APPROXIMATE SIMULTANEOUS SIGNIFICANCE INTERVALS FOR RESIDUAL AUTOCORRELATIONS OF AUTOREGRESSIVE MOVING‐AVERAGE TIME SERIES MODELS

Abstract. Bonferroni‐type inequalities are used to approximate probabilities of the joint distribution of residual autocorrelation coefficients from an autoregressive moving‐average time series model. The approximations are useful for testing the goodness of fit of the model can be used to find critical values of a test of whether the largest residual autocorrelation is significantly different from zero. The approximation based on the first‐order Bonferroni inequality is simple to use and adequate in practice. Copyright © 1993, Wiley Blackwell. All rights reserved