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

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  • Hui, Yongchang
  • Wong, Wing-Keung
  • Bai, Zhidong
  • Zhu, Zhenzhen

Abstract

In this paper, we propose a quick, efficient, and easy method to examine whether a time series Yt possesses any nonlinear feature. 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. We find that our proposed test can be used to detect any nonlinearity for the variable being examined and detect GARCH models in the innovations. 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.

Suggested Citation

  • Hui, Yongchang & Wong, Wing-Keung & Bai, Zhidong & Zhu, Zhenzhen, 2016. "A New Nonlinearity Test to Circumvent the Limitation of Volterra Expansion with Applications," MPRA Paper 75216, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:75216
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    Cited by:

    1. Nguyen Huu Hau & Tran Trung Tinh & Hoa Anh Tuong & Wing-Keung Wong, 2020. "Review of Matrix Theory with Applications in Education and Decision Sciences," Advances in Decision Sciences, Asia University, Taiwan, vol. 24(1), pages 28-69, March.
    2. Zhihui Lv & Amanda M. Y. Chu & Michael McAleer & Wing-Keung Wong, 2019. "Modelling Economic Growth, Carbon Emissions, and Fossil Fuel Consumption in China: Cointegration and Multivariate Causality," IJERPH, MDPI, vol. 16(21), pages 1-35, October.
    3. Vo, Duc, 2019. "The Impact of Foreign Direct Investment on Environment Degradation: Evidence from Emerging Markets in Asia," MPRA Paper 103292, University Library of Munich, Germany.
    4. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Tinbergen Institute Discussion Papers 18-024/III, Tinbergen Institute.
    5. Chow, Sheung Chi & Vieito, João Paulo & Wong, Wing Keung, 2019. "Do both demand-following and supply-leading theories hold true in developing countries?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 536-554.
    6. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," JRFM, MDPI, vol. 11(1), pages 1-29, March.
    7. Wenjing Xie & João Paulo Vieito & Ephraim Clark & Wing-Keung Wong, 2020. "Could Mergers Become More Sustainable? A Study of the Stock Exchange Mergers of NASDAQ and OMX," Sustainability, MDPI, vol. 12(20), pages 1-25, October.
    8. Pedro Antonio Martín Cervantes & Nuria Rueda López & Salvador Cruz Rambaud, 2019. "A Causal Analysis of Life Expectancy at Birth. Evidence from Spain," IJERPH, MDPI, vol. 16(13), pages 1-14, July.
    9. Kim-Hung Pho & Thi Diem-Chinh Ho & Tuan-Kiet Tran & Wing-Keung Wong, 2019. "Moment Generating Function, Expectation And Variance Of Ubiquitous Distributions With Applications In Decision Sciences: A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(2), pages 65-150, June.
    10. Anh Hoang To & Dao Thi-Thieu Ha & Ha Minh Nguyen & Duc Hong Vo, 2019. "The Impact of Foreign Direct Investment on Environment Degradation: Evidence from Emerging Markets in Asia," IJERPH, MDPI, vol. 16(9), pages 1-24, May.
    11. Riza Demirer & Rangan Gupta & Zhihui Lv & Wing-Keung Wong, 2019. "Equity Return Dispersion and Stock Market Volatility: Evidence from Multivariate Linear and Nonlinear Causality Tests," Sustainability, MDPI, vol. 11(2), pages 1-15, January.
    12. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, And Big Data: Connections," Advances in Decision Sciences, Asia University, Taiwan, vol. 22(1), pages 36-94, December.
    13. Kim-Hung Pho & Tuan-Kiet Tran & Thi Diem-Chinh Ho & Wing-Keung Wong, 2019. "Optimal Solution Techniques in Decision Sciences A Review," Advances in Decision Sciences, Asia University, Taiwan, vol. 23(1), pages 114-161, March.
    14. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(1), pages 1-29, March.
    15. Choi, Insu & Lee, Myounggu & Kim, Hyejin & Kim, Woo Chang, 2023. "Elucidating Directed Statistical Dependencies: Investigating Global Financial Market Indices' Influence on Korean Short Selling Activities," Pacific-Basin Finance Journal, Elsevier, vol. 79(C).

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    More about this item

    Keywords

    Nonlinearity; U-statistics; Volterra expansion; sunspots; efficient market;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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