The Impact of Memory Dependency on Precision Forecast - An Analysis on Different Types of Time Series Databases

Ricardo Moraes Muniz da Silva, Mauricio Kugler, Taizo Umezaki

2017

Abstract

Time series forecasting is an important type of quantitative method in which past observations of a set of variables are used to develop a model describing their relationship. The Autoregressive Integrated Moving Average (ARIMA) model is a commonly used method for modelling time series. It is applied when the data show evidence of nonstationarity, which is removed by applying an initial differencing step. Alternatively, for time series in which the long-run average decays more slowly than an exponential decay, the Autoregressive Fractionally Integrated Moving Average (ARFIMA) model is used. One important issue on time series forecasting is known as the short and long memory dependency, which corresponds to how much past history is necessary in order to make a better prediction. It is not always clear if a process is stationary or what is the influence of the past samples on the future value, and thus, which of the two models, is the best choice for a given time series. The objective of this research is to have a better understanding this dependency for an accurate prediction. Several datasets of different contexts were processed using both models, and the prediction accuracy and memory dependency were compared.

References

  1. Aryal, D. R., Wang, Y., 2003. Neural Network Forecasting of the Production Level of Chinese Construction Industry. Journal of Comparative International Management, vol. 6, no. 2, pp. 45-64.
  2. Khashei M., Bijari M., 2011. A New Hybrid Methodology for Nonlinear Time Series Forecasting. Modelling and Simulation in Engineering, Article ID 379121, 5 pages.
  3. Gourieroux, C. S., Monfort, A., 1997. Time Series and Dynamic Models, Cambridge University Press.
  4. Granger, C. W. J., Joyeux, R., 1980. An introduction to long memory time series models and fractional differencing. Journal of Time Series Analysis, vol. 1, no. 1, pp. 15-29.
  5. Hosking, J. R. M., 1984. Modelling Persistence in Hydrological Time Series using Fractional Differencing. Water Resources Research, vol. 20, no. 12, pp. 1898-1908.
  6. Box, G. E. P., Jenkins, G. M., 1976. Time series analysis: forecasting and control, Holden Day. San Francisco, 1st edition.
  7. Contreras-Reyes, J. E., Palma, W. 2013. Statistical analysis of autoregressive fractionally integrated moving average models in R. Computational Statistics, vol. 28, no. 5, pp. 2309-2331.
  8. Dickey, D. A., Fuller, W. A., 1979. Distribution of the estimators for autoregressive time series with unit root. Journal of the American Statistical Association, vol. 74, no. 366, pp. 427-431.
  9. Granger, C. W. J., 1989. Combining forecasts - Twenty years later. Journal of Forecasting, vol. 8, no. 3, pp. 167-173.
  10. Souza, L. R., Smith, J., 2004. Effects of temporal aggregation on estimates and forecasts of fractionally integrated processes: a Monte-Carlo study. International Journal of Forecasting, vol. 20, no. 3, pp. 487-502.
  11. Zhang, G. P., 2003. Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, vol. 50, pp. 159-175.
  12. Baum, C. F., 2000. Tests for stationarity of a time series. Stata Technical Bulletin, vol. 57, pp. 36-39.
  13. Fildes, R., Makridakis, S., 1995. The impact of empirical accuracy studies on time series analysis and forecasting, International Statistical Review, vol. 63, no. 3, pp. 289-308.
  14. Boutahar, M., Khalfaoui, R., 2011. Estimation of the long memory parameter in non stationary models: A Simulation Study, HAL id: halshs-00595057.
  15. Moghadam, R. A., Keshmirpour, M., 2011. Hybrid ARIMA and Neural Network Model for Measurement Estimation in Energy-Efficient Wireless Sensor Networks, In ICIEIS2011, International Conference on Informatics Engineering and Information Science. Springer, vol. 253, pp. 35-48.
  16. Palma, W., 2007. Long-Memory Time Series: Theory and Methods, Wiley-Interscience, John Wiley & Sons. Hoboken.
  17. Anderson, M. K., 2000. Do long-memory models have long memory? International Journal of Forecasting, vol. 16, no. 1, pp. 121-124.
  18. Hurvich C. M., Ray, B. K., 1995. Estimation of the memory parameter for nonstationary or noninvertible fractionally integrated processes. Journal of Time Series Analysis, vol. 16, no. 1, pp. 17-42.
  19. Geweke, J., Porter-Hudak, S., 1983. The estimation and application of long-memory time series models. Journal of Time Series Analysis, vol. 4, no. 4, pp. 221- 238.
  20. Shitan, M., Jin Wee P.M., Ying Chin, L., Ying Siew, L., 2008. Arima and Integrated Arfima Models for Forecasting Annual Demersal and Pelagic Marine Fish Production in Malaysia, Malaysian Journal of Mathematical Sciences, vol. 2, no. 2, pp. 41-54.
  21. Amadeh, H., Amini, A., Effati, F., 2013. ARIMA and ARFIMA Prediction of Persian Gulf Gas-Oil F.O.B. Iranian Journal of Investment Knowledge, vol. 2, no. 7, pp. 213-230.
  22. Baillie, R. T., 1996. Long memory processes and fractional integration in econometrics. Journal of Econometrics, vol. 73, no. 1, pp. 5-59.
  23. Sowell, F., 1992. Modelling long-run behaviour with the fractional ARIMA model. Journal of Monetary Economics, vol. 29, no. 2, pp. 277-302.
  24. Priestley, M. B., 1981. Spectral Analysis and Time Series, Academic Press. London.
  25. Chan, W. S., 1992. A note on time series model specification in the presence outliers, Journal of Applied Statistics, vol. 19, pp. 117-124.
  26. Chan, W. S., 1995. Outliers and financial time series modelling: a cautionary note. Mathematics and Computers in Simulation, vol. 39, no. 3-4, pp. 425- 430.
  27. Lichman, M., 2013. UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.
  28. Brazilian Stock Market BM&F Bovespa. Accessed on April 2016. [http://www.bmfbovespa.com.br] Lucas, D. D., Yver Kwok, C., Cameron-Smith, P., Graven, H., Bergmann, D., Guilderson, T. P., Weiss, R., Keeling, R., 2015. Designing optimal greenhouse gas observing networks that consider performance and cost. Geoscientific Instrumentation, Methods and Data Systems, vol. 4, no. 1, pp. 121-137.
  29. Tüfekci, P., 2014. Prediction of full load electrical power output of a base load operated combined cycle power plant using machine learning methods. International Journal of Electrical Power & Energy Systems, vol. 60, pp. 126-140.
  30. Kaya, H., Tüfekci, P., Gürgen, S. F., 2012. Local and Global Learning Methods for Predicting Power of a Combined Gas & Steam Turbine, In ICETCEE2012, International Conference on Emerging Trends in Computer and Electronics Engineering, pp. 13-18.
  31. Akbilgic, O., Bozdogan, H., Balaban, M. E., 2013. A novel Hybrid RBF Neural Networks model as a forecaster, Statistics and Computing, vol. 24, no. 3, pp. 365-375.
  32. Brown, M. S., Pelosi, M. J., Dirska, H., 2013. DynamicRadius Species-Conserving Genetic Algorithm for the Financial Forecasting of Dow Jones Index Stocks. In MLDM2013, 9th International Conference on Machine Learning and Data Mining in Pattern Recognition, Springer, pp. 27-41.
  33. Alireza, E., Ahmad J., 2009. Long Memory Forecasting of Stock Price Index Using a Fractionally Differenced Arma Model. Journal of Applied Sciences Research, vol. 5, no. 10, pp. 1721-1731.
  34. Yule, G. U., 1926. Why do we sometimes get nonsensecorrelations between time series? A study in sampling and the nature of time-series. Journal of the Royal Statistical Society, vol. 89, no. 1, pp. 1-63.
  35. Engle, R. F., Smith A. D., 1999. Stochastic permanent breaks. Review of Economics and Statistics, vol. 81, no. 4, pp. 553-574.
  36. Taylor, J. W., Menezes, L. M., McSharry, P. E., 2006. A comparison of univariate methods for forecasting electricity demand up to a day ahead, International Journal of Forecasting, vol. 22, no. 1, pp. 1-16.
Download


Paper Citation


in Harvard Style

Moraes Muniz da Silva R., Kugler M. and Umezaki T. (2017). The Impact of Memory Dependency on Precision Forecast - An Analysis on Different Types of Time Series Databases . In Proceedings of the 6th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM, ISBN 978-989-758-222-6, pages 575-582. DOI: 10.5220/0006203405750582


in Bibtex Style

@conference{icpram17,
author={Ricardo Moraes Muniz da Silva and Mauricio Kugler and Taizo Umezaki},
title={The Impact of Memory Dependency on Precision Forecast - An Analysis on Different Types of Time Series Databases},
booktitle={Proceedings of the 6th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},
year={2017},
pages={575-582},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006203405750582},
isbn={978-989-758-222-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 6th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,
TI - The Impact of Memory Dependency on Precision Forecast - An Analysis on Different Types of Time Series Databases
SN - 978-989-758-222-6
AU - Moraes Muniz da Silva R.
AU - Kugler M.
AU - Umezaki T.
PY - 2017
SP - 575
EP - 582
DO - 10.5220/0006203405750582