Does first differencing reduce autocorrelation? Consider the models y t = 'x t + t ,

Does first differencing reduce autocorrelation? Consider the models y_t = β'x_t + ε_t, where ε_t = ρε_t−1 + u_t and ε_t = u_t −λu_t−1. Compare the autocorrelation of ε_t in the original model with that of v_t in y_t − y_t−1 = β (x_t −x_t−1)+v_t, where v_t = ε_t −ε_t−1.