Surveys in Mathematics and its Applications

ISSN 1842-6298
Volume 1 (2006), 1 - 12


Alexandra Colojoară

Abstract. The paper studies the seasonal time series as elements of a (finite dimensional) Hilbert space and proves that it is always better to consider a trend together with a seasonal component even the time series seams not to has one. We give a formula that determines the seasonal component in function of the considered trend that permits to compare the different kind of trends.

2000 Mathematics Subject Classification: 62M10.
Keywords: seasonal time series, model, regressor.

Full text


  1. G.E.P. Box, G.C. Jenkins and G.M.Reinsel, Time Series Analysis. Forecasting and Control. Third edition, Prentice Hall, Inc., Englewood Cliffs, NJ, 1994. MR1312604(95m:62191). Zbl 0858.62072.

  2. P.J. Brockwell and R.A. Davis, Introduction to time series and forecasting. Second edition, Springer Texts in Statistics, Springer-Verlag, New York, 2002. MR1894099(2002m:62002). Zbl 0994.62085.

  3. Chatfield, The Analysis of Time Series. An Introduction. Fifth edition, Texts in Statistical Science Series. Chapman Hall, London, 1996. MR1410749(97e:62117). Zbl 0870.62068.

  4. C. Gourieux et A. Monfort, Series Temporelles et modeles Dynamiques, Economica, Paris, 1990.

Acknowledgement. This work is partially supported by CEEX grant PR-D11-PT00-48/2005 and by PICS 3450.

Alexandra Colojoară
University of Bucharest,
Bd. Regina Elisabeta, Nr. 4-12, Bucharest,