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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Understanding the time-varying structure of complex temporal systems is oneof the main challenges of modern time series analysis. In this paper, we showthat every uniformly-positive-definite-in-covariance and sufficientlyshort-range dependent non-stationary and nonlinear time series can be wellapproximated globally by a white-noise-driven auto-regressive (AR) process ofslowly diverging order. To our best knowledge, it is the first time such astructural approximation result is established for general classes ofnon-stationary time series. A high dimensional $\mathcal{L}^2$ test and anassociated multiplier bootstrap procedure are proposed for the inference of theAR approximation coefficients. In particular, an adaptive stability test isproposed to check whether the AR approximation coefficients are time-varying, afrequently-encountered question for practitioners and researchers of timeseries. As an application, globally optimal short-term forecasting theory andmethodology for a wide class of locally stationary time series are establishedvia the method of sieves.

Auto-Regressive Approximations to Non-stationary Time Series, with Inference and Applications