Geodesic
A method for finding smoothly varying rules in Multidimensional time series
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 11, pp. 2020-2040 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An approach to discovering rules in nonstationary $k$-valued Multidimensional time series is proposed. It allows one to discover rules that are subject to “smooth” structural changes with the course of time. A measure of rule similarity is proposed to describe such changes, and its application in the form of weight in the graph of rules is discussed. The discovered rules can be used to predict the next elements in the multidimensional time series, to analyze the phenomenon described by this multidimensional time series, and to model it. This allows one to use the proposed algorithm for predicting time series and for examining and describing the processes that can be represented by a multidimensional time series. Means for the direct practical application of the proposed methods of the analysis and prediction of time series are described, and the use of those methods for the short-range prediction of a real-life multidimensional time series consisting of the stock prices of companies operating in similar fields is discussed. 
@article{ZVMMF_2009_49_11_a9,
     author = {N. V. Filipenkov},
     title = {A~method for finding smoothly varying rules in {Multidimensional} time series},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2020--2040},
     year = {2009},
     volume = {49},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a9/}
}
TY  - JOUR
AU  - N. V. Filipenkov
TI  - A method for finding smoothly varying rules in Multidimensional time series
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 2020
EP  - 2040
VL  - 49
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a9/
LA  - ru
ID  - ZVMMF_2009_49_11_a9
ER  - 
%0 Journal Article
%A N. V. Filipenkov
%T A method for finding smoothly varying rules in Multidimensional time series
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 2020-2040
%V 49
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a9/
%G ru
%F ZVMMF_2009_49_11_a9
N. V. Filipenkov. A method for finding smoothly varying rules in Multidimensional time series. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 11, pp. 2020-2040. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_11_a9/

[1] Anderson T., Statisticheskii analiz vremennykh ryadov, Mir, M., 1976

[2] Boks Dzh., Dzhenkins G., Analiz vremennykh ryadov, prognoz i upravlenie, Mir, M., 1974

[3] Engle R. F., Kroner K. F., “Multivariate simultaneous generalized ARCH”, Econometric Theory, 11 (1993), 122–150 | DOI | MR

[4] Hannan E. J., Multiple time series, John Wiley and Sons, N.Y., 1970 | MR | Zbl

[5] Lukashin Yu. P., Adaptivnye metody kratkosrochnogo prognozirovaniya vremennykh ryadov, Finansy i statistika, M., 2003 | MR

[6] Morchen F., Ultsch A., “Mining hierarchical temporal patterns in multivariate time series”, Proc. 27th Ann. German Conf. Artificial Intelligence, 2004, 17–140

[7] Agrawal R., Imielinski T., Swamiet A., “Mining association rules between sets of items in large databases”, Proc. Conf. Management of Data, Washington, USA, 1993, 207–216

[8] Agrawal R., Srikant R., “Mining sequential patterns”, Proc. 11th Internat. Conf. on Data Engng., Taiwan, 1995, 3–14

[9] Mannila H., Toivonen H., Verkamo A. I., “Discovery of frequent episodes in event sequences”, Data Mining and Knowledge Discovery, 1:3 (1997), 259–289 | DOI

[10] Das G., Lin K., Mannila H. et al., “Rule discovery from time series”, Proc. 4th Internat. Conf. Knowledge Discovery and Data Mining, New York, USA, 1998, 16–22

[11] Sayal M., Detecting time correlations in time-series data streams, HP Labs, Palo Alto, 2004

[12] Morchen F., Ultsch A., “Optimizing time series discretization for knowledge discovery”, Proc. 11th Internat. Conf. Knowledge Discovery and Data Mining, Chicago, USA, 660–665

[13] Brown R. G., Smoothing forecasting and prediction of discrete time series, Prentice-Hall, New York, 1963

[14] Trigg D. W., Leach A. G., “Exponential smoothing with an adaptive response rate”, Operat. Res. Quart., 18:1 (1967), 53–59 | DOI

[15] Engle R. F., ARCH: Selected readings, Oxford Univ. Press, Oxford, 1995

[16] Rao A. G., Shapiro A., “Adaptive smoothing using evolutionary spectra”, Management Sci., 17:3 (1970), 208–218 | DOI | Zbl

[17] Zadeh L. A., Ragazzini J. R., “An extension of Wiener's theory of prediction”, J. Appl. Phys., 21 (1950), 645–655 | DOI | MR

[18] Zadeh L. A., Ragazzini J. R., “The analysis of sampled-data systems”, Applic. and Industry (AIEE), 71 (1952), 225–234

[19] Barsegyan A. A., Kupriyanov M. S., Stepanenko V. V., Kholod I. I., Metody i modeli analiza dannykh: OLAP i Data Mining, BKhV-Peterburg, SPb., 2004

[20] Zhuravlev Yu. I., Izbrannye nauchnye trudy, Magistr, M., 1998

[21] Rudakov K. V., Algebraicheskaya teoriya universalnykh i lokalnykh ogranichenii dlya algoritmov raspoznavaniya, Dis. $\dots$ dokt. fiz.-matem. nauk, VTs RAN, M., 1992

[22] Pudil P., Ferri F. J., Novovicova J. et al., “Floating search methods for feature selection”, Pattern Recognition Lett., 15:10 (1994), 1119–1125 | DOI

[23] Kristofides H., Teoriya grafov. Algoritmicheskii podkhod, Mir, M., 1978 | MR