Sieve bootstrap based prediction intervals and unit root tests for time series
"The application of the sieve bootstrap procedure, which resamples residuals obtained by fitting a finite autoregressvie (AR) approximation to empirical time series, to obtaining prediction intervals for integrated, long-memory, and seasonal time series as well as constructing a test for seasonal unit roots, is considered. The advantage of this resampling method is that it does not require knowledge about the underlying process generating a given time series and has been shown to work well for ARMA processes. We extend the application of the sieve bootstrap to ARIMA and FARIMA processes. The asymptotic properties of the sieve bootstrap prediction intervals for such processes are established, and the finite sample properties are examined by employing Monte Carlo simulations. The Monte Carlo simulation study shows that the proposed method works well for both ARIMA and FARIMA processes. Following the existing sieve bootstrap frame-work for testing unit roots for nonseasonal processes, we propose new bootstrap-based unit root tests for seasonal time series. In this procedure, the bootstrap distributions of the well known Dickey-Hasza-Fuller (DHF) seasonal test statistics are obtained and utilized to determine the critical points for the test. The asymptotic properties of the proposed method are established and a Monte Carlo simulation study is employed to demonstrate that the proposed unit root tests yield higher powers compared to the DHF test. Also, a sieve bootstrap method is implemented to obtaining prediction intervals for time series with seasonal unit roots. The asymptotic properties of the proposed prediction intervals are established and a Monte Carlo simulation study is carried out to examine the finite sample validity. Finally, we derive expressions for the asymptotic distributions of the Dickey-Fuller (DHF) type test statistics, under weakly dependent errors and show that they can be expressed as functional of the standard Brownian motions. Currently, the asymptotic results are available only for non-seasonal time series"--Abstract, page v.
Autoregressive Integrated Moving Average (ARIMA), Fractional Auto-Regressive Integrated Moving Average (FARIMA), Mathematics, Statistics and Probability
Missouri University of Science and Technology
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