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On the Distribution of the Sample Autocorrelation Coefficients

SSRN Electronic Journal
2008
  • 1
    Citations
  • 4,300
    Usage
  • 0
    Captures
  • 0
    Mentions
  • 0
    Social Media
Metric Options:   Counts1 Year3 Year

Metrics Details

  • Citations
    1
    • Citation Indexes
      1
  • Usage
    4,300
    • Abstract Views
      3,588
    • Downloads
      712
  • Ratings
    • Download Rank
      72,697

Article Description

Sample autocorrelation coefficients are widely used to test the randomness of a time series. Despite its unsatisfactory performance, the asymptotic normal distribution is often used to approximate the distribution of the sample autocorrelation coefficients. This is mainly due to the lack of an efficient approach in obtaining the exact distribution of sample autocorrelation coefficients. In this paper, we provide an efficient algorithm for evaluating the exact distribution of the sample autocorrelation coefficients. Under the multivariate elliptical distribution assumption, the exact distribution as well as exact moments and joint moments of sample autocorrelation coefficients are presented. In addition, the exact mean and variance of various autocorrelation based tests are provided. Actual size properties of the Box-Pierce and Ljung-Box tests are investigated, and they are shown to be poor when the number of lags is moderately large relative to the sample size. Using the exact mean and variance of the Box-Pierce test statistic, we propose an adjusted Box-Pierce test that has a far superior size property than the traditional Box-Pierce and Ljung-Box tests.

Bibliographic Details

Raymond Kan; Xiaolu Wang

Elsevier BV

Sample autocorrelation coefficient; Finite sample distribution; Rank one update

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