Prediction of Long-Range Dependent Time Series Data with Performance Guarantee
Modelling and predicting long-range dependent time series data can find important and practical applications in many areas such as telecommunications and finance. In this paper, we consider Fractional Autoregressive Integrated Moving Average (FARIMA) processes which provide a unified approach to characterising both short-range and long-range dependence. We compare two linear prediction methods for predicting observations of FARIMA processes, namely the Innovations Algorithm and Kalman Filter, from the computational complexity and prediction performance point of view. We also study the problem of Prediction with Expert Advice for FARIMA and propose a simple but effective way to improve the prediction performance. Alongside the main experts (FARIMA models) we propose to use some naive methods (such as Least-Squares Regression) in order to improve the performance of the system. Experiments on publicly available datasets show that this construction can lead to great improvements of the prediction system. We also compare our approach with a traditional method of model selection for the FARIMA model, namely Akaike Information Criterion.
KeywordsCovariance Explosive Nism Odour
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- 1.Bisaglia, L.: Model selection for long-memory models. Quaderni di Statistica 4 (2002)Google Scholar
- 2.Blok, H.J.: On The Nature Of The Stock Market: Simulations And Experiments. PhD Thesis, University of British Columbia, Canada (2000)Google Scholar
- 5.Dethe, C.G., Wakde, D.G.: On the prediction of packet process in network traffic using FARIMA time-series model. J. of Indian Inst. of Science 84, 31–39 (2004)Google Scholar
- 9.Kalman, R.E.: A new approach to linear filtering and prediction problems. Journal of Basic Engineering 82, 34–45 (1960)Google Scholar
- 14.Palmo, W.: Long-Memory Time Series. Theory and Methods. Wiley Series in Probability and Statistics (2007)Google Scholar
- 15.Paxson, V.: Fast Approximation of Self-Similar Network Traffic. Technical report LBL-36750/UC-405 (1995)Google Scholar
- 16.Shu, Y., Jin, Z., Zhang, L., Wang, L., Yang, O.W.W.: Traffic prediction using FARIMA models. In: IEEE International Conf. on Communication, vol. 2, pp. 891–895 (1999)Google Scholar
- 19.Vovk, V.: Prediction with expert advice for the Brier game (2008), http://arxiv.org/abs/0710.0485
- 20.Willinger, W., Paxson, V., Riedi, R.H., Taqqu, M.S.: Long-range dependence and data network traffic. Theory And Applications Of Long-Range Dependence, 373–407 (2003)Google Scholar
- 21.Xue, F.: Modeling and Predicting Long-range Dependent Traffic with FARIMA Processes. In: Proc. of 1999 International Symposium on Communication (1999)Google Scholar
- 22.Xue, F., Liu, J., Zhang, L., Yang, O.W.W.: Traffic Modelling Based on FARIMA Models. In: Proc. IEEE Canadian Conference on Electrical and Computer Eng. (1999)Google Scholar