Distribution of test statistics under parameter uncertainty for time series data: an application to testing skewness, kurtosis and normality

Anil K. Bera, Osman Doğan, Süleyman Taşpınar

Research output: Contribution to journalArticlepeer-review

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 languageEnglish (US)
Pages (from-to)253-272
Number of pages20
JournalHacettepe Journal of Mathematics and Statistics
Volume51
Issue number1
DOIs
StatePublished - 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

Fingerprint

Dive into the research topics of 'Distribution of test statistics under parameter uncertainty for time series data: an application to testing skewness, kurtosis and normality'. Together they form a unique fingerprint.

Cite this