When time‐series data contain a periodic/seasonal component, the usual block bootstrap procedures are not directly applicable. We propose a modification of the block bootstrap – the generalized seasonal block bootstrap (GSBB) – and show its asymptotic consistency without undue restrictions on the relative size of the period and block size. Notably, it is exactly such restrictions that limit the applicability of other proposals of block bootstrap methods for time series with periodicities. The finite‐sample performance of the GSBB is also illustrated by means of a small simulation experiment.

The correlation function of an almost periodically correlated process { X(t); t € I R } has the Fourier series R(t+r,t) = ^ εχρ(ίλ^ί). This paper gives conditions under A k eA which the natural estimator for a(A. ,r) is strongly consistent and asymptotically normal.

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