[Forum SIS] DEC Seminar - May 7th

[Raffaella Piccarreta]

Dear all 
we are glad to announce the next 


DEC - Statistics Seminar 
Università Bocconi, 
Room 3-E4-SR03 
Via Rontgen 1 - 3rd floor 
Time: 12:30pm 

The DEC seminar schedule is available at http://www.unibocconi.eu/statseminar 

Thursday, May 7th 


Simone Vantini 
(Politecnico di Milano) 



"Constrained Functional Time Series: One-day Ahead Prediction of Daily Demand and Offer Curves" 

Abstract 

Motivated by market dynamic modeling in the Italian Natural Gas Balancing Platform, we propose a model to analyze time series of bounded and monotonic functions. In detail, we provide the constrained functions with a suitable pre-Hilbert structure and introduce a useful isometric bijective map associating each possible bounded and monotonic function to an unconstrained. We then introduce a functional-to-functional autoregressive model that we use to predict the entire demand/offer function. We estimate the model by minimizing the squared L^2 distance between functional data and functional predictions with a penalty term based on the Hilbert-Schmidt squared norm of autoregressive lagged operators. We have proved that the solution always exist, unique and that it is linear on the data with respect to the introduced geometry thus guaranteeing that the plug-in predictions of future entire demand/offer functions satisfy all required constraints. We also provide an explicit expression for estimates and predictions. The approach is of general interest and can be generalized in any situation in which one has to deal with constrained monotonic functions (strictly positive or bounded) which evolve through time (e.g., dose response functions right-censored survival curves or cumulative distribution functions). 

References: 
Canale, A., Vantini, S. (2014): Constrained Functional Time Series: an Application to Demand and Supply Curves in the Italian Natural Gas Balancing Platform, MOX report 42/2014, Dept. of Mathematics - Politecnico di Milano. 
Available at mox.polimi.it 

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Raffaella Piccarreta 
DEC - Department of Decision Sciences, 
Universita' L.Bocconi, via Guglielmo Röntgen 1 (3rd floor, room D1-09). 20136, Milano. 
email: piccarreta a unibocconi.it 
tel. +39-02-58365659 / fax +39-02-58365630 

Web page (ENGLISH VERSION): http://faculty.unibocconi.eu/raffaellapiccarreta/ 
(ITALIAN VERSION): http://faculty.unibocconi.it/raffaellapiccarreta/ 
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