### Randy Sitter Technometrics Session

Organizer: David Steinberg, Tel Aviv UniversitySession Chair: Vijay Nair, University of Michigan

**On Modeling and Forecasting Time Series of Smooth Curves**

Haipeng Shen

University of North Carolina Chapel Hill

We consider modeling a time series of smooth curves and develop methods for forecasting such curves and dynamically updating the forecasts. The research problem is motivated by efficient operations management of telephone customer service centers, where forecasts of daily call arrival rate profiles are needed for service agent staffing and scheduling purposes. Our methodology has three components: dimension reduction through a smooth factor model, time series modeling and forecasting of the factor scores, and dynamic updating using penalized least squares. The proposed methods will be illustrated via the motivating application and simulation studies.

**Online Prediction under Model Uncertainty Via Dynamic Model Averaging: Application to a Cold Rolling Mill**

Adrian Raftery

University of Washington

We consider the problem of online prediction when it is uncertain what the best prediction model to use is. We develop a method called Dynamic Model Averaging (DMA) in which a state space model for the parameters of each model is combined with a Markov chain model for the correct model. This allows the "correct" model to vary over time. The state space and Markov chain models are both specified in terms of forgetting, leading to a highly parsimonious representation. As a special case, when the model and parameters do not change, DMA is a recursive implementation of standard Bayesian model averaging, called recursive model averaging (RMA). The method is applied to the problem of predicting the output strip thickness for a cold rolling mill, where the output is measured with a time delay. We found that when only a small number of physically motivated models were considered and one was clearly best, the method quickly converged to the best model, and the cost of model uncertainty was small; indeed DMA performed slightly better than the best physical model. When model uncertainty and the number of models considered were large, our method ensured that the penalty for model uncertainty was small. At the beginning of the process, when control is most difficult, we found that DMA over a large model space led to better predictions than the single best performing physically motivated model. We also applied the method to several simulated examples, and found that it recovered both constant and time-varying regression parameters and model specifications quite well. This is joint work with Miroslav Karny and Pavel Ettler.