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Box-Pierce Test

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 n, using the first m sample autocorrelations rho^^_k, its statistic is

Q_(BP)=nsum_(k=1)^mrho^^_k^2.

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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