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Forecasting time series with multivariate copulas

100%

Simard C., Rémillard B.

Dependence Modeling

2015

tom 3

nr 1

In this paper we present a forecasting method for time series using copula-based models for multivariate time series. We study how the performance of the predictions evolves when changing the strength of the different possible dependencies, as well as the structure of the dependence. We also look at the impact of the marginal distributions. The impact of estimation errors on the performance of the predictions is also considered. In all the experiments, we compare predictions from our multivariate method with predictions from the univariate version which has been introduced in the literature recently. To simplify implementation, a test of independence between univariate Markovian time series is proposed. Finally, we illustrate the methodology by a practical implementation with financial data.

Prediction of time series by statistical learning: general losses and fast rates

42%

Alquier P., Li X., Wintenberger O.

Dependence Modeling

2013

tom 1

65-93

We establish rates of convergences in statistical learning for time series forecasting. Using the PAC-Bayesian approach, slow rates of convergence √ d/n for the Gibbs estimator under the absolute loss were given in a previous work [7], where n is the sample size and d the dimension of the set of predictors. Under the same weak dependence conditions, we extend this result to any convex Lipschitz loss function. We also identify a condition on the parameter space that ensures similar rates for the classical penalized ERM procedure. We apply this method for quantile forecasting of the French GDP. Under additional conditions on the loss functions (satisfied by the quadratic loss function) and for uniformly mixing processes, we prove that the Gibbs estimator actually achieves fast rates of convergence d/n. We discuss the optimality of these different rates pointing out references to lower bounds when they are available. In particular, these results bring a generalization the results of [29] on sparse regression estimation to some autoregression.

Ograniczanie wyników

2 Dependence Modeling

1 Alquier P.

1 Li X.

1 Rémillard B.

1 Simard C.

1 Wintenberger O.

1 2015

1 2013

Wyniki wyszukiwania

Forecasting time series with multivariate copulas

Prediction of time series by statistical learning: general losses and fast rates