Time series prediction via aggregation : an oracle bound including numerical cost

Andres Sanchez-Perez (1)

1 LTCI - Laboratoire Traitement et Communication de l'Information

We address the problem of forecasting a time series meeting the Causal Bernoulli Shift model, using a parametric set of predictors. The aggregation technique provides a predictor with well established and quite satisfying theoretical properties expressed by an oracle inequality for the prediction risk. The numerical computation of the aggregated predictor usually relies on a Markov chain Monte Carlo method whose convergence should be evaluated. In particular, it is crucial to bound the number of simulations needed to achieve a numerical precision of the same order as the prediction risk. In this direction we present a fairly general result which can be seen as an oracle inequality including the numerical cost of the predictor computation. The numerical cost appears by letting the oracle inequality depend on the number of simulations required in the Monte Carlo approximation. Some numerical experiments are then carried out to support our findings.

Mots clés: aggregation methods; MCMC; Causal Bernoulli Shifts

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Andres Sanchez-Perez. Time series prediction via aggregation : an oracle bound including numerical cost. Anestis Antoniadis; Jean-Michel Poggi; Xavier Brossat. Modeling and Stochastic Learning for Forecasting in High Dimensions, Jun 2013, France. 217 (1), Springer International Publishing, pp.243-265, 2015, Lecture Notes in Statistics - Proceedings, 978-3-319-18732-7. ⟨10.1007/978-3-319-18732-7⟩. ⟨hal-00905418v4⟩