skip to main content
10.1145/3097983.3098113acmconferencesArticle/Chapter ViewAbstractPublication PageskddConference Proceedingsconference-collections
research-article
Public Access

Mixture Factorized Ornstein-Uhlenbeck Processes for Time-Series Forecasting

Published: 04 August 2017 Publication History

Abstract

Forecasting the future observations of time-series data can be performed by modeling the trend and fluctuations from the observed data. Many classical time-series analysis models like Autoregressive model (AR) and its variants have been developed to achieve such forecasting ability. While they are often based on the white noise assumption to model the data fluctuations, a more general Brownian motion has been adopted that results in Ornstein-Uhlenbeck (OU) process. The OU process has gained huge successes in predicting the future observations over many genres of time series, however, it is still limited in modeling simple diffusion dynamics driven by a single persistent factor that never evolves over time. However, in many real problems, a mixture of hidden factors are usually present, and when and how frequently they appear or disappear are unknown ahead of time. This imposes a challenge that inspires us to develop a Mixture Factorized OU process (MFOUP) to model evolving factors. The new model is able to capture the changing states of multiple mixed hidden factors, from which we can infer their roles in driving the movements of time series. We conduct experiments on three forecasting problems, covering sensor and market data streams. The results show its competitive performance on predicting future observations and capturing evolution patterns of hidden factors as compared with the other algorithms.

References

[1]
I. Adelman and C. T. Morris. A factor analysis of the interrelationship between social and political variables and per capita gross national product. The Quarterly Journal of Economics, pages 555--578, 1965.
[2]
C. Aggarwal, Y. Xie, and P. Yu. On dynamic data-driven selection of sensor streams. In ACM SIGKDD Conference on Knowledge Discovery and Data Mining, August 2011.
[3]
W. J. Anderson. Continuous-time Markov chains: an applications-oriented approach. Springer Science & Business Media, 2012.
[4]
O. E. Barndorff-Nielsen and N. Shephard. Non-gaussian ornstein--uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(2):167--241, 2001.
[5]
D. A. Bessler. Relative prices and money: a vector autoregression on brazilian data. American Journal of Agricultural Economics, 66(1):25--30, 1984.
[6]
C. M. Bishop. Pattern recognition and machine learning. springer, 2006.
[7]
P. Bonnet, J. Gehrke, and P. Seshadri. Towards sensor database systems. In Mobile Data Management, pages 3--14. Springer, 2001.
[8]
G. E. Box, G. M. Jenkins, and G. C. Reinsel. Time series analysis: forecasting and control, volume 734. John Wiley & Sons, 2011.
[9]
G. E. Box and D. A. Pierce. Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American statistical Association, 65(332):1509--1526, 1970.
[10]
R. G. Brown. Smoothing, forecasting and prediction of discrete time series. Courier Corporation, 2004.
[11]
C. K. Carter and R. Kohn. On gibbs sampling for state space models. Biometrika, 81(3):541--553, 1994.
[12]
D.-I. Curiac, O. Banias, F. Dragan, C. Volosencu, and O. Dranga. Malicious node detection in wireless sensor networks using an autoregression technique. June 2007.
[13]
J. Friedman and Y. Shachmurove. Co-movements of major european community stock markets: A vector autoregression analysis. Global Finance Journal, 8(2):257--277, 1998.
[14]
Y. Grenier. Time-dependent arma modeling of nonstationary signals. Acoustics, Speech and Signal Processing, IEEE Transactions on, 31(4):899--911, 1983.
[15]
J. D. Hamilton. Time series analysis, volume 2. Princeton university press Princeton, 1994.
[16]
A. C. Harvey. Forecasting, structural time series models and the Kalman filter. Cambridge university press, 1990.
[17]
T. Hida. Brownian motion. Springer, 1980.
[18]
R. A. Holley and D. W. Stroock. Generalized ornstein-uhlenbeck processes and infinite particle branching brownian motions. Publications of the Research Institute for Mathematical Sciences, 14(3):741--788, 1978.
[19]
I. Karatzas and S. Shreve. Brownian motion and stochastic calculus, volume 113. Springer Science & Business Media, 2012.
[20]
K.-j. Kim. Financial time series forecasting using support vector machines. Neurocomputing, 55(1):307--319, 2003.
[21]
H.-M. Krolzig. Predicting markov-switching vector autoregressive processes. Technical report, University of Oxford, Department of Economics, 2000.
[22]
T. C. Mills and R. N. Markellos. The econometric modelling of financial time series. Cambridge University Press, 2008.
[23]
S. Nassar, K.-P. SCHWARZ, N. EL-SHEIMY, and A. Noureldin. Modeling inertial sensor errors using autoregressive (ar) models. Navigation, 51(4):259--268, 2004.
[24]
E. Nicolato and E. Venardos. Option pricing in stochastic volatility models of the ornstein-uhlenbeck type. Mathematical finance, 13(4):445--466, 2003.
[25]
B. Øksendal. Stochastic differential equations. Springer, 2003.
[26]
S. Papadimitriou, J. Sun, and C. Faloutsos. Streaming pattern discovery in multiple time-series. In Proceedings of the 31st international conference on Very large data bases, pages 697--708. VLDB Endowment, 2005.
[27]
G.-J. Qi, C. Aggarwal, D. Turaga, D. Sow, and P. Anno. State-driven dynamic sensor selection and prediction with state-stacked sparseness. In Proceedings of the 21th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pages 945--954. ACM, 2015.
[28]
K. H. Riitters, R. O'neill, C. Hunsaker, J. D. Wickham, D. Yankee, S. Timmins, K. Jones, and B. Jackson. A factor analysis of landscape pattern and structure metrics. Landscape ecology, 10(1):23--39, 1995.
[29]
H. Rue, S. Martino, and N. Chopin. Approximate bayesian inference for latent gaussian models by using integrated nested laplace approximations. Journal of the royal statistical society: Series b (statistical methodology), 71(2):319--392, 2009.
[30]
T. H. Rydberg. The normal inverse gaussian lévy process: simulation and approximation. Communications in statistics. Stochastic models, 13(4):887--910, 1997.
[31]
N. D. Sidiropoulos, R. Bro, and G. B. Giannakis. Parallel factor analysis in sensor array processing. Signal Processing, IEEE Transactions on, 48(8):2377--2388, 2000.
[32]
S. J. Taylor. Modelling financial time series. 2007.
[33]
R. S. Tsay. Analysis of financial time series, volume 543. John Wiley & Sons, 2005.
[34]
D. Tulone and S. Madden. Paq: Time series forecasting for approximate query answering in sensor networks. In Wireless Sensor Networks, pages 21--37. Springer, 2006.
[35]
A. S. Weigend. Time series prediction: forecasting the future and understanding the past. Santa Fe Institute Studies in the Sciences of Complexity, 1994.

Cited By

View all
  • (2023)Reassessing Deep Learning in Time Series: Predicting Time with Foresight2023 International Conference on Advances in Computation, Communication and Information Technology (ICAICCIT)10.1109/ICAICCIT60255.2023.10465902(1379-1384)Online publication date: 23-Nov-2023
  • (2021)Causal Mechanism Transfer Network for Time Series Domain Adaptation in Mechanical SystemsACM Transactions on Intelligent Systems and Technology10.1145/344503312:2(1-21)Online publication date: 9-Mar-2021

Index Terms

  1. Mixture Factorized Ornstein-Uhlenbeck Processes for Time-Series Forecasting

    Recommendations

    Comments

    Information & Contributors

    Information

    Published In

    cover image ACM Conferences
    KDD '17: Proceedings of the 23rd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
    August 2017
    2240 pages
    ISBN:9781450348874
    DOI:10.1145/3097983
    Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

    Sponsors

    Publisher

    Association for Computing Machinery

    New York, NY, United States

    Publication History

    Published: 04 August 2017

    Permissions

    Request permissions for this article.

    Check for updates

    Author Tag

    1. mixture factorized ornstein-uhlenbeck process (mfoup)

    Qualifiers

    • Research-article

    Funding Sources

    • NSF
    • 973 program of China

    Conference

    KDD '17
    Sponsor:

    Acceptance Rates

    KDD '17 Paper Acceptance Rate 64 of 748 submissions, 9%;
    Overall Acceptance Rate 1,133 of 8,635 submissions, 13%

    Upcoming Conference

    KDD '25

    Contributors

    Other Metrics

    Bibliometrics & Citations

    Bibliometrics

    Article Metrics

    • Downloads (Last 12 months)71
    • Downloads (Last 6 weeks)7
    Reflects downloads up to 05 Mar 2025

    Other Metrics

    Citations

    Cited By

    View all
    • (2023)Reassessing Deep Learning in Time Series: Predicting Time with Foresight2023 International Conference on Advances in Computation, Communication and Information Technology (ICAICCIT)10.1109/ICAICCIT60255.2023.10465902(1379-1384)Online publication date: 23-Nov-2023
    • (2021)Causal Mechanism Transfer Network for Time Series Domain Adaptation in Mechanical SystemsACM Transactions on Intelligent Systems and Technology10.1145/344503312:2(1-21)Online publication date: 9-Mar-2021

    View Options

    View options

    PDF

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader

    Login options

    Figures

    Tables

    Media

    Share

    Share

    Share this Publication link

    Share on social media