Site maintenance: Ilka Miloucheva

• Box-Jenkins methodology, or Auto-Regressive Integrated Moving Average (ARIMA) modelling techniques – introduction [BJR 94], [BD 02], [Pow 99].
• An ARIMA (p,d,q) model is an extension of a set of time series models called
• autoregressive of order p denoted by AR(p)
• moving average of order q denoted by MA(q), and
• autoregressive moving average denoted by ARMA(p,q).
• ARIMA model of order (p,d,q) is simply an ARMA (p,q) model that is differenced d times, i.e. d is parameter giving the degree of differentiation.
• ARIMA falls under the class of linear time series forecasting, because it postulates a linear dependency of the future value on the past values.
• A long-term Traffic Prediction based on ARIMA for the NSFNET Backbone [GP 94].
• Fractional ARIMA are used for prediction of long-range dependent traffic [Il 00].
• Using ARIMA for univariate and multivariate time series prediction of performance data describing large wide area data transfers [VSF 02].
• Forecasting in the context of modelling co-evolving time sequence data [YSJ 00].
• Outliers based on ARIMA for financial time series data prediction [GM 96] realised in the public domain econometrics software [MC 02]

References

• G. Box and G. Jenkins, G. Reinsel, Time series Analysis: Forecasting and control, revised ed., Prentice Hall , 3rd Edition
• P.J. Brockwell, R.A. Davis, Introduction to Time Series and Forecasting, Springer Verlag, 2002
• R. S. Povinelli. The time series data mining: identifying temporal patterns for characterisation and prediction of time series events, Dissertation, Wisconsin 1999
• N.K. Groschwitz and G.C. Polyzos, "A Time-Series Model of Long-term Traffic on the NSFNET Backbone," Proc. IEEE International Conference on Communications (ICC'94), New Orleans, LA, pp. 1400-1404, May 1994.
• B.-K. Yi, N.D. Sidiropoulos, T. Johnson, H.V. Jagadish. C. Faloutsos. A. Biliris, Online Data Mining for Co-volving Time Series, ICDE 2000
• S. Vazhkudai, J.Schorf, I.Foster, Predicting the performance of wide area data transfers. In 16th International Parallel and distributed Processing symposium (IPDPS). 2002, Fort Lauderdale, Florida: IEEE Press
• J. Ilow, ``Forecasting Network Traffic Using FARIMA Models with Heavy Tailed Innovations'', ICASSP 2000, Istanbul, Turkey, June 2000.
• B. Fischer, C. Planas (2000), "Large Scale Fitting of Regression Models with ARIMA Errors," Journal of Official Statistics, 16, 173-184.
• G. Caporello, A. Maravall and F. J. Sanchez, Program TSW Reference Manual, Banco de Espana, 2001
• B. C. Monsell “An Update of the Development of the X-12-ARIMA Seasonal Adjustment Program”, Modeling Seasonality and Periodicity, Proceedings of the 3 rd International Symposium on Frontiers of Time Series Modeling, The Institute of Statistical Mathematics, Tokyo: Japan, January 2002.
• GÓMEZ, V. and MARAVALL, A. (1996), "Programs TRAMO (Time series Regression with Arima noise, Missing observations, and Outliers) and SEATS (Signal Extraction in Arima Time Series). Instructions for the User", Working Paper 9628, Servicio de Estudios, Banco de España.
• A. Maravall and G. Caporello, A TOOL FOR QUALITY CONTROL OF TIME SERIES DATA Program TERROR, Bank of Spain, Presented at the conference “Challenges to Central Bank Statistical Activities”, Irving Fisher Committee (ISI) and Bank for International Settlements, Basel, August 2002.