Abstract
Amongst the wealth of available machine learning algorithms for forecasting time series, linear regression has remained one of the most important and widely used methods, due to its simplicity and interpretability. A disadvantage, however, is that a linear regression model may often have higher error than models that are produced by more sophisticated techniques. In this paper, we investigate the use of a grouping based quadratic mean loss function for improving the performance of linear regression. In particular, we propose segmenting the input time series into groups and simultaneously optimizing both the average loss of each group and the variance of the loss between groups, over the entire series. This aims to produce a linear model that has low overall error, is less sensitive to distribution changes in the time series and is more robust to outliers. We experimentally investigate the performance of our method and find that it can build models which are different from those produced by standard linear regression, whilst achieving significant reductions in prediction errors.
This is a preview of subscription content, log in via an institution to check access.
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
Tsay, R.S.: Analysis of Financial Time Series. Wiley-Interscience (2005)
Hulten, G., Spencer, L., et al.: Mining time-changing data streams. In: Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, California, pp. 97–106 (2001)
Keogh, E., Kasetty, S.: On the Need for Time Series Data Mining Benchmarks: A Survey and Empirical Demonstration. Data Mining and Knowledge Discovery 7(4), 349–371 (2003)
Dong, G., Han, J., et al.: Online mining of changes from data streams: Research problems and preliminary results. In: Proceedings of the 2003 ACM SIGMOD Workshop on Management and Processing of Data Streams (2003)
Liu, X., Zhang, R., et al.: Incremental Detection of Distribution Change in Stock Order Streams. In: 26th International Conference on Data Engineering Conference, ICDE (2010)
Teo, C.H., Vishwanthan, S.V.N., Smola, A.J., Le, Q.V.: Bundle methods for regularized risk minimization. Journal of Machine Learning Research 11, 311–365 (2010)
Liu, W., Chawla, S.: A Quadratic Mean based Supervised Learning Model for Managing Data Skewness. In: Proceedings of the Eleventh SIAM International Conference on Data Mining, pp. 188–198 (2011)
Vellaisamy, K., Li, J.: Multidimensional decision support indicator (mDSI) for time series stock trend prediction. In: Zhou, Z.-H., Li, H., Yang, Q. (eds.) PAKDD 2007. LNCS (LNAI), vol. 4426, pp. 841–848. Springer, Heidelberg (2007)
Cheng, H., Tan, P.-N., Gao, J., Scripps, J.: Multistep-ahead time series prediction. In: Ng, W.-K., Kitsuregawa, M., Li, J., Chang, K. (eds.) PAKDD 2006. LNCS (LNAI), vol. 3918, pp. 765–774. Springer, Heidelberg (2006)
Liu, Z., Yu, J.X., Lin, X., Lu, H., Wang, W.: Locating motifs in time-series data. In: Ho, T.-B., Cheung, D., Liu, H. (eds.) PAKDD 2005. LNCS (LNAI), vol. 3518, pp. 343–353. Springer, Heidelberg (2005)
Web enabled scientific services and applications, http://www.wessa.net/stocksdata.wasp
Hyndman, R.J.: S&P quarterly index online database, http://robjhyndman.com/tsdldata/data/9-17b.dat
Muller, K.-R., Smola, A.J., Rätsch, G., Schölkopf, B., Kohlmorgen, J., Vapnik, V.: Using Support Vector Machines for Time Series Prediction (2000)
Liu, X., Wu, X., Wang, H., Zhang, R., Bailey, J., Kotagiri, R.: Mining distribution change in stock order streams. In: IEEE 26th International Conference on Data Engineering, ICDE (2010)
Wilcox, R.R.: Introduction to Robust Estimation and Hypothesis Testing. Elsevier Academic Press, New York (2005)
Evgeniou, T., Pontil, M.: Regularized multi–task learning. In: Proceedings of the Tenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 109–117 (2004)
Adhikari, R., Agrawal, R.K.: A novel weighted ensemble technique for time series forecasting. In: Tan, P.-N., Chawla, S., Ho, C.K., Bailey, J. (eds.) PAKDD 2012, Part I. LNCS, vol. 7301, pp. 38–49. Springer, Heidelberg (2012)
Khoa, N.L.D., Chawla, S.: Robust outlier detection using commute time and eigenspace embedding. In: Zaki, M.J., Yu, J.X., Ravindran, B., Pudi, V. (eds.) PAKDD 2010, Part II. LNCS, vol. 6119, pp. 422–434. Springer, Heidelberg (2010)
Widiputra, H., Pears, R., Kasabov, N.: Multiple time-series prediction through multiple time-series relationships profiling and clustered recurring trends. In: Huang, J.Z., Cao, L., Srivastava, J. (eds.) PAKDD 2011, Part II. LNCS, vol. 6635, pp. 161–172. Springer, Heidelberg (2011)
Cheng, H., Tan, P.-N.: Semi-supervised learning with data calibration for long-term time series forecasting. In: Proceeding of the 14th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (2008)
Meesrikamolkul, W., Niennattrakul, V., Ratanamahatana, C.A.: Shape-based clustering for time series data. In: Tan, P.-N., Chawla, S., Ho, C.K., Bailey, J. (eds.) PAKDD 2012, Part I. LNCS, vol. 7301, pp. 530–541. Springer, Heidelberg (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ristanoski, G., Liu, W., Bailey, J. (2013). Time Series Forecasting Using Distribution Enhanced Linear Regression. In: Pei, J., Tseng, V.S., Cao, L., Motoda, H., Xu, G. (eds) Advances in Knowledge Discovery and Data Mining. PAKDD 2013. Lecture Notes in Computer Science(), vol 7818. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37453-1_40
Download citation
DOI: https://doi.org/10.1007/978-3-642-37453-1_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37452-4
Online ISBN: 978-3-642-37453-1
eBook Packages: Computer ScienceComputer Science (R0)