A new nonlinearity test to circumvent the limitation of Volterra expansion with application

Yongchang HUI, Wing Keung WONG, Zhidong BAI, Zhen Zhen ZHU

Research output: Journal PublicationsJournal Article (refereed)

5 Citations (Scopus)

Abstract

In this paper, we propose a quick and efficient method to examine whether a time series Xt possesses any nonlinear feature by testing a kind of dependence remained in the residuals after fitting Xt with a linear model. The advantage of our proposed nonlinearity test is that it is not required to know the exact nonlinear features and the detailed nonlinear forms of the variable being examined. Another advantage of our proposed test is that there is no over-rejection problem which exists in some famous nonlinearity tests. Our proposed test can also be used to test whether the hypothesized model, including linear and nonlinear, to the variable being examined is appropriate as long as the residuals of the model being used can be estimated. Our simulation study shows that our proposed test is stable and powerful. We apply our proposed statistic to test whether there is any nonlinear feature in the sunspot data. The conclusion drawn from our proposed test is consistent with those from other well-established tests.
Original languageEnglish
Pages (from-to)365-374
Number of pages10
JournalJournal of the Korean Statistical Society
Volume46
Issue number3
DOIs
Publication statusPublished - 1 Sep 2017
Externally publishedYes

Fingerprint

Volterra
Nonlinearity
Sunspots
Rejection
Statistic
Linear Model
Time series
Simulation Study
Testing
Model

Keywords

  • Dependence
  • Dependent test
  • Nonlinear test
  • Nonlinearity
  • Sunspots
  • Volterra expansion

Cite this

HUI, Yongchang ; WONG, Wing Keung ; BAI, Zhidong ; ZHU, Zhen Zhen. / A new nonlinearity test to circumvent the limitation of Volterra expansion with application. In: Journal of the Korean Statistical Society. 2017 ; Vol. 46, No. 3. pp. 365-374.
@article{971c3cd89cee4ecdbaea0244e24b7e73,
title = "A new nonlinearity test to circumvent the limitation of Volterra expansion with application",
abstract = "In this paper, we propose a quick and efficient method to examine whether a time series Xt possesses any nonlinear feature by testing a kind of dependence remained in the residuals after fitting Xt with a linear model. The advantage of our proposed nonlinearity test is that it is not required to know the exact nonlinear features and the detailed nonlinear forms of the variable being examined. Another advantage of our proposed test is that there is no over-rejection problem which exists in some famous nonlinearity tests. Our proposed test can also be used to test whether the hypothesized model, including linear and nonlinear, to the variable being examined is appropriate as long as the residuals of the model being used can be estimated. Our simulation study shows that our proposed test is stable and powerful. We apply our proposed statistic to test whether there is any nonlinear feature in the sunspot data. The conclusion drawn from our proposed test is consistent with those from other well-established tests.",
keywords = "Dependence, Dependent test, Nonlinear test, Nonlinearity, Sunspots, Volterra expansion",
author = "Yongchang HUI and WONG, {Wing Keung} and Zhidong BAI and ZHU, {Zhen Zhen}",
year = "2017",
month = "9",
day = "1",
doi = "10.1016/j.jkss.2016.11.006",
language = "English",
volume = "46",
pages = "365--374",
journal = "Journal of the Korean Statistical Society",
issn = "1226-3192",
publisher = "Korean Statistical Society",
number = "3",

}

A new nonlinearity test to circumvent the limitation of Volterra expansion with application. / HUI, Yongchang; WONG, Wing Keung; BAI, Zhidong; ZHU, Zhen Zhen.

In: Journal of the Korean Statistical Society, Vol. 46, No. 3, 01.09.2017, p. 365-374.

Research output: Journal PublicationsJournal Article (refereed)

TY - JOUR

T1 - A new nonlinearity test to circumvent the limitation of Volterra expansion with application

AU - HUI, Yongchang

AU - WONG, Wing Keung

AU - BAI, Zhidong

AU - ZHU, Zhen Zhen

PY - 2017/9/1

Y1 - 2017/9/1

N2 - In this paper, we propose a quick and efficient method to examine whether a time series Xt possesses any nonlinear feature by testing a kind of dependence remained in the residuals after fitting Xt with a linear model. The advantage of our proposed nonlinearity test is that it is not required to know the exact nonlinear features and the detailed nonlinear forms of the variable being examined. Another advantage of our proposed test is that there is no over-rejection problem which exists in some famous nonlinearity tests. Our proposed test can also be used to test whether the hypothesized model, including linear and nonlinear, to the variable being examined is appropriate as long as the residuals of the model being used can be estimated. Our simulation study shows that our proposed test is stable and powerful. We apply our proposed statistic to test whether there is any nonlinear feature in the sunspot data. The conclusion drawn from our proposed test is consistent with those from other well-established tests.

AB - In this paper, we propose a quick and efficient method to examine whether a time series Xt possesses any nonlinear feature by testing a kind of dependence remained in the residuals after fitting Xt with a linear model. The advantage of our proposed nonlinearity test is that it is not required to know the exact nonlinear features and the detailed nonlinear forms of the variable being examined. Another advantage of our proposed test is that there is no over-rejection problem which exists in some famous nonlinearity tests. Our proposed test can also be used to test whether the hypothesized model, including linear and nonlinear, to the variable being examined is appropriate as long as the residuals of the model being used can be estimated. Our simulation study shows that our proposed test is stable and powerful. We apply our proposed statistic to test whether there is any nonlinear feature in the sunspot data. The conclusion drawn from our proposed test is consistent with those from other well-established tests.

KW - Dependence

KW - Dependent test

KW - Nonlinear test

KW - Nonlinearity

KW - Sunspots

KW - Volterra expansion

UR - http://commons.ln.edu.hk/sw_master/6696

U2 - 10.1016/j.jkss.2016.11.006

DO - 10.1016/j.jkss.2016.11.006

M3 - Journal Article (refereed)

VL - 46

SP - 365

EP - 374

JO - Journal of the Korean Statistical Society

JF - Journal of the Korean Statistical Society

SN - 1226-3192

IS - 3

ER -