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Network Anomaly Detection Based on Statistical Models with Long-Memory Dependence

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 365))

Abstract

The paper presents an attempt to anomaly detection in network traffic using statistical models with long memory. Tests with the GPH estimator were used to check if the analysed time series have the long-memory property. The tests were performed for three statistical models known as ARFIMA, FIGARCH and HAR-RV. Optimal selection of model parameters was based on a compromise between the model’s coherence and the size of the estimation error.

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References

  1. Baillie, R., Bollerslev, T., Mikkelsen, H.: Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics 74, 3–30 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  2. Beran, J.A.: Statistics for Long-Memory Processes. Chapman and Hall (1994)

    Google Scholar 

  3. Box, G.E., Jenkins, M.G.: Time series analysis forecasting and control, 2nd edn. Holden-Day, San Francisco (1976)

    MATH  Google Scholar 

  4. Box, G., Jenkins, G., Reinsel, G.: Time series analysis. Holden-day, San Francisco (1970)

    MATH  Google Scholar 

  5. Corsi, F.: A simple approximate long-memory model of realized volatility. Journal of Financial Econometrics 7, 174–196 (2009)

    Article  Google Scholar 

  6. Crato, N., Ray, B.K.: Model Selection and Forecasting for Long-range Dependent Processes. Journal of Forecasting 15, 107–125 (1996)

    Article  Google Scholar 

  7. Engle, R.: Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation. Econometrica 50, 987–1008 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  8. Geweke, J., Porter-Hudak, S.: The Estimation and Application of Long Memory Time Series Models. Journal of Time series Analysis (4), 221–238 (1983)

    Google Scholar 

  9. Granger, C.W.J., Joyeux, R.: An introduction to long-memory time series models and fractional differencing. Journal of Time Series Analysis 1, 15–29 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  10. Hosking, J.: Fractional differencing. Biometrika (68), 165–176 (1981)

    Google Scholar 

  11. Hurst, H.R.: Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers 1, 519–543 (1951)

    Google Scholar 

  12. Robinson, P.M.: Log-periodogram regression of time series with long range dependence. Annals of Statistics 23, 1048–1072 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  13. Saganowski, Ł., Goncerzewicz, M., Andrysiak, T.: Anomaly Detection Preprocessor for SNORT IDS System. In: Choraś, R.S. (ed.) Image Processing and Communications Challenges 4. AISC, vol. 184, pp. 225–232. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  14. SNORT - Intrusion Detection System, https://www.snort.org/

  15. Kali Linux, https://www.kali.org/

  16. Andrysiak, T., Saganowski, Ł., Choraś, M., Kozik, R.: Network Traffic Prediction and Anomaly Detection Based on ARFIMA Model. In: de la Puerta, J.G., et al. (eds.) International Joint Conference SOCO’14-CISIS’14-ICEUTE’14. AISC, vol. 299, pp. 545–554. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  17. Wei, L., Ghorbani, A.: Network Anomaly Detection Based on Wavelet Analysis. EURASIP Journal on Advances in Signal Processing 2009 (2009), doi:10.1155/2009/837601

    Google Scholar 

  18. Xie, M., Hu, J., Han, S., Chen, H.-H.: Scalable Hypergrid k-NN-Based Online Anomaly Detection in Wireless Sensor Networks. IEEE Transactions on Parallel & Distributed Systems 24(8), 1661–1670 (2013), doi:10.1109/TPDS.2012.261

    Article  Google Scholar 

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Correspondence to Tomasz Andrysiak .

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Andrysiak, T., Saganowski, Ł. (2015). Network Anomaly Detection Based on Statistical Models with Long-Memory Dependence. In: Zamojski, W., Mazurkiewicz, J., Sugier, J., Walkowiak, T., Kacprzyk, J. (eds) Theory and Engineering of Complex Systems and Dependability. DepCoS-RELCOMEX 2015. Advances in Intelligent Systems and Computing, vol 365. Springer, Cham. https://doi.org/10.1007/978-3-319-19216-1_1

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  • DOI: https://doi.org/10.1007/978-3-319-19216-1_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19215-4

  • Online ISBN: 978-3-319-19216-1

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