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).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
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.
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.
Anderson, T.W., and Takemura, A. 1984. Why do noninvertible moving averages occur? Technical report no. 13, Department of Statistics, Stanford University.
Ball, R., and P. Brown. 1968. An empirical evaluation of accounting income numbers. Journal of Accounting Research 6: 159–178.
Box, G.E.P., and G.M. Jenkins. 1970. Time series analysis: Forecasting and control. San Francisco: Holden-Day.
Chow, G.C. 1975. Analysis and control of dynamic economic systems. New York: Wiley.
Dunsmuir, W.T.M., and E.J. Hannan. 1976. Vector linear time series models. Advances in Applied Probability 8(2): 339–364.
Fama, E.F. 1970. Efficient capital markets: A review of theory and empirical work. Journal of Finance 25(2): 383–471.
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.
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.
Granger, C.W.J. 1969. Investigating causal relationships by econometric models and cross-spectral methods. Econometrica 37(3): 424–438.
Granger, C.W.J., and P. Newbold. 1977. Forecasting economic time series. New York: Academic.
Hannan, E.J. 1969a. The identification of vector mixed autoregressive-moving average systems. Biometrika 56(1): 223–225.
Hannan, E.J. 1969b. The estimation of mixed moving average autoregressive systems. Biometrika 56(3): 579–593.
Hannan, E.J. 1970. Multiple time series. New York: Wiley.
Hannan, E.J. 1971. The identification problem for multiple equation systems with moving average errors. Econometrica 39(5): 751–765.
Hannan, E.J. 1980. The estimation of the order of an ARMA process. Annals of Statistics 8(5): 1071–1081.
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.
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.
Harvey, A.C. 1981. Time series models. Oxford: Philip Allan.
Harvey, A.C., and G.D.A. Phillips. 1979. The estimation of regression models with ARMA disturbances. Biometrika 66(1): 49–58.
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.
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.
Kalman, R.E. 1960. A new approach to linear filtering and prediction problems. Transactions of the ASME -Journal of Basic Engineering 82D: 35–45.
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.
Liu, T.C. 1960. Underidentification, structural estimation, and forecasting. Econometrica 28(4): 855–865.
Lütkepohl, H. 1982. Non-causality due to omitted variables. Journal of Econometrics 19: 367–378.
Lütkepohl, H. 1985. Comparison of criteria for estimating the order of a vector autoregressive process. Journal of Time Series Analysis 6(1): 35–52.
Meinhold, R.J., and N.D. Singpurwalla. 1983. Understanding the Kalman filter. American Statistician 37: 123–127.
Nerlove, M. 1972. Lags in economic behaviour. Econometrica 40(2): 221–251.
Nerlove, M., D.M. Grether, and J.L. Carvalho. 1979. Analysis of economic time series: A synthesis. New York: Academic.
Newbold, P. 1974. The exact likelihood function for a mixed autoregressive-moving average process. Biometrika 61(3): 423–426.
Pierce, D.A., and L.D. Haugh. 1977. Causality in temporal systems: Characterizations and a survey. Journal of Econometrics 5(3): 265–293.
Quinn, B.G. 1980. Order determination for a multivariate autoregression. Journal of the Royal Statistical Society, Series B 42(2): 182–185.
Rissanen, H. 1978. Modelling by shortest data description. Automatica 14(5): 465–471.
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.
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.
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.
Schwarz, G. 1978. Estimating the dimension of a model. Annals of Statistics 6(2): 461–464.
Shibata, R. 1976. Selection of the order of an autoregressive model by the AIC. Biometrika 63(1): 117–126.
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.
Sims, C.A. 1972. Money income and causality. American Economic Review 62(4): 540–552.
Sims, C.A. 1980. Macroeconomics and reality. Econometrica 48(1): 1–47.
Slutsky, E. 1927. The summation of random causes as the source of cyclic processes. Trans. Econometrica 5: 105–146.
Tiao, G.C., and G.E.P. Box. 1981. Modeling multiple time series with applications. Journal of the American Statistical Association 76: 802–816.
Walker, G. 1931. On periodicity in series of related terms. Proceedings of the Royal Society of London, Series A 131: 518–532.
Wallis, K.F. 1977. Multiple time series analysis and the final form of econometric models. Econometrica 45(6): 1481–1497.
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.
Whiteman, C.H. 1983. Linear rational expectations models. Minneapolis: University of Minnesota Press.
Whittle, P. 1983. Prediction and regulation by linear least squares methods, 2nd revised. Minneapolis: University of Minnesota Press.
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.
Wold, H. 1938. A study in the analysis of stationary time series. Stockholm: Almqvist and Wiksell.
Yamamoto, T. 1981. Prediction of multivariate autoregressive-moving average models. Biometrika 68(2): 485–492.
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.
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.
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.
Author information
Authors and Affiliations
Editor information
Copyright information
© 2018 Macmillan Publishers Ltd.
About this entry
Cite this entry
Nerlove, M. (2018). Autoregressive and Moving-Average Time-Series Processes. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_623
Download citation
DOI: https://doi.org/10.1057/978-1-349-95189-5_623
Published:
Publisher Name: Palgrave Macmillan, London
Print ISBN: 978-1-349-95188-8
Online ISBN: 978-1-349-95189-5
eBook Packages: Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences