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Bootstrap predictive inference for ARIMA processes
Author(s) -
Pascual Lorenzo,
Romo Juan,
Ruiz Esther
Publication year - 2004
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2004.01713.x
Subject(s) - autoregressive integrated moving average , autoregressive model , mathematics , monte carlo method , inference , representation (politics) , bootstrap aggregating , prediction interval , process (computing) , computer science , statistics , time series , artificial intelligence , politics , operating system , political science , law
. 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 finite‐sample 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 moving‐average components.