Records and 2-block records of 1-dependent stationary sequences under local dependence

Abstract We first study the records of several examples of 1-dependent stationary sequences X n , some of them which satisfy a local independence condition introduced in Haiman (1987a), whereas the other do not satisfy this condition. For the second category (called with local dependence), we then extend a result of the above cited paper by proving, (under some regularity conditions on the joint distribution of ( X 1 , X 2 , X 3 )), that the 2-block record times of X n a.s. coincide, (via a translation of the time index and from some index on) with the record times of an appropriately constructed i.i.d. sequence n , whereas the 2-block record values of X n and the record values of n are imbricate.