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- θt − ˆ θt , which is intended to capture the (average) accuracy of the algorithm’s estimates. Its evolution through time is also associated with the speed with which the algorithm is able to adjust its estimates to the time-varying system, and optimization of tracking performance is in general associated to a minimization of MSD, mainly through control of the gain parameter. In attempting to do so, however, one is confronted with a well known tradeoff between speed and accuracy in the estimates provided by the algorithms: on one extreme, tracking can be slower than the system actual time variations, but with less noisy estimates; on the other extreme, tracking can be made as rapid as the time-varying context, but with estimates much more contaminated by noise (see e.g. Benveniste et al., 1990, Part I, Chapters 1 and 4).
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- Missing observation for 1995q4 in vintage 1996q1: as a result of the US federal government shutdown in late 1995, the observation for 1995q4 was missing in the 1996q1 vintage. Fortunately, this is the only point in this dataset that this happens. We fulfill this gap by using the observation available in the March 1996 monthly vintage for the same series. Incidentally, the SPF 1996q1 median backcast for 1995q4 is identical to the value later observed in March 1996, thence, our simplifying procedure is not favoring any method. Caveat on SPF’s forecasts for Real GDP: forecasts for real GDP were not asked in the surveys prior to 1981q3. To extend this series of forecast back to 1968q4, real GDP prior to 1981q3 is computed by using the formula (nominal GDP / GDP prices) * 100. D Tables
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- Robustness: In a context of model misspecification, an estimator is said to be robust if it does not magnify the effect of modeling errors on estimation errors, and the SG algorithm is known to be the maximally robust algorithm in this sense (see Hassibi et al., 1996; Evans et al., 2010, pp. 240242) . Loosely speaking, in a worst case of misspecification the magnitude of the prediction errors obtained from the SG estimation will never exceed the magnitude of the true model disturbances.
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