We study the finite sample performance of predictors in the functional (Hilbertian) autoregressive model X n+1 = Ψ(X n ) + ε n . Our extensive empirical study based on simulated and real data reveals that predictors of the formΨ(X n ) are practically optimal in a sense that their prediction errors are comparable with those of the infeasible perfect predictor Ψ(X n ). The predictionsΨ(X n ) cannot be improved by an improved estimation of Ψ , nor by a more refined prediction approach which uses predictive factors rather than the functional principal components. We also discuss the practical limits of predictions that are feasible using the functional autoregressive model. These findings have not been established by theoretical work currently available, and may serve as a practical reference to the properties of predictors of functional data.

Objective The Dyspnea Index (DI) is a validated patient‐reported outcome (PRO) instrument that has been used in the management of laryngotracheal stenosis (LTS). The minimal clinically important difference (MCID) is an established concept to help determine the change in a PRO instrument that reflects meaningful change for the patient. It is not known what change in the DI is of clinical significance in airway surgery. This study aims to determine the MCID for the DI in patients undergoing surgical treatment for LTS. Methods This is a prospective cohort study in which 26 patients with LTS completed the DI (score range 0 to 40) before and 6 to 8 weeks postoperatively, in addition to a Global Ratings Change Questionnaire (GRCQ), scored from −7 to +7, at the postoperative interval. A hypothesis test was carried out to test the association between GRCQ and change in DI. The MCID for change in DI was determined using anchor‐based analysis. Results Overall mean change in DI was −11, and mean change in GRCQ was +5. Change in DI scores were significantly different among the improvement and no improvement groups (P value <0.002). Area under the receiver operating curve was 0.92, demonstrating high discriminatory ability of the change in DI score. A change of −4 was determined to be the threshold that discriminated between significant improvement and no improvement. Conclusion A decrease of 4 in the DI can be considered as the MCID for patients with LTS after surgical treatment. Level of Evidence 2b Laryngoscope, 130:1775–1779, 2020