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On nonparametric estimation in nonlinear AR(1)-models

✍ Scribed by Marc Hoffmann

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
165 KB
Volume
44
Category
Article
ISSN
0167-7152

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✦ Synopsis

We estimate the mean function and the conditional variance (the volatility function) of a nonlinear ÿrst-order autoregressive model nonparametrically. Minimax rates of convergence are established over a scale of Besov bodies Bspq and a range of global L p error measurements, for 16p ‘ ∞. We propose an estimating procedure based on a martingale regression approximation scheme. This enables us to implement wavelet thresholding and obtain adaptation results with respect to an unknown degree of smoothness.

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