Abstract
In this paper, we analyze the distribution of the statistic of a test for identifying the type of correlated time series. The rule for selecting a model suitable to the data is based on the comparison between the normalized prediction errors of the Whittle estimator applied to the candidate models. We consider one application of the test: assessing the significance of increasing the number of parameters within a given class of models. The results obtained demonstrate that the Weibull distribution is a good approximation for the distribution of the test statistic.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beran, J.: Statistics for Long-Memory Processes. Chapman and Hall, Boca Raton (1994)
Beran, J., Shreman, R., Taqqu, M.S., Willinger, W.: Long-Range Dependence in Variable-Bit-Rate video traffic. IEEE Transactions on Communications 43(2/4), 1566–1579 (1995)
Cox, D.R., Isham, V.: Point Processes. Chapman and Hall, Boca Raton (1980)
Cox, D.R.: Long-Range Dependence: A review. In: Statistics: An Appraisal, pp. 55–74. Iowa State University Press, Iowa (1984)
Crovella, M.E., Bestavros, A.: Self-similarity in World Wide Web traffic: Evidence and possible causes. IEEE/ACM Transactions on Networking 5(6), 835–846 (1997)
Duffield, N.: Queueing at large resources driven by long-tailed M/G/∞ processes. Queueing Systems 28(1/3), 245–266 (1987)
Eliazar, I.: The M/G/∞ system revisited: Finiteness, summability, long-range dependence and reverse engineering. Queueing Systems 55(1), 71–82 (2007)
Erramilli, A., Narayan, O., Willinger, W.: Experimental queueing analysis with Long-Range Dependent packet traffic. IEEE/ACM Transactions on Networking 4(2), 209–223 (1996)
Garrett, M.W., Willinger, W.: Analysis, modeling and generation of self-similar VBR video traffic. In: Proc. ACM SIGCOMM 1994, London, UK, pp. 269–280 (1994)
Hurst, H.E.: Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers 116, 770–799 (1951)
Jiang, M., Nikolic, M., Hardy, S., Trajkovic, L.: Impact of self-similarity on wireless data network performance. In: Proc. IEEE ICC 2001, Helsinki, Finland, pp. 477–481 (2001)
Krunz, M., Makowski, A.: Modeling video traffic using M/G/∞ input processes: A compromise between Markovian and LRD models. IEEE Journal on Selected Areas in Communications 16(5), 733–748 (1998)
Leland, W.E., Taqqu, M.S., Willinger, W., Wilson, D.V.: On the self-similar nature of Ethernet traffic (extended version). IEEE/ACM Transactions on Networking 2(1), 1–15 (1994)
Li, S.Q., Hwang, C.L.: Queue response to input correlation functions: Discrete spectral analysis. IEEE/ACM Transactions on Networking 1(5), 317–329 (1993)
Likhanov, N., Tsybakov, B., Georganas, N.D.: Analysis of an ATM buffer with self-similar (“fractal”) input traffic. In: Proc. IEEE INFOCOM 1995, Boston, MA, USA, pp. 985–992 (1995)
López, J.C., López, C., Suárez, A., Fernández, M., Rodríguez, R.F.: On the use of self-similar processes in network simulation. ACM Transactions on Modeling and Computer Simulation 10(2), 125–151 (2000)
Norros, I.: A storage model with self-similar input. Queueing Systems 16, 387–396 (1994)
Novak, M.: Thinking in patterns: Fractals and related phenomena in nature. World Scientific, Singapore
Paxson, V., Floyd, S.: Wide-area traffic: The failure of Poisson modeling. IEEE/ACM Transactions on Networking 3(3), 226–244 (1995)
Resnick, S., Rootzen, H.: Self-similar communication models and very heavy tails. Annals of Applied Probability 10(3), 753–778 (2000)
Sousa, M.E., Suárez, A., López, C., Fernández, M., López, J.C., Rodríguez, R.F.: Fast simulation of self-similar and correlated processes. Mathematics and Computers in Simulation 80(10), 2040–2061 (2010)
Sousa, M.E., Suárez, A., Rodríguez, R.F., López, C.: Flexible adjustment of the short-term correlation of LRD M/G/∞-based processes. Lecture Notes in Theoretical Computer Science 261, 131–145 (2010)
Sousa, M.E., Suárez, A., Fernández, M., López, J.C., López, C., Rodríguez, R.F.: Application of a hypothesis test for discriminating long-memory processes to the M/G/∞ process. In: Proc. Statistical Methods of Signal and Data Processing, Kiev, Ukraine (2010)
Suárez, A., López, J.C., López, C., Fernández, M., Rodríguez, R.F., Sousa, M.E.: A new heavy-tailed discrete distribution for LRD M/G/∞ sample generation. Performance Evaluation 47(2/3), 197–219 (2002)
Tsoukatos, K.P., Makowski, A.M.: Heavy traffic analysis for a multiplexer driven by M/G/∞ input processes. In: Proc. 15th International Teletraffic Congress, Washington, DC, USA, pp. 497–506 (1997)
Whittle, P.: Estimation and information in stationary time series. Arkiv Matematick 2(23), 423–434 (1953)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sousa-Vieira, M.E. (2011). Analysis of the Distribution of the Statistic of a Test for Discriminating Correlated Processes. In: Balandin, S., Koucheryavy, Y., Hu, H. (eds) Smart Spaces and Next Generation Wired/Wireless Networking. ruSMART NEW2AN 2011 2011. Lecture Notes in Computer Science, vol 6869. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22875-9_32
Download citation
DOI: https://doi.org/10.1007/978-3-642-22875-9_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22874-2
Online ISBN: 978-3-642-22875-9
eBook Packages: Computer ScienceComputer Science (R0)