English, Article, Journal or magazine article edition: Expectation of Quadratic Forms in Normal and Nonnormal Variables with Econometric Applications Yong Bao; Aman Ullah

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Physical Description
  • preprint
Language
  • English

Edition details

Title
  • Expectation of Quadratic Forms in Normal and Nonnormal Variables with Econometric Applications
Author
  • Yong Bao
  • Aman Ullah
Physical Description
  • preprint
Notes
  • We derive some new results on the expectation of quadratic forms in normal and nonnormal variables. Using a nonstochastic operator, we show that the expectation of the product of an arbitrary number of quadratic forms in noncentral normal variables follows a recurrence formula. This formula includes the existing result for central normal variables as a special case. For nonnormal variables, while the existing results are available only for quadratic forms of limited order (up to 3), we derive analytical results to a higher order 4. We use the nonnormal results to study the effects of nonnormality on the finite sample mean squared error of the OLS estimator in an AR(1) model and the QMLE in an MA(1) model.
  • Expectation; Quadratic form; Nonnormality
  • RePEc:ucr:wpaper:200907
Language
  • English
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