Testing for Multivariate Volatility Functions
نویسندگان
چکیده
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) of 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 limit behavior of the proposed tests is investigated, and practical feasibility is shown via simulation studies. We further illustrate our methods with some real financial data.
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