Bootstrap predictive inference for ARIMA processes

Abstract

In this study, we propose a new bootstrap strategy to obtain prediction intervals for autoregressive integrated moving-average processes. Its main advantage over other bootstrap methods previously proposed for autoregressive integrated processes is that variability due to parameter estimation can be incorporated into prediction intervals without requiring the backward representation of the process. Consequently, the procedure is very flexible and can be extended to processes even if their backward representation is not available. Furthermore, its implementation is very simple. The asymptotic properties of the bootstrap prediction densities are obtained. Extensive finitesample Monte Carlo experiments are carried out to compare the performance of the proposed strategy vs. alternative procedures. The behaviour of our proposal equals or outperforms the alternatives in most of the cases. Furthermore, our bootstrap strategy is also applied for the first time to obtain the prediction density of processes with movingaverage components.

25 years of time series forecasting

“…A series of papers on using the bootstrap to compute prediction intervals for an AR model has appeared beginning with Masarotto (1990), and including McCullough (1994McCullough ( , 1996, Grigoletto (1998), Clements & Taylor (2001) and Kim (2004b). Similar procedures for other models have also been considered including ARIMA models (Pascual et al, 2001(Pascual et al, , 2004(Pascual et al, , 2005, Wall & Stoffer (2002), VAR (Kim, 1999(Kim, , 2004a, ARCH (Reeves, 2005) and regression (Lam & Veall, 2002). It seems likely that such bootstrap methods will become more widely used as computing speeds increase due to their better coverage properties.…”

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.…”

Robust Unit Commitment Including Frequency Stability Constraints

“…The process is repeated until the levels of VGT for the whole day (or days) under consideration have been forecasted. The iterative use of the re-sampling procedure developed by Pascual et al [18] is a key element of the described method.…”