On the range of validity of the autoregressive sieve bootstrap

By Jens-Peter Kreiss, Efstathios Paparoditis, Dimitris Nicolas Politis. 2012

141 citations recorded by the source corpus.

We explore the limits of the autoregressive (AR) sieve bootstrap, and show that its applicability extends well beyond the realm of linear time series as has been previously thought. In particular, for appropriate statistics, the AR-sieve bootstrap is valid for stationary processes possessing a general Wold-type autoregressive representation with respect to a white noise; in essence, this includes all stationary, purely nondeterministic processes, whose spectral density is everywhere positive. Our main theorem provides a simple and effective tool in assessing whether the AR-sieve bootstrap is asymptotically valid in any given situation. In effect, the large-sample distribution of the statistic in question must only depend on the first and second order moments of the process; prominent examples include the sample mean and the spectral density. As a counterexample, we show how the AR-sieve bootstrap is not always valid for the sample autocovariance even when the underlying process is linear.

Subfields: Economics and Econometrics, Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f6994ab9affb68b0ea27f95fe920ad7293f68889

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Citations in the corpus

Covariance matrix estimation and linear process bootstrap for multivariate time series of possibly increasing dimension (2015, background): “The requirement of condition (A3) fits into the theory for the univariate autoregressive sieve bootstrap as obtained in Kreiss, Paparoditis and Politis (2011).”
The asymptotic size and power of the augmented Dickey–Fuller test for a unit root (2018, unknown): “…Xt−1(εt,p − εt) = p∑ j=1 (aj,p − aj)n−1 n∑ t=p+1 Xt−1Ut−j + ∞∑ j=p+1 ajn −1 n∑ t=p+1 Xt−1Ut−j, if follows using n−1 ∑n t=p+1 Xt−1Ut−j = OP(1) and Baxter’s inequality, cf. Lemma 2.2 of Kreiss et al. (2011), that ∣∣∣∣∣∣ n−1 n∑ t=p+1 Xt−1(εt,p − εt) ∣∣∣∣∣∣ ≤ OP ∞∑ j=p+1 |aj| → 0, as p → ∞.”
Detection of Multiple Structural Breaks in Multivariate Time Series (2013, background): “…all assumptions of Theorems 3.3 and 3.4 are rather standard in the framework of AR(∞) bootstrap (see, e.g., Berg, Paparoditis, and Politis 2010 or Kreiss, Paparoditis, and Politis 2011 among others) and that condition (ii) in Theorem 3.3 is proved in Hannan and Kavalieris (1986) for the least…”