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 study the problem of forecasting a time series for a Causal Bernoulli Shifts (CBS) model using a parametric family of predictors. The aggregation technique provides a forecaster with well established and quite satisfying theoretical properties expressed in the form of an oracle inequality for the prediction risk. The main advantage of this result is that it does not require to specify a particular model on the data. The numerical computation of the aggregated predictor usually relies on a Markov chain Monte Carlo method whose performances 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 error. In this direction we present a fairly general result which can be seen as an oracle inequality which includes the numerical cost of the predictor computation. Again it is not required to specify a particular model on the data. The numerical cost appears by letting the oracle inequality depend on the number of simulations required in the MCMC approximation. Using different priors, some numerical experiments are then carried out to support our findings.

Mots clés: Causal Bernoulli Shifts; aggregation methods; MCMC

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

Andres Sanchez-Perez. Time series prediction via aggregation : an oracle bound including numerical cost. 2013. ⟨hal-00905418v1⟩