An improved method for uniform simulation of stable minimum phase real ARMA (p,q) processes

Andrieu, Christophe; Doucet, Arnaud

doi:10.1109/97.763147

Cited by 10 publications

(2 citation statements)

References 6 publications

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“…This behaviour is similar in both cases presented in Figure 1. As expected, the risk of the approximated predictor does not converge as log 3 T/T 1/2 .…”

Section: Algorithm 2: Independent Hastings Samplersupporting

confidence: 74%

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Time Series Prediction via Aggregation: An Oracle Bound Including Numerical Cost

Sanchez-Perez

2015

Modeling and Stochastic Learning for Forecasting in High Dimensions

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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. Problem statement and main assumptionsReal stable autoregressive processes of a fixed order, referred to as AR(d) processes, are one of the simplest examples of CBS. They are defined as the stationary solution of(2.1)where the (ξ t ) t∈Z are i.i.d. real random variables with E[ξ t ] = 0 and E[ξ 2 t ] = 1.

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“…This behaviour is similar in both cases presented in Figure 1. As expected, the risk of the approximated predictor does not converge as log 3 T/T 1/2 .…”

Section: Algorithm 2: Independent Hastings Samplersupporting

confidence: 74%

“…It relies in the Levinson-Durbin recursion algorithm. We also implemented the numerical improvements of [3]. Set ε = 0.1.…”

Section: Algorithm 2: Independent Hastings Samplermentioning

confidence: 99%