An improvement of weak stationary test of time series and non-linear causal analysis.

点击翻译按钮获取中文摘要

A weakly stationary process, whose time parameter space is a finite interval, is called a local and weakly stationary process. Okabe and Nakano constructed Test(S) which states a criterion that multi-dimensional data are a realization of a local and weakly stationary process. In this study, we propose a revised test of Test(S), say R-Test(S) . R-Test(S) has a better efficient than Test(S) when non-linear data are tested. We apply R-Test(S) to well-known data, sunspot numbers and Lynx in Canada from 1921 to 1934. We worked up R-Test(S) into the paper "On a revised test of Test(S) in time series" .We defined two kinds of causality. One is linear local causality and other is non-linear local causality. We introduce a causal value between time series. Furthermore, we propose a test which tests the linear local causality between given time series. As an application, The causal relation between sunspot numbers and Lynx in Canada are analyzed. We worked up R-Test(S) into the paper. "On a causal function between time series" .