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Testing for multivariate volatility functions using minimum volume sets and inverse regression

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  • Polonik, Wolfgang
  • Yao, Qiwei

Abstract

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed facilitate the investigation for different features such as if a multivariate regression function is (i) constant, (ii) of a bathtub shape, and (iii) in a given parametric form. The inference based on those tests may be further enhanced through associated diagnostic plots. Although the potential use of those ideas is much wider, we focus on the inference for multivariate volatility functions in this paper, i.e. we test for (i) heteroscedasticity, (ii) the so-called ‘smiling effect’, and (iii) some parametric volatility models. The asymptotic behavior of the proposed tests is investigated, and practical feasibility is shown via simulation studies. We further illustrate our methods with real financial data.

Suggested Citation

  • Polonik, Wolfgang & Yao, Qiwei, 2008. "Testing for multivariate volatility functions using minimum volume sets and inverse regression," LSE Research Online Documents on Economics 24132, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:24132
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    References listed on IDEAS

    as
    1. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    2. Chen, Min & An, Hong Zhi, 1997. "A Kolmogorov-Smirnov type test for conditional heteroskedasticity in time series," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 321-331, May.
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    More about this item

    Keywords

    Brownian bridge; empirical process; ARCH models; heteroscedasticity; integral stochastic order; level set; smiling effect;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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