The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Autoregressive and Moving-Average Time-Series Processes

  • Marc Nerlove
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_623

Abstract

Characterization of time series by means of autoregressive (AR) or moving-average (MA) processes or combined autoregressive moving-average (ARMA) processes was suggested, more or less simultaneously, by the Russian statistician and economist, E. Slutsky (1927), and the British statistician G.U. Yule (1921, 1926, 1927). Slutsky and Yule observed that if we begin with a series of purely random numbers and then take sums or differences, weighted or unweighted, of such numbers, the new series so produced has many of the apparent cyclic properties that are thought to characterize economic and other time series. Such sums or differences of purely random numbers are the basis for ARMA models of the processes by which many kinds of economic time series are assumed to be generated, and thus form the basis for recent suggestions for analysis, forecasting and control (e.g., Box and Jenkins 1970).

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Bibliography

  1. Akaike, H. 1973. Information theory and an extension of the maximum likelihood principle. In Second international symposium on information theory, ed. B.N. Petrov and F. Csaki, 267–287. Budapest: Akademiai Kiado.Google Scholar
  2. Anderson, T.W. 1980. Maximum likelihood estimation for vector autoregressive moving average models. In Directions in time series, ed. D.R. Brillinger and G.C. Tiao, 49–59. Hayward: Institute of Mathematical Statistics.Google Scholar
  3. Anderson, T.W., and Takemura, A. 1984. Why do noninvertible moving averages occur? Technical report no. 13, Department of Statistics, Stanford University.Google Scholar
  4. Ball, R., and P. Brown. 1968. An empirical evaluation of accounting income numbers. Journal of Accounting Research 6: 159–178.CrossRefGoogle Scholar
  5. Box, G.E.P., and G.M. Jenkins. 1970. Time series analysis: Forecasting and control. San Francisco: Holden-Day.Google Scholar
  6. Chow, G.C. 1975. Analysis and control of dynamic economic systems. New York: Wiley.Google Scholar
  7. Dunsmuir, W.T.M., and E.J. Hannan. 1976. Vector linear time series models. Advances in Applied Probability 8(2): 339–364.CrossRefGoogle Scholar
  8. Fama, E.F. 1970. Efficient capital markets: A review of theory and empirical work. Journal of Finance 25(2): 383–471.CrossRefGoogle Scholar
  9. Fama, E.F., M. Jensen, L. Fisher, and R. Roll. 1969. The adjustment of stock market prices to new information. International Economic Review 10(1): 1–21.CrossRefGoogle Scholar
  10. Feige, E.L., and D.K. Pierce. 1979. The casual causal relation between money and income: Some caveats for time series analysis. The Review of Economics and Statistics 61(4): 521–533.CrossRefGoogle Scholar
  11. Granger, C.W.J. 1969. Investigating causal relationships by econometric models and cross-spectral methods. Econometrica 37(3): 424–438.CrossRefGoogle Scholar
  12. Granger, C.W.J., and P. Newbold. 1977. Forecasting economic time series. New York: Academic.Google Scholar
  13. Hannan, E.J. 1969a. The identification of vector mixed autoregressive-moving average systems. Biometrika 56(1): 223–225.Google Scholar
  14. Hannan, E.J. 1969b. The estimation of mixed moving average autoregressive systems. Biometrika 56(3): 579–593.CrossRefGoogle Scholar
  15. Hannan, E.J. 1970. Multiple time series. New York: Wiley.CrossRefGoogle Scholar
  16. Hannan, E.J. 1971. The identification problem for multiple equation systems with moving average errors. Econometrica 39(5): 751–765.CrossRefGoogle Scholar
  17. Hannan, E.J. 1980. The estimation of the order of an ARMA process. Annals of Statistics 8(5): 1071–1081.CrossRefGoogle Scholar
  18. Hannan, E.J., and D.F. Nicholls. 1972. The estimation of mixed regression, autoregression, moving average and distributed lag models. Econometrica 40(3): 529–547.CrossRefGoogle Scholar
  19. Hannan, E.J., and B.G. Quinn. 1979. The determination of the order of an autoregression. Journal of the Royal Statistical Society, Series B 41(2): 190–195.Google Scholar
  20. Harvey, A.C. 1981. Time series models. Oxford: Philip Allan.Google Scholar
  21. Harvey, A.C., and G.D.A. Phillips. 1979. The estimation of regression models with ARMA disturbances. Biometrika 66(1): 49–58.Google Scholar
  22. Hillmer, S.C., and G.C. Tiao. 1979. Likelihood function of stationary multiple autoregressive moving average models. Journal of the American Statistical Association 74(367): 652–660.CrossRefGoogle Scholar
  23. Judge, G.G., W.E. Griffiths, R.C. Hill, H. Lütkepohl, and T.C. Lee. 1985. The theory and practice of econometrics, 2nd ed. New York: Wiley.Google Scholar
  24. Kalman, R.E. 1960. A new approach to linear filtering and prediction problems. Transactions of the ASME -Journal of Basic Engineering 82D: 35–45.CrossRefGoogle Scholar
  25. Kashyap, R.L. 1980. Inconsistency of the AIC rule for estimating the order of AR models. IEEE Transactions on Automatic Control 25(5): 996–998.CrossRefGoogle Scholar
  26. Liu, T.C. 1960. Underidentification, structural estimation, and forecasting. Econometrica 28(4): 855–865.CrossRefGoogle Scholar
  27. Lütkepohl, H. 1982. Non-causality due to omitted variables. Journal of Econometrics 19: 367–378.CrossRefGoogle Scholar
  28. Lütkepohl, H. 1985. Comparison of criteria for estimating the order of a vector autoregressive process. Journal of Time Series Analysis 6(1): 35–52.CrossRefGoogle Scholar
  29. Meinhold, R.J., and N.D. Singpurwalla. 1983. Understanding the Kalman filter. American Statistician 37: 123–127.Google Scholar
  30. Nerlove, M. 1972. Lags in economic behaviour. Econometrica 40(2): 221–251.CrossRefGoogle Scholar
  31. Nerlove, M., D.M. Grether, and J.L. Carvalho. 1979. Analysis of economic time series: A synthesis. New York: Academic.Google Scholar
  32. Newbold, P. 1974. The exact likelihood function for a mixed autoregressive-moving average process. Biometrika 61(3): 423–426.CrossRefGoogle Scholar
  33. Pierce, D.A., and L.D. Haugh. 1977. Causality in temporal systems: Characterizations and a survey. Journal of Econometrics 5(3): 265–293.CrossRefGoogle Scholar
  34. Quinn, B.G. 1980. Order determination for a multivariate autoregression. Journal of the Royal Statistical Society, Series B 42(2): 182–185.Google Scholar
  35. Rissanen, H. 1978. Modelling by shortest data description. Automatica 14(5): 465–471.CrossRefGoogle Scholar
  36. Sargan, J.D., and A. Bhargava. 1983. Maximum likelihood estimation of regression models with moving average errors when the root lies on the unit circle. Econometrica 51(3): 799–820.CrossRefGoogle Scholar
  37. Sargent, T.J., and C.A. Sims. 1977. Business cycle modeling without pretending to have too much a priori economic theory. In New methods of business cycle research, ed. C.A. Sims. Minneapolis: Federal Reserve Bank of Minneapolis.Google Scholar
  38. Scholes, M. 1972. The market for securities: Substitution versus price pressure and the effects of information on share prices. Journal of Business 45(2): 179–211.CrossRefGoogle Scholar
  39. Schwarz, G. 1978. Estimating the dimension of a model. Annals of Statistics 6(2): 461–464.CrossRefGoogle Scholar
  40. Shibata, R. 1976. Selection of the order of an autoregressive model by the AIC. Biometrika 63(1): 117–126.CrossRefGoogle Scholar
  41. Shibata, R. 1980. Asymptotically efficient estimates of the order of a model for estimating parameters of a linear process. Annals of Statistics 8(5): 1147–1164.Google Scholar
  42. Sims, C.A. 1972. Money income and causality. American Economic Review 62(4): 540–552.Google Scholar
  43. Sims, C.A. 1980. Macroeconomics and reality. Econometrica 48(1): 1–47.CrossRefGoogle Scholar
  44. Slutsky, E. 1927. The summation of random causes as the source of cyclic processes. Trans. Econometrica 5: 105–146.Google Scholar
  45. Tiao, G.C., and G.E.P. Box. 1981. Modeling multiple time series with applications. Journal of the American Statistical Association 76: 802–816.Google Scholar
  46. Walker, G. 1931. On periodicity in series of related terms. Proceedings of the Royal Society of London, Series A 131: 518–532.CrossRefGoogle Scholar
  47. Wallis, K.F. 1977. Multiple time series analysis and the final form of econometric models. Econometrica 45(6): 1481–1497.CrossRefGoogle Scholar
  48. Wallis, K.F., and W.T. Chan. 1978. Multiple time series modeling: Another look at the mink–muskrat interaction. Applied Statistics 27(2): 168–175.CrossRefGoogle Scholar
  49. Whiteman, C.H. 1983. Linear rational expectations models. Minneapolis: University of Minnesota Press.Google Scholar
  50. Whittle, P. 1983. Prediction and regulation by linear least squares methods, 2nd revised. Minneapolis: University of Minnesota Press.Google Scholar
  51. Wilson, G.T. 1973. The estimation of parameters in multivariate time series models. Journal of the Royal Statistical Society, Series B 35(1): 76–85.Google Scholar
  52. Wold, H. 1938. A study in the analysis of stationary time series. Stockholm: Almqvist and Wiksell.Google Scholar
  53. Yamamoto, T. 1981. Prediction of multivariate autoregressive-moving average models. Biometrika 68(2): 485–492.CrossRefGoogle Scholar
  54. Yule, G.U. 1921. On the time-correlation problem with special reference to the variate-difference correlation method. Journal of the Royal Statistical Society 84: 497–526.CrossRefGoogle Scholar
  55. Yule, G.U. 1926. Why do we sometimes get nonsense correlations between time series? A study in sampling and the nature of time series. Journal of the Royal Statistical Society 89: 1–64.CrossRefGoogle Scholar
  56. Yule, G.U. 1927. On a method for investigating periodicities in disturbed series with special reference to Wolfer’s sunspot numbers. Philosophical Transactions of the Royal Society of London, Series A 226: 267–298.CrossRefGoogle Scholar

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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Marc Nerlove
    • 1
  1. 1.