wt}是满足某些混合条件的马氏链.后者需要做更多的工作，但也有更大的进一步发展的希望。通过一组模拟实验研究了有限样本性质f（x）。
We derive an asymptotic theory of nonparametric estimation for an nonlinear transfer function model Z(t) = f (Xt) + Wt where {Xt} and {Zt} are observed nonstationary processes and {Wt} is a stationary process. IN econometrics this can be interpreted as a nonlinear cointegration type relationship, but we believe that our results have wider interest. The class of nonstationary processes allowed for {Xt} is a subclass of the class of null recurrent.. Markov chains. This subclass contains the random walk model and the unit root processes. WE derive the asymptotics of an nonparametric estimate of f(z) under two alternative sets of assumptions on {Wt}: i) {Wt} is a linear process ii) {Wt} is a Markov chain satisfying some mixing conditions. The latter requires considerably more work but also holds larger promise for further developments. The finite sample properties f(x) are studied via a set of simulation experiments.