  We study analytically the statistics of multiple sign changes in a discrete
non-Markovian sequence ,\psi_i=\phi_i+\phi_{i-1} (i=1,2....,n) where \phi_i's
are independent and identically distributed random variables each drawn from a
symmetric and continuous distribution \rho(\phi). We show that the probability
P_m(n) of m sign changes upto n steps is universal, i.e., independent of the
distribution \rho(\phi). The mean and variance of the number of sign changes
are computed exactly for all n>0. We show that the generating function {\tilde
P}(p,n)=\sum_{m=0}^{\infty}P_m(n)p^m\sim \exp[-\theta_d(p)n] for large n where
the `discrete' partial survival exponent \theta_d(p) is given by a nontrivial
formula, \theta_d(p)=\log[{{\sin}^{-1}(\sqrt{1-p^2})}/{\sqrt{1-p^2}}] for 0\le
p\le 1. We also show that in the natural scaling limit when m is large, n is
large but but keeping x=m/n fixed, P_m(n)\sim \exp[-n \Phi(x)] where the large
deviation function \Phi(x) is computed. The implications of these results for
Ising spin glasses are discussed.
