Given past, observations of a process, { y j , j < i}, suppose we arc interested in constructing one-step-ahead predictors of y i , denoted by $ i l i l . We show that, irrespective of whether the process { y j } is stationary or non-stationary, or whether it is scalaror vector-valued, the H2-optimal one-step-ahead predictor is also H"optimal. Since the H2 and H" paradigms represent fundamental...