Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Time series analysis

  • Christina M. Mastrangelo
  • James R. Simpson
  • Douglas C. Montgomery
Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_1045

INTRODUCTION

A time series is an ordered sequence of observations. This ordering is usually through time, although other dimensions, such as spatial ordering, are sometimes encountered. A time series can be continuous, as when an electrical signal such as voltage is recorded. Typically, however, most industrial time series are observed and recorded at specific time intervals and are said to be discrete time series. If only one variable is observed, the time series is said to be univariate. However, some time series involve simultaneous observations on several variables. These are called multivariate time series.

There are three general objectives for studying time series: 1) understanding and modeling of the underlying mechanism that generates the time series, 2) prediction of future values, and 3) control of some system for which the time series is a performance measure. Examples of the third application occur frequently in industry. Almost all time series exhibit some structural...

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References

  1. [1]
    Abraham, B. and Ledolter, J. (1983). Statistical Methods for Forecasting. John Wiley, New York.Google Scholar
  2. [2]
    Akaike, H. (1976). “Canonical Correlations Analysis of Time Series and the Use of an Information Criterion,” Advances and Case Studies in System Identification, R. Mehra and D.G. Lainiotis, eds., Academic Press, New York.Google Scholar
  3. [3]
    Box, G.E.P. and Jenkins, G.M. (1976). Time Series Analysis, Forecasting and Control, revised edition, Holden-Day, San Francisco.Google Scholar
  4. [4]
    Box, G.E.P. and Pierce, D.A. (1970). “Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models,” Jl. American Statistical Association, 64. Google Scholar
  5. [5]
    Box, G.E.P. and Tiao, G.C. (1975). “Intervention Analysis with Applications to Economic and Environmental Problems,” Jl. American Statistical Association, 70, 70–79.Google Scholar
  6. [6]
    Brown, R.G. (1962). Smoothing, Forecasting and Prediction of Discrete Time Series, Prentice-Hall, Englewood Cliffs, New Jersey.Google Scholar
  7. [7]
    Chang, I., Tiao, G.C., and Chen, C. (1988). “Estimations of Time Series Parameters in the Presence of Outliers,” Technometrics, 30, 193–204.Google Scholar
  8. [8]
    Cleveland, W.S. (1972). “The Inverse Autocorrelations of a Time Series and Their Applications,” Technometrics, 14, 277–293.Google Scholar
  9. [9]
    Cogger, K.O. (1974). “The Optimality of General-Order Exponential Smoothing,” Operations Research, 22, 858–867.Google Scholar
  10. [10]
    Fox, A.J. (1972). “Outliers in Time Series,” Jl. Royal Statistical Society, Ser. B, 43, 350–363.Google Scholar
  11. [11]
    Fuller, W.A. (1996). Introduction to Statistical Time Series, John Wiley, New York.Google Scholar
  12. [12]
    Goodman, J.L. (1974). “A New Look at Higher-Order Exponential Smoothing for Forecasting,” Operations Research, 22, 880–888.Google Scholar
  13. [13]
    Granger, G.W.C. and Newbold, P. (1977). Forecasting Economic Time Series, Academic Press, New York.Google Scholar
  14. [14]
    Hanan, E.J. (1970). Multiple Time Series, John Wiley, New York.Google Scholar
  15. [15]
    Harvey, A.C. (1981). The Econometric Analysis of Time Series, John Wiley, New York.Google Scholar
  16. [16]
    Holt, C.C. (1957). “Forecasting Trends and Seasonal by Exponentially Weighted Moving Averages,” ONR Memorandum No. 52, Carnegie Institute of Technology. Google Scholar
  17. [17]
    Jenkins, G.M. (1979). Practical Experiences with Modeling and Forecasting Time Series, GJM Publications, Lancaster, England.Google Scholar
  18. [18]
    Kalman, R.E. (1960). “A New Approach to Linear Filtering and Prediction Problems,” ASME Jl. Basic Engineering for Industry, Ser. D, 82, 35–45.Google Scholar
  19. [19]
    Ljung, G.M. and Box, G.E.P. (1978). “On a Measure of Lack of Fit in Time Series Models,” Biometrika, 65, 297–303.Google Scholar
  20. [20]
    Marquardt, D.W. (1963). “An Algorithm for least Squares Estimation of Nonlinear Parameters,” Jl. Society of Industrial and Applied Mathematics, 2, 431–441.Google Scholar
  21. [21]
    McKenzie, E. (1978). The Monitoring of Exponentially Weighted Forecasts,” Jl. Operational Research Society, 29. Google Scholar
  22. [22]
    Montgomery, D.C., Johnson, L.A., and Gardiner, J.S. (1990). Forecasting and Time Series Analysis, 2nd ed., McGraw-Hill, New York.Google Scholar
  23. [23]
    Montgomery, D.C. and Weatherby, G. (1980). “Modeling and Forecasting Time Series Using Transfer Function and Intervention Methods” AIIE Transactions, 12, 289–307.Google Scholar
  24. [24]
    Pandit, S.M. and Wu, S.M. (1974). “Exponential Smoothing as a Special Case of a Linear Stochastic System,” Operations Research, 22, 868–879.Google Scholar
  25. [25]
    Tsay, R.S. (1986). “Nonlinearity Tests for Time Series,” Biometrika, 73, 461–466.Google Scholar
  26. [26]
    Whittle, P. (1963). Prediction and Regulation by Linear Least-Square Methods. Van Nostrand, Princeton, New Jersey.Google Scholar
  27. [27]
    Wichern D.W. and Jones, R.H. (1977). “Assessing the Input of Market Disturbances Using Intervention Analysis,” Management Science, 21, 329–337.Google Scholar
  28. [28]
    Winters, P.R. (1960). “Forecasting Sales by Exponentially Weighted Moving Averages,” Operations Re-search, 22, 858–867.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Christina M. Mastrangelo
    • 1
  • James R. Simpson
    • 2
  • Douglas C. Montgomery
    • 3
  1. 1.University of VirginiaCharlottesvilleUSA
  2. 2.Florida State UniversityTallahasseeUSA
  3. 3.Arizona State UniversityTempeUSA