Bernoulli Processes with Non-Positive Correlations

We deal with sequences of dependent Bernoulli variables with non positive correlations. Some special models for 1-dependent and 2-dependent 0–1 valued variables are analyzed, namely Bernoulli variables obtained by clipping a linear combination of iid variables. Formulas describing dependence of their correlation function on the clipping parameters are derived. The lower bound for the sum of autocorrelations of Bernoulli variables obtained by clipping a Gaussian process is provided.