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Non-parametric seasonal unit root tests under periodic non-stationary volatility.

ABSTRACT: This paper presents a new non-parametric seasonal unit root testing framework that is robust to periodic non-stationary volatility in innovation variance by making an extension to the fractional seasonal variance ratio unit root tests of Eroğlu et al. (Econ Lett 167:75-80, 2018). The setup allows for both periodic heteroskedasticity structure of Burridge and Taylar (J Econ 104(1):91-117, 2001) and non-stationary volatility structure of Cavaliere and Taylor (Econ Theory 24(1):43-71, 2008). We show that the limiting null distributions of the variance ratio tests depend on nuisance parameters derived from the underlying volatility process. Monte Carlo simulations show that the standard variance ratio tests can be substantially oversized in the presence of such effects. Consequently, we propose wild bootstrap implementations of the variance ratio tests. Wild bootstrap resampling schemes are shown to deliver asymptotically pivotal inference. The simulation evidence depicts that the proposed bootstrap tests perform well in practice and essentially correct the size problems observed in the standard fractional seasonal variance ratio tests, even under extreme patterns of heteroskedasticity.

Supplementary information

The online version contains supplementary material available at 10.1007/s00180-022-01211-w.

SUBMITTER: Gog Ebakan KCL

PROVIDER: S-EPMC8901101 | biostudies-literature | 2022

REPOSITORIES: biostudies-literature

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Non-parametric seasonal unit root tests under periodic non-stationary volatility.

Gög Ebakan Kemal Çag Lar KÇL Eroglu Burak Alparslan BA

Computational statistics 20220307 5

This paper presents a new non-parametric seasonal unit root testing framework that is robust to periodic non-stationary volatility in innovation variance by making an extension to the fractional seasonal variance ratio unit root tests of Eroğlu et al. (Econ Lett 167:75-80, 2018). The setup allows for both periodic heteroskedasticity structure of Burridge and Taylar (J Econ 104(1):91-117, 2001) and non-stationary volatility structure of Cavaliere and Taylor (Econ Theory 24(1):43-71, 2008). We sho ...[more]

PMID: 35283559

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Project description:Since the emergence of the SARS-CoV-2 virus, research into the existence, extent, and pattern of seasonality has been of the highest importance for public health preparation. This study uses a novel bandpass bootstrap approach called the Variable Bandpass Periodic Block Bootstrap to investigate the periodically correlated components including seasonality within US COVID-19 mortality. Bootstrapping to produce confidence intervals for periodic characteristics such as the seasonal mean requires preservation of the periodically correlated component's correlation structure during resampling. While other existing bootstrap methods can preserve the periodically correlated component correlation structure, filtration of that periodically correlated component's frequency from interference is critical to bootstrap the periodically correlated component's characteristics accurately and efficiently. The Variable Bandpass Periodic Block Bootstrap filters the periodically correlated time series to reduce interference from other components such as noise. This greatly reduces bootstrapped confidence interval size and outperforms the statistical power and accuracy of other methods when estimating the periodic mean sampling distribution. Variable Bandpass Periodic Block Bootstrap analysis of US COVID-19 mortality periodically correlated components is provided and compared against alternative bootstrapping methods. Results show that both methods find a significant seasonal component, but the Variable Bandpass Periodic Block Bootstrap produces smaller confidence intervals and only the Variable Bandpass Periodic Block Bootstrap found significant components at the second through the fifth harmonics of the seasonal component, as well as weekly component. This crucial evidence supporting the presence of a seasonal pattern and existence of additional periodically correlated components, their timing, and confidence intervals for their effect which will aid prediction and preparation for future COVID-19 responses.

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Non-parametric seasonal unit root tests under periodic non-stationary volatility.

Supplementary information

Publications

Non-parametric seasonal unit root tests under periodic non-stationary volatility.

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