×

zbMATH — the first resource for mathematics

Dilemmas of robust analysis of economic data streams. (English) Zbl 1349.62579
Summary: Data streams (streaming data) consist of continuously observed, non-equally spaced and temporally evolving multidimensional data sequences that challenge our computational and/or inferential capabilities. In economics, data streams are among others related to electricity consumption monitoring, Internet user behavior in exploring, or order book forecasting in high-frequency financial markets. In this paper, we point out and discuss several open problems related to robust data stream analysis and propose three robust and conceptually very simple approaches in this context. We apply the proposals to real data sets related to the activity of investors in the futures contracts market.

MSC:
62P20 Applications of statistics to economics
62P05 Applications of statistics to actuarial sciences and financial mathematics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ch. Anagnostopuoulos, D. K. Tasoulis, N. M. Adams, N. G. Pavlidis, and D. J. Hand, “Online linear and quadratic discriminant analysis with adaptive forgetting for streaming classification,” Stat. Anal. Data Mining, No. 5, 139-166 (2012).
[2] Ch. C. Aggerwal, Data Streams — Models and Algorithms, Springer, Berlin (2007).
[3] Cuevas, A; Febrero, M; Fraiman, R, Robust estimation and classification for functional data via projection-based depth notions, Comput. Stat. Data Anal., 22, 481-496, (2007) · Zbl 1195.62032
[4] L. Devroye, L. Gorfi, and L. Gabor, A Probabilistic Theory of Pattern Recognition, Springer-Verlag, New York (1996).
[5] J. Durbin and S. J. Koopman, Time Series Analysis by State Space Methods, Oxford University Press, Oxford (2001). · Zbl 0995.62504
[6] Dyckerhoff, R, Data depths satisfying the projection property, Allgemeines Stat. Arch., 88, 163-190, (2004) · Zbl 1294.62112
[7] R. Frainman and G. Muniz, “Trimmed means for functional data,” Test, 10, No. 2, 419-440 (2007). · Zbl 1016.62026
[8] M. M. Gaber, “Advances in data stream mining,” WIREs Data Mining Knowl. Discov., No. 2, 79-85 (2012). · Zbl 1195.62032
[9] M. G. Genton and A. Lucas, “Comprehensive definitions of breakdown points for independent and dependent observations,” J. R. Stat., Soc. Ser. B, 65, 81-84 (2003). · Zbl 1063.62038
[10] T. Górecki and M. Krzyśko, “Functional principal component analysis,” in: Data Analysis Methods and its Applications, J. Pociecha and R. Decker (eds.), Beck, Warsaw (2012), pp. 71-87.
[11] J. Hajek, Theory of Rank Tests, Academia, Prague (1967). · Zbl 0161.38102
[12] L. Horvath and P. Kokoszka, Inference for Functional Data with Applications, Springer, New York (2012). · Zbl 1279.62017
[13] P. Huber, Data Analysis: What Can Be Learned From the Past 50 Years, Springer, Wiley (2011). · Zbl 1281.62023
[14] Hyndeman, HL, Forecasting functional time series (with discussion), J. Korean Stat. Soc., 38, 199-221, (2009) · Zbl 1293.62267
[15] R. J. Hyndman, A. B. Koehler, J. B. Ord, and R. D. Snyder, Forecasting with Exponential Smoothing: the State Space Approach, Springer-Verlag, Berlin (2008). · Zbl 1211.62165
[16] D. Kosiorowski, “Functional regression in short term prediction of economic time series,” Stat. Trans., 15, No. 4 (2014). · Zbl 1106.62334
[17] D. Kosiorowski, “Two procedures for robust monitoring of probability distributions of economic data streams induced by depth functions,” Oper. Res. Dec., 25, No. 1 (2015). · Zbl 1395.62358
[18] D. Kosiorowski and Z. Zawadzki, “DepthProc: An R package for robust exploration of multidimensional economic phenomena,” http://arxiv.org/pdf/1408.4542.pdf (2014). · Zbl 1100.62564
[19] D. Kosiorowski and Z. Zawadzki. “Selected issues related to online calculation of multivariate robust measures of location and scatter,” in: Proceedings from VIIIth A. Zelia International Conference, UEK w Krakowie (2014), pp.17-34.
[20] Li, J; Liu, RY, New nonparametric tests of multivariate locations and scales using data depth, Stat. Sci., 19, 686-696, (2004) · Zbl 1100.62564
[21] Liu, RY, Control charts for multivariate processes, J. Am. Stat. Assoc., 90, 1380-1387, (1995) · Zbl 0868.62075
[22] Liu, RY; Parelius, JM; Singh, K, Multivariate analysis by data depth: descriptive statistics, graphics and inference (with discussion), Ann. Stat., 27, 783-858, (1999) · Zbl 0984.62037
[23] C. Loader, Local Regression and Likelihood, Springer, New York (1999). · Zbl 0929.62046
[24] R. A. Maronna, R. D. Martin, and V. J. Yohai, Robust Statistics — Theory and Methods. Wiley, Chichester (2006). · Zbl 1094.62040
[25] Mosler, K; Becker, C (ed.); Fried, R (ed.); Kuhnt, S (ed.), Depth statistics, 17-34, (2013), New York
[26] S. Muthukrishan, Data Streams: Algorithms and Applications, Now Publishers, New York (2006).
[27] N. Hautsch, Econometrics of Financial High-Frequency Data, Springer, Heidelberg (2012). · Zbl 1248.91004
[28] Paindavaine, D; Bever, G, Nonparametrically consistent depth-based classifiers, Bernoulli, 21, 62-85, (2015) · Zbl 1359.62258
[29] Paindavaine, D; Bever, G, From depth to local depth: a focus on centrality, J. Am. Stat. Assoc., 105, 1105-1119, (2013) · Zbl 06224990
[30] J. O. Ramsay, G. Hooker, and S. Graves, Functional Data Analysis with R and Matlab, Springer, New York (2009). · Zbl 1179.62006
[31] B. Sch¨olkopf and A.J. Smola, Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond, MIT Press, Cambridge (2002).
[32] Stockis, J-P; Franke, J; Kamgaing, JT, On geometric ergodicity of charme models, J. Time Ser. Anal., 31, 141-152, (2010) · Zbl 1223.62151
[33] Todorov, V; Filzmoser, P, An object-oriented framework for robust multivariate analysis, J. Stat. Soft., 32, 1-47, (2009)
[34] Zhang, J, Some extensions of tukey’s depth function, J. Multivar. Anal., 82, 134-165, (2002) · Zbl 1010.62058
[35] Zuo, Y; He, X, On the limiting distributions of multivariate depth-based rank sum statistics and related tests, Ann. Stat., 34, 2879-2896, (2006) · Zbl 1114.62020
[36] Zuo, Y; Serfling, R, General notions of statistical depth function, Ann. Stat., 28, 461-482, (2000) · Zbl 1106.62334
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.