The Box-Pierce test is a portmanteau test for whether the first several autocorrelations of
a time series are jointly zero. For a series of length
, using the first 
sample autocorrelations 
, its statistic is
Under the null hypothesis of no autocorrelation, the statistic is approximately chi-squared
distributed. The Ljung-Box test modifies the
statistic to improve its finite-sample approximation.
See also
Autocorrelation,
Ljung-Box
Test,
Portmanteau Test
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References
Box, G. E. P. and Pierce, D. A. "Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series
Models." J. Amer. Statist. Assoc. 65, 1509-1526, 1970. https://doi.org/10.1080/01621459.1970.10481180.
Cite this as:
Weisstein, Eric W. "Box-Pierce Test."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Box-PierceTest.html
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