Prediction formulas for multi-step forecasts and geometric distributed leads of stationary time series are derived using classical, frequency domain methods. Starting with the Wold representation, optimal squared-error loss predictions are derived using the analytic function theory approach of Whittle. This approach is easily adapted to the problem of making predictions that are robust under model misspecification. Forecasts and expected present value calculations are illustrated under both objectives for low-order autoregressive and moving average processes.
KeywordsBlaschke factors Contour integral Cross-equation restrictions Distributed leads Frequency domain problems Least squares Linear least squares projection Minimum norm interpolation problem Min-max problem Misspecification Prediction formulas Rational expectations Riesz–Fisher th Robustness Squared-error loss optimal prediction Time domain problems Wiener–Hopf equation Wold decomposition th Wold representation
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