Abstract
We propose specification tests for the variance of a diffusion that do not require complete knowledge of the functional form under the null. We first propose a test for the constancy of the variance that, under the null of constancy, has a limiting normal distribution, while under the alternative of either unconditional or conditional heteroskedasticity it diverges at an appropriate rate. We then propose a test for the null of a parametric specification against the alternative of a more general functional form. Under the null, the test has a well-defined limiting distribution, normal in the unconditional and mixed normal in the conditional heteroskedasticity case; under the alternative, it diverges.
Original language | English (US) |
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Pages (from-to) | 253-270 |
Number of pages | 18 |
Journal | Journal of Time Series Analysis |
Volume | 20 |
Issue number | 3 |
DOIs | |
State | Published - May 1999 |
Keywords
- Diffusion processes
- Heteroskedasticity
- Local times
- Nonparametric estimation
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics