Although one can, under certain (but not, however, generally valid) restricted preconditions, base the production of short-term predictions on the fact that the conditions that generated a time series’ past behavior will... [ view full abstract ]
Although one can, under certain (but not, however, generally valid) restricted preconditions, base the production of short-term predictions on the fact that the conditions that generated a time series’ past behavior will tend to stay constant in the future, for predictions with a medium-term or longer horizon, these preconditions generally become entirely unsustainable. (And in the case of large variability in the development of a time series, this problem is expressed much more dramatically.)
Both classical and stochastic prediction models attempt to overcome this unfavorable circumstance through the construction of prediction confidence intervals. Stochastic prediction ranges of this sort are, however, burdened with certain serious flaws: choosing a high confidence leads to such a wide prediction band that the prediction is, in practice, typically quite unusable (and moreover, generally not even this wide breadth for the prediction interval will actually ensure that the influence of ceteris paribus is overcome), while choosing a low confidence can lead to the prediction’s falling completely outside of real future development, and moreover a low confidence value can cause users to distrust the entire process.
One frequent way in which real-world practice (and especially economic practice) attempts to deal with the construction of predictions is the utilization of expert estimates (application of the principle of rational expectations). These are constructed through the refining of the opinions of various experts, who, through their subjective opinions, produce a sort of resultant; despite not being parametrized, this resultant generally approaches reality sufficiently faithfully.
The present article attempts to apply a similar principle, but rather than using expert estimates for this, it instead mutually confronts—“in the role of experts”—a wide range of time-series models (after all, each time-series model incorporates a unique approach to the given dataset), and then attempts to construct from this confrontation a non-stochastic prediction (the results achieved are of course no longer a typical extrapolation). A prediction is thus created in a form that we have termed a non-stochastic prediction interval.
The advantage of a non-stochastic prediction interval is a fundamental narrowing of the prediction interval thus produced and a considerable weakening of ceteris paribus. This weakening happens due to the fact that, with the application of a number of widely varying models, these models enter into mutual interaction, and the influence of ceteris paribus is thereby to no small extent eliminated (thus there is an analogy here with expert estimates). Its disadvantage lies in the impossibility of interpreting the produced prediction interval in a probability-based way, i.e. of adjudging probabilities to the values contained in this interval. However, it offers a replacement: a narrower interval that is generally interpretable and better corresponds to reality and to the practical needs in response to which predictions are formed.
