Asymptotic solutions of a generalized eigenvalue problem

This paper provides a solution of a generalized eigenvalue problem for a fractional integrated processes. To this end two random matrices are constructed in order to take into account the stationarity properties of the differences of a fractional p-variate integrated process. The matrices are defined by some weight functions and the difference orders are assumed to vary in a continuous and discrete range. The asymptotic behavior of these matrices is obtained imposing some conditions on the weight functions. Using Bierens (1987) and Andersen et al. (1983) results, a generalized eigenvalues problem is solved.