Abstract
In this paper we propose a novel estimator for the time-varying covariance of locally stationary time series. This new approach is based on costationary combinations, that is, time-varying deterministic combinations of locally stationary time series that are second-order stationary. We show with a simulation example that the new estimator has smaller variance than other approaches exclusively based on the evolutionary cross-periodogram, and can therefore be appealing in a large number of applications.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Cardinali, A., Nason, G.P.: Costationarity of locally stationary time series. J. Time Ser. Econom. 2(2), 1–19 (2010)
Cardinali, A., Nason, G.P.: Costationarity of locally stationary time series using costat. J. Stat. Softw. 55(1):1–22 (2013)
Dahlhaus, R.: Fitting time series models to nonstationary processes. Ann. Stat. 25, 1–37 (1997)
Meyer, Y.: Wavelets and operators. Proc. Symp. Appl. Math. 47, 35–57 (1993)
Nason, G., von Sachs, R.: Wavelets in time series analysis. Phil. Trans. R. Soc. Lond. A 357, 2511–2526 (1999)
Nason, G., von Sachs, R., Kroisandt, G.: Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. J. R. Stat. Soc. B 62, 271–292 (2000)
Nason, G.P.: Wavelet Methods in Statistics with R. Springer, New York (2008)
Ombao, H., Van Bellegem, S.: Coherence analysis of nonstationary time series: a linear filtering point of view. IEEE Trans. Signal Proc. 56(6):2259–2266 (2008)
Priestley, M.: Spectral Analysis and Time Series. Academic, New York (1983)
Priestley, M.: Non-Linear and Non-Stationary Time Series Analysis. Academic, San Diego (1988)
Sanderson, J., Fryzlewicz, P., Jones, M.: Estimating linear dependence between nonstationary time series using the locally stationary wavelet model. Biometrika 97, 435–446 (2010)
Acknowledgements
I am grateful to Guy Nason for reading a preliminary version of the manuscript and for providing useful comments. All errors are my own responsibility.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer Science+Business Media New York
About this paper
Cite this paper
Cardinali, A. (2014). Local Covariance Estimation Using Costationarity. In: Akritas, M., Lahiri, S., Politis, D. (eds) Topics in Nonparametric Statistics. Springer Proceedings in Mathematics & Statistics, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0569-0_6
Download citation
DOI: https://doi.org/10.1007/978-1-4939-0569-0_6
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-0568-3
Online ISBN: 978-1-4939-0569-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)