STAT244.Lecture.02 5

STAT244.Lecture.02 5 - Testing for Autocorrelations...

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Unformatted text preview: Testing for Autocorrelations Ljung-Box test: Q (m) = T (T + 2) m X n=1 eh /(T − h ) ∼ χ 2 ˆ2 m H0 : e1 = e2 = · · · = em = 0 √ For heavy-tails, rate of convergnece of ACF is slower than T ; hence asymptotic confidence intervals are wider than above; models for volatility must be carefully assessed. The Ljung–Box test is a type of statistical test of whether any of a group of autocorrelations of a time series are different from zero. Instead of testing randomness at each distinct lag, it tests the "overall" randomness based on a number of lags, and is therefore a portmanteau test. ...
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