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Univariate ARMA Processes

  • Jan Beran
Chapter

Abstract

If q = 0, then X t is also called an autoregressive process of order p, or AR(p) process. If p = 0, then X t is also called a moving average process of order p, or MA(q) process.

References

  1. Andrews, G. E., Askey, R., & Roy, R. (1999). Special functions. Cambridge: Cambridge University Press.Google Scholar
  2. Dhrymes, P. (1997). Time series, unit roots and cointegration. Bingley, UK: Emerald Group Publishing Limited.Google Scholar
  3. Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of American Statistical Association, 74, 427–431.Google Scholar
  4. Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55, 251–276.Google Scholar
  5. Gradshteyn, I. S., & Ryzhik, I. M. (1965). Table of integrals, series, and products. New York: Academic Press.Google Scholar
  6. Granger, C. W. J., & Newbold, P. (1974). Spurious regressions in econometrics. Journal of Econometrics, 2(2), 111–120.Google Scholar
  7. Johansen, S. (1995). Likelihood-based inference in cointegrated vector autoregressive models. Oxford: Oxford University Press.Google Scholar
  8. Lang, S. (2003). Complex analysis (4th ed.). New York: Springer.Google Scholar
  9. Lighthill, M. J. (1962). Introduction to Fourier analysis and generalised functions. Cambridge monographs on mechanics and applied mathematics. Cambridge University Press: Cambridge.Google Scholar
  10. Lütkepohl, H. (2006). New introduction to multiple time series analysis. Berlin: Springer.Google Scholar
  11. Phillips, P. C. B. (1986). Understanding spurious regressions in econometrics. Journal of Econometrics, 33(3), 311–340.Google Scholar
  12. Said, E., & Dickey, D. A. (1984). Testing for unit roots in autoregressive moving average models of unknown order. Biometrika, 71, 599–607.Google Scholar
  13. Zygmund, A. (1968). Trigonometric series (Vol. 1). Cambridge: Cambridge University Press.Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Jan Beran
    • 1
  1. 1.Department of Mathematics and StatisticsUniversity of KonstanzKonstanzGermany

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