Abstract
Biological processes are inherently dynamic. From the tiniest molecule in our cells, to cells themselves, tissues, organisms and systems, nothing is essentially static. This includes the study of development, disease, and the action of drugs and aging. Continuous dynamic interactions at different spatial and temporal scales are ubiquitous and only through modeling the dynamics can we achieve a systems level knowledge in biology and genetics (Bar-Joseph et al., Nat. Rev. Genet. 13(8):552–564, 2012), [3]. Time series analysis is available in the Wolfram Language, and in this chapter we introduce the basic capabilities available through a variety of examples.
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
Akaike, H.: Information theory and an extension of the maximum likelihood principle. In: 2nd Inter. Symp. on Information Theory, Akademiai Kidao, 1973 (1973)
Ashburner, M., Ball, C.A., Blake, J.A., Botstein, D., Butler, H., Cherry, J.M., Davis, A.P., Dolinski, K., Dwight, S.S., Eppig, J.T.: Gene ontology: tool for the unification of biology. Nat. Genet. 25(1), 25–29 (2000)
Bar-Joseph, Z., Gitter, A., Simon, I.: Studying and modelling dynamic biological processes using time-series gene expression data. Nat. Rev. Genet. 13(8), 552–64 (2012)
Box, G.E.P., Pierce, D.A.: Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. J. Am. Stat. Assoc. 65(332), 1509–1526 (1970). https://doi.org/10.1080/01621459.1970.10481180
Bretthorst, G.L.: Generalizing the lomb-scargle periodogram. pp. 241–245. IOP INSTITUTE OF PHYSICS PUBLISHING LTD
Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods. Springer Series in Statistics, 2nd edn. Springer, Berlin, New York (1991)
Chatfield, C.: The Analysis of Time Series: an Introduction. CRC press, Boca Raton (2016)
Chen, R., Mias, G.I., Li-Pook-Than, J., Jiang, L., Lam, H.Y., Chen, R., Miriami, E., Karczewski, K.J., Hariharan, M., Dewey, F.E., Cheng, Y., Clark, M.J., Im, H., Habegger, L., Balasubramanian, S., O’Huallachain, M., Dudley, J.T., Hillenmeyer, S., Haraksingh, R., Sharon, D., Euskirchen, G., Lacroute, P., Bettinger, K., Boyle, A.P., Kasowski, M., Grubert, F., Seki, S., Garcia, M., Whirl-Carrillo, M., Gallardo, M., Blasco, M.A., Greenberg, P.L., Snyder, P., Klein, T.E., Altman, R.B., Butte, A.J., Ashley, E.A., Gerstein, M., Nadeau, K.C., Tang, H., Snyder, M.: Personal omics profiling reveals dynamic molecular and medical phenotypes. Cell 148(6), 1293–307 (2012)
Kanehisa, M., Goto, S.: Kegg: kyoto encyclopedia of genes and genomes. Nucl. Acids Res. 28(1), 27–30 (2000)
Kirchgässner, G., Wolters, J., Hassler, U.: Introduction to Modern Time Series Analysis. Springer Science & Business Media, Berlin (2012)
Ljung, G.M., Box, G.E.P.: On a measure of lack of fit in time series models. Biometrika 65(2), 297–303 (1978). https://doi.org/10.1093/biomet/65.2.297
Lomb, N.: Least-squares frequency analysis of unequally spaced data. Astrophys. Space Sci. 39(2), 447–462 (1976)
Madsen, H.: Time Series Analysis. CRC Press, Boca Raton (2007)
Mias, G., Snyder, M.: Personal genomes, quantitative dynamic omics and personalized medicine. Quant. Biol. 1(1), 71–90 (2013)
Mias, G.I., Snyder, M.: Multimodal dynamic profiling of healthy and diseased states for future personalized health care. Clin. Pharmacol. Ther. 93(1), 29–32 (2013)
Mias, G.I., Yusufaly, T., Roushangar, R., Brooks, L.R., Singh, V.V., Christou, C.: Mathiomica: An integrative platform for dynamic omics. Sci. Rep. 6, 37–237 (2016)
Scargle, J.: Studies in astronomical time series analysis. ii-statistical aspects of spectral analysis of unevenly spaced data. Astrophys. J. 263, 835–853 (1982)
Scargle, J.: Studies in astronomical time series analysis. iii-fourier transforms, autocorrelation functions, and cross-correlation functions of unevenly spaced data. Astrophys. J. 343, 874–887 (1989)
The UniProt Consortium: Uniprot: the universal protein knowledgebase. Nucl. Acids Res. 45(D1), D158–D169 (2017)
UniProt, C.: Uniprot: a hub for protein information. Nucl. Acids Res. 43(Database issue), D204–12 (2015)
Van Dongen, H.P., Ruf, T., Olofsen, E., VanHartevelt, J.H., Kruyt, E.W.: Analysis of problematic time series with the lomb-scargle method, a reply to ’emphasizing difficulties in the detection of rhythms with lomb-scargle periodograms’. Biol. Rhythm Res. 32(3), 347–54 (2001)
Wolfram Alpha LLC: Wolfram\(\mid \)Alpha (2017). Accessed Nov 2017
Wolfram Research, Inc.: Mathematica, Version 11.2. Champaign, IL (2017)
Zhao, W., Agyepong, K., Serpedin, E., Dougherty, E.R.: Detecting periodic genes from irregularly sampled gene expressions: A comparison study. EURASIP J. Bioinform. Syst. Biol. 2008 (2008)
Author information
Authors and Affiliations
Corresponding author
11.1 Electronic supplementary material
Below is the link to the electronic supplementary material.
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Mias, G. (2018). Time Series Analysis. In: Mathematica for Bioinformatics. Springer, Cham. https://doi.org/10.1007/978-3-319-72377-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-72377-8_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-72376-1
Online ISBN: 978-3-319-72377-8
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)