Forecasting time series with sieve bootstrap

Abstract

In this paper we propose bootstrap methods for constructing nonparametric prediction intervals for a general class of linear processes. Our approach uses the AR(∞)-sieve bootstrap procedure based on residual resampling from an autoregressive approximation to the given process. We present a Monte Carlo study comparing the ÿnite sample properties of the sieve bootstrap with those of alternative methods. Finally, we illustrate the performance of the proposed method with a real data example.MSC: 62M10; 62M20; 62G09

Computationally efficient bootstrap prediction intervals for returns and volatilities in ARCH and GARCH processes

“…Recently, the sieve bootstrap has been gaining popularity for constructing prediction intervals for linear processes. In particular, Thombs and Schucany (TS) (1990) and Cao et al (1997) consider the performance of sieve bootstrap prediction intervals for fi nite AR(p) models, while Alonso et al (2002Alonso et al ( , 2003 extend the sieve bootstrap algorithm to the AR(∞) model with absolutely summable coeffi cients, and Pascual et al (2004) apply the sieve bootstrap procedure to integrated ARMA (ARIMA) processes. Here we adopt the sieve bootstrap idea for developing prediction intervals for returns and volatility in GARCH(p, q) processes.…”

Vol. 3, No. 1 (Full Issue)

“…It has been shown by Alonso et al (2002) and (2003) that, for general linear process, if an AR approximation that grows with the sample size is used, it can derive a bootstrap for building prediction intervals that has the two following properties: first, the procedure is consistent, that is, it generates as prediction a random variable that converges in conditional distribution to the concerning variable; second, Monte Carlo simulations show that the proposed procedure provides better coverage results than previous methods in general cases. This article describes a Fortran routine that implement this sieve bootstrap prediction procedure.…”

“…The following models are used: Cao et al (1997), the moving average model 2 by Pascual et al (2001) and the model 3 by Alonso et al (2002). Notice that neither model 2 nor model 3 admit a finite AR representation.…”

“…Thus, the proposed bootstrap prediction intervals could be applied to this more general class of linear models without specifying a finite dimensional model as in previous bootstrap proposals. Alonso et al (2002) and (2003) Notice that in (5) the bootstrap autoregressive coefficient is used, WYWPhi, this allows us to incorporate the parameter estimation variability in the prediction intervals.…”

On sieve bootstrap prediction intervals

“…In Alonso et al (2002) we propose an AR(∞)-sieve bootstrap procedure to construct prediction intervals for a general class of linear models that includes stationary and invertible ARMA processes. We illustrate with an extensive Monte Carlo study showing that sieve bootstrap prediction intervals provide better coverage results than some previous methods in general cases (see also Alonso et al where the starting p observations are equals to X .…”