A New Nonlinearity Test to Circumvent the Limitation of Volterra Expansion with Applications

Posted: 6 Mar 2015 Last revised: 9 Mar 2016

See all articles by Zhidong Bai

Zhidong Bai

Northeast Normal University

Yongchang Hui

Hong Kong Baptist University (HKBU)

Wing-Keung Wong

Asia University, Department of Finance

Date Written: August 29, 2014

Abstract

In this paper, we propose a quick and efficient method to examine whether a time series Yt possesses any nonlinear feature by testing a kind of dependence remained in the residuals after fitting Yt 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 Yt. It 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 and whether the S&P 500 index follows a random walk model. The conclusion drawn from our proposed test is consistent those from other tests.

Keywords: Nonlinearity, U-statistics, Volterra expansion, sunspots, efficient market, simulation

JEL Classification: C01, C12, G10

Suggested Citation

Bai, Zhidong and Hui, Yongchang and Wong, Wing-Keung, A New Nonlinearity Test to Circumvent the Limitation of Volterra Expansion with Applications (August 29, 2014). Available at SSRN: https://ssrn.com/abstract=2568326

Zhidong Bai

Northeast Normal University ( email )

Changchun
China

Yongchang Hui

Hong Kong Baptist University (HKBU) ( email )

Kowloon
Hong Kong

Wing-Keung Wong (Contact Author)

Asia University, Department of Finance ( email )

Taiwan
Taiwan

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