Box-Pierce test

In econometrics the Box-Pierce test is a portmanteau test for autocorrelated errors. The Box-Pierce statistic is computed as the weighted sum of squares of a sequence of autocorrelations. [Box, G. E. P. and Pierce, D. A., "Distribution of the Autocorrelations in Autoregressive Moving Average Time Series Models", Journal of American Statistical Association, 65 (1970): 1509-1526.] :$Q\; =\; T\; sum^s\_\{k=1\}\; r^2\_k.$Another portmanteau test is the Ljung-Box test, which is a preferred version of the Box-Pierce test,because the Box-Pierce statistic has poor performance in small samples. The Ljung-Box statistic is better for all sample sizes including small ones.

References