You are not currently logged in.
Access JSTOR through your library or other institution:
If You Use a Screen ReaderThis content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Local Polynomial Estimation with a FARIMA-GARCH Error Process
Jan Beran and Yuanhua Feng
Vol. 7, No. 5 (Oct., 2001), pp. 733-750
Published by: International Statistical Institute (ISI) and the Bernoulli Society for Mathematical Statistics and Probability
Stable URL: http://www.jstor.org/stable/3318539
Page Count: 18
You can always find the topics here!Topics: Polynomials, Martingales, Random variables, Semiparametric modeling, Statism, Time series, Time series models, Parametric models, Central limit theorem, Sample mean
Were these topics helpful?See somethings inaccurate? Let us know!
Select the topics that are inaccurate.
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Preview not available
This paper considers estimation of the trend function g as well as its vth derivative g(v) in a so-called semi-parametric FARIMA-GARCH model by local polynomial fits. The focus is on the derivation of the asymptotic normality of ĝ(v). A central limit theorem based on martingale theory is developed. Asymptotic normality of the sample mean of a FARIMA-GARCH process is proved. These results are then used to show the asymptotic normality of ĝ(v). As an auxiliary result, the weak consistency of a weighted sum is obtained for second-order stationary time series with short or long memory under very weak conditions. Formulae for the mean integrated square error and the asymptotically optimal bandwidth of ĝ(v) are also given.
Bernoulli © 2001 Bernoulli Society for Mathematical Statistics and Probability