A Monte Carlo strategy for structured multiple-step-ahead time series prediction

Forecasting a time series multiple-step-ahead is a challenging problem for several reasons: the accumulation of errors, the noise, and the complexity of the dependency between past and far future which has to be inferred on the basis of a limited amount of data. Traditional approaches to multi-step-ahead forecasting reduce the problem to a series of single-output prediction tasks. This is notably the case of the Iterated and the Direct approaches. More recently, multiple-output approaches appeared and stressed the multivariate and structured nature of the output to be predicted. This paper intends to go a step further in this direction by formulating the problem of multi-step-ahed forecasting as a problem of conditional multivariate estimation which can be addressed by a Monte Carlo importance sampling strategy. The interesting aspect of the approach is that this probabilistic formulation allows a natural integration of the traditional Iterated and Direct approaches. The extensive assessment of our algorithm with the NN5, NN3 and a synthetic benchmark shows that this approach is promising and competitive with the state-of-the-art.