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

Wolfgang Polonik and Qiwei Yao

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: Brownian bridge; empirical process; ARCH models; heteroscedasticity; integral stochastic order; level set; smiling effect (search for similar items in EconPapers)
JEL-codes: C1 J1 (search for similar items in EconPapers)
Date: 2008-11
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Published in Journal of Econometrics, November, 2008, 147(1), pp. 151-162. ISSN: 0304-4076

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