Christiana Drake,

Oskar Knapik,

Jacek Leśków


In recent years, there has been a growing interest in modeling cyclostationary time series. The survey of Gardner and others [5] is quoting over 1500 different recently published papers that are dedicated to this topic. Data that can be reasonable modeled with such time series is often incomplete. To our knowledge, no systematic research has been conducted on that problem. This paper attempts to fill this gap. In this paper we propose to use EM algorithms to extend estimation for situation when some observations are missing.

Słowa kluczowe: (almost) periodically correlated time series, cyclostationary signals, EM algorithm, missing data

Brockwell P.J., Davis R.A., Introduction to time series and forecasting, Springer, 2002.

Dempster A.P., Laird N.M. and Rubin D.B., Maximum Likelihood from Incomplete Data via The EM Algorithm (with discussion), J. Roy. Statist. Soc. B, Vol. 39, 1977, 1—38.

Galbraith R.F., Galbraith J.I., On the inverses of some patterned matrices arising in the theory of stationary time series, Journal of Applied Probability, Vol. 11, 1974, 63—71.

Gardner W.A., Representation and estimation of cyclostationary processes, IEEE Transactions on Information Theory, Vol. 19, No. 3, 1973, 375—376.

Gardner W.A., Napolitano A., Paura L., Cyclostationarity: Half a century of research, Signal Processing, Vol. 86, No. 4, 2006, 639—697.

Giannakis,G.B, Dandawate, A.V., Consistent Kth-order time-frequency representations for (almost) cyclostationary signals, in: IEEE-SP International Symposium on Time-Frequency and Time-Scale Analysis, Victoria, BC, Canada, 79 October 1992, 123—126.

Ghogho, M., Garel, B., Maximum likelihood estimation of amplitude-modulated time series, Signal Processing, Vol. 75, 1999 99—116.

Hamilton J.D., Time Series Analysis, Princeton University Press, 1994.

Hurd H. L., Miamee A., Periodically Correlated Random Sequences: Spectral Theory and Practice (Wiley Series in Probability and Statistics), Wiley-Interscience, 2007.

Little R.J.A., Rubin D.B., Statistical Analysis with Missing Data. John Wiley & Sons, New York, 2nd edn., 2002.

Schaffer J.L., Analysis of Incomplete Multivariate Data. Chapman & Hall/CRC, 1997.

Stefanakos Ch.N., Athanassoulis G.A., A unified methodology for the analysis, completion and simulation of nonstationary time series with missing values, with application to wave data, Applied Ocean Research, Vol. 23, Issue 4, 2001, 207—220.

Verbyla A.P., A note on the inverse covariance matrix of the autoregressive process, Australian Journal of Statistics, Vol. 27, Issue 2, 1985, 221—224.

Wu C.F.J., On the convergence properties of the EM algorithm, Annals of Statistics, Vol. 11, 1983, 95—103.