Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Oracally Efficient Estimation of Functional-Coefficient Autoregressive
  Models   Nonlinear autoregressive models are very useful for modeling many natural
processes, however, the size of the class of these models is large.
Functional-coefficient autoregressive models (FCAR) are useful structures for
reducing the size of the class of these models. Although this structure reduces
the class of nonlinear models, it is broad enough to include some common time
series models as specific cases. A recent development in estimating nonlinear
time series data is the spline backfitted kernel (SBK) method. This method
combines the computational speed of splines with the asymptotic properties of
kernel smoothing. To estimate a component function in the model, all other
component functions are pre-estimated with splines and then the difference is
taken of the observed time series and the pre-estimates. This difference is
then used as pseudo-responses for which kernel smoothing is used to estimate
the function of interest. By constructing the estimates in this way, the method
does not suffer from the curse of dimensionality. In this paper, we adapt the
SBK method to FCAR models.

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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: math
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org