English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper discusses asymptotic distributions of various estimators of theunderlying parameters in some regression models with long memory (LM) Gaussiandesign and nonparametric heteroscedastic LM moving average errors. In thesimple linear regression model, the first-order asymptotic distribution of theleast square estimator of the slope parameter is observed to be degenerate.However, in the second order, this estimator is $n^{1/2}$-consistent andasymptotically normal for $h+H<3/2$; nonnormal otherwise, where $h$ and $H$ areLM parameters of design and error processes, respectively. Thefinite-dimensional asymptotic distributions of a class of kernel typeestimators of the conditional variance function $\sigma^2(x)$ in a more generalheteroscedastic regression model are found to be normal whenever $H<(1+h)/2$,and non-normal otherwise. In addition, in this general model,$\log(n)$-consistency of the local Whittle estimator of $H$ based on pseudoresiduals and consistency of a cross validation type estimator of $\sigma^2(x)$are established. All of these findings are then used to propose a lack-of-fittest of a parametric regression model, with an application to some currencyexchange rate data which exhibit LM.

Asymptotic inference in some heteroscedastic regression models with long memory design and errors