Perspectives on Constrained Forecasting

Reply to Discussions of Multivariate dynamic modeling for Bayesian forecasting of business revenue

“…Including full forecast uncertainty can significantly expand perspectives on the applied impact of decision analysis that recognizes second‐level uncertainty beyond the normal analysis that conditions on optimal forecast decisions. As noted in response to Korobilis and Montoya‐Blandón, we also stress the explicit study of full predictive uncertainties of loss as a general principle in Bayesian decision analysis (e.g., Reference 3). Finally, on our technical use of “plug‐in” multi‐scale forecasts as a computational short‐cut of the full Bayesian analysis, evaluation across various metrics and decision‐making settings could indeed be useful.…”

“…The latter includes but is not limited to the use and integration of multiple forms of external information into a forecasting model. The roles of subjective model adjustments as well as decision‐guided automatic interventions have been foremost in the Bayesian forecasting community (e.g., Reference 1, chapters 1 and 11 and references therein; References 2 and 3). This broad perspective on the contributions of formal modeling, and the needs for models to be open and responsive to many kinds of end‐user interests as well as multiple forms of potential interventions in sequential evolution over time, is fundamental to operational forecasting.…”

“…While Bayesian dynamic models are naturally open to incorporating such information– either by treating some values as missing as the discussants note, or by exploring temporal multi‐scale structure– this is a key and open area for near‐term research. We also note the connections with research on imposing constraints (especially partial stochastic constraints) on forecast distributions from a given model; advances in methodology for coherent analysis within a Bayesian framework will be relevant to that (e.g., References 11 and 3).…”

“…We note the use of multiple different loss functions in some of our prior work on retail forecasting 12,13 including the introduction of new classes of ZAPE loss functions for contexts involving forecasting non‐negative integer time series. We also stress a broader decision analysis view that explicitly includes investigation of full predictive uncertainties of loss– rather than just following the typical “act on the optimal decision”– that can highlight potentially important practical considerations (e.g., Reference 3).…”

“…On some specific points, we note the questions of (i) forecast (system) reconciliation, (ii) unreliable covariates (“signals”) and the dynamics and uncertainty in promotion campaigns (and intervention “experiments” more generally), with linked questions of causality, and (iii) post‐hoc forecast adjustments and broader issues of user manipulation/modification of outputs of formal forecast models. Our prior work bearing on forecast (system) reconciliation has been touched on above, including in response to Korobilis and Montoya‐Blandón, in connection with forecast model combination and imposing constraints on a given model informed by external information (or forecasts from other models; (e.g., References 11 and 3, and references therein)). These comments also connect this stream of methodology to the integration into down‐stream decision making by potentially multiple end‐users, and the developing literature on forecast model‐external data synthesis.…”