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Properties of the sieve bootstrap for fractionally integrated and non-invertible processes. (English) Zbl 1164.62053
This paper deals with the investigation of the consequences of applying the sieve bootstrap under regularity conditions that are sufficiently general to encompass both fractionally integrated and non-invertible processes. The sieve bootstrap is obtained by approximating the data-generating process by an autoregression, whose order \(h\) increases with the sample size \(T\). The author establishes the validity of the sieve bootstrap for \(| d|<1/2\) and shows that when the sieve bootstrap is used to approximate the distribution of a general class of statistics then the error rate will be of an order smaller than \(T^{(1/2)(\beta+\max\{0,d\}-1)}\), \(\beta>0\). Simulation experiments examine the distribution of the maximum likelihood estimator \(\tilde d_{T}\) of \(d\) for the fractional noise process \((1-z)^{d}y(t)=\varepsilon(t)\), where \(\varepsilon(t)\) is standard Gaussian white noise.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G09 Nonparametric statistical resampling methods
Software:
KernSmooth
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