Abstract
In this paper, we provide a general result under some high level assumptions that shows how to account for the parameter uncertainty problem in test statistics formulated with the quasi maximum likelihood (QML) estimator. We use our general result to develop various test statistics for testing skewness, kurtosis and normality for time series data. We show that the asymptotic distributions of our test statistics coincide with the asymptotic distributions of some tests suggested in the literature. Thus, our general result provides a unified approach for test statistics formulated with the QML estimator for time series data.
Original language | English (US) |
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Pages (from-to) | 253-272 |
Number of pages | 20 |
Journal | Hacettepe Journal of Mathematics and Statistics |
Volume | 51 |
Issue number | 1 |
DOIs | |
State | Published - 2022 |
Keywords
- MLE
- Normality tests
- QMLE
- asymptotic variance
- inference
- kurtosis
- parameter uncertainty
- skewness
- test statistics
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Statistics and Probability
- Geometry and Topology