Skip to main content

Time Series Analysis

  • Reference work entry
  • First Online:
Book cover The New Palgrave Dictionary of Economics

Abstract

The analysis of economic time series is central to a wide range of applications, including business cycle measurement, financial risk management, policy analysis based on structural dynamic econometric models, and forecasting. This article provides an overview of the problems of specification, estimation and inference in linear stationary and ergodic time series models as well as non-stationary models, the prediction of future values of a time series and the extraction of its underlying components. Particular attention is devoted to recent advances in multiple time series modelling, the pitfalls and opportunities of working with highly persistent data, and models of nonlinear dependence.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 6,499.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 8,499.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

  • Adelman, I. 1965. Long cycles – Fact or artifact? American Economic Review 60: 443–463.

    Google Scholar 

  • Akaike, H. 1970. Statistical predictor identification. Annals of the Institute of Statistical Mathematics 22: 203–217.

    Article  Google Scholar 

  • Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control 19: 716–723.

    Article  Google Scholar 

  • Andersen, T., T. Bollerslev, P. Christoffersen, and F. Diebold. 2006a. Volatility and correlation forecasting. In Handbook of economic forecasting, ed. G. Elliott, C. Granger, and A. Zimmermann. Amsterdam: North-Holland.

    Google Scholar 

  • Andersen, T., T. Bollerslev, and F. Diebold. 2006b. Parametric and nonparametric volatility measurement. In Handbook of financial economics, ed. L. Hansen and Y. Ait-Sahalia. Amsterdam: North-Holland.

    Google Scholar 

  • Anderson, T. 1971. The statistical analysis of time series. New York: Wiley.

    Google Scholar 

  • Anderson, T. 1977. Estimation for autoregressive moving average models in the time and frequency domains. Annals of Statistics 5: 842–865.

    Article  Google Scholar 

  • Anderson, T., and A. Takemura. 1986. Why do noninvertible moving averages occur? Journal of Time Series Analysis 7: 235–254.

    Article  Google Scholar 

  • Ansley, C. 1979. An algorithm for the exact likelihood of a mixed autoregressivemoving average process. Biometrika 66: 59–65.

    Article  Google Scholar 

  • Baillie, R. 1996. Long memory processes and fractional integration in econometrics. Journal of Econometrics 73: 5–59.

    Article  Google Scholar 

  • Baillie, R., T. Bollerslev, and H.-O. Mikkelsen. 1996. Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 74: 3–30.

    Article  Google Scholar 

  • Bates, J., and C. Granger. 1969. The combination of forecasts. Operational Research Quarterly 20: 451–468.

    Article  Google Scholar 

  • Bell, W., and S. Hillmer. 1984. Issues involved with seasonal analysis of economic time series. Journal of Business and Economic Statistics 2: 291–349.

    Google Scholar 

  • Bernanke, B. 1986. Alternative explanations of the money-income correlation. Carnegie-Rochester Conference Series on Public Policy 25: 49–100.

    Article  Google Scholar 

  • Bernanke, B., and I. Mihov. 1998. Measuring monetary policy. Quarterly Journal of Economics 113: 869–902.

    Article  Google Scholar 

  • Beveridge, W. 1921. Weather and harvest cycles. Economic Journal 31: 429–452.

    Article  Google Scholar 

  • Beveridge, W. 1922. Wheat prices and rainfall in western Europe. Journal of the Royal Statistical Society 85: 412–459.

    Article  Google Scholar 

  • Blanchard, O., and D. Quah. 1989. The dynamic effects of aggregate demand and supply disturbances. American Economic Review 79: 655–673.

    Google Scholar 

  • Boivin, J., and S. Ng. 2005. Understanding and comparing factor-based forecasts. International Journal of Central Banking 1 (3): 117–152.

    Google Scholar 

  • Bollerslev, T. 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31: 307–327.

    Article  Google Scholar 

  • Box, G., and G. Jenkins. 1970. Time series analysis: Forecasting and control. San Francisco: Holden-Day.

    Google Scholar 

  • Box, G., S. Hillmer, and G. Tiao. 1978. Analysis and modeling of seasonal time series. In Seasonal analysis of economic time series, ed. A. Zellner. Washington, DC: Bureau of the Census, Department of Commerce.

    Google Scholar 

  • Brillinger, D. 1975. Time series: Data analysis and theory. New York: Holt.

    Google Scholar 

  • Burman, J. 1980. Seasonal adjustment by signal extraction. Journal of the Royal Statistical Society. Series A 143: 321–337.

    Article  Google Scholar 

  • Burridge, P., and K. Wallis. 1985. Calculating the variance of seasonally adjusted series. Journal of the American Statistical Association 80: 541–552.

    Article  Google Scholar 

  • Cappé, O., E. Moulines, and T. Ryden. 2005. Inference in hidden Markov models. New York: Springer-Verlag.

    Google Scholar 

  • Chambers, M. 1998. Long memory and aggregation in macroeconomic time series. International Economic Review 39: 1053–1072.

    Article  Google Scholar 

  • Christiano, L., and T. Fitzgerald. 2003. The band pass filter. International Economic Review 44: 435–465.

    Article  Google Scholar 

  • Christoffersen, P., and F. Diebold. 1996. Further results on forecasting and model selection under asymmetric loss. Journal of Applied Econometrics 11: 561–571.

    Article  Google Scholar 

  • Christoffersen, P., and F. Diebold. 1997. Optimal prediction under asymmetric loss. Econometric Theory 13: 808–817.

    Article  Google Scholar 

  • Cournot, A. 1838. Researches into the mathematical principles of the theory of wealth. Trans. N. Bacon. New York: Macmillan, 1927.

    Google Scholar 

  • Diebold, F., and A. Inoue. 2001. Long memory and regime switching. Journal of Econometrics 105: 131–159.

    Article  Google Scholar 

  • Doob, J. 1953. Stochastic processes. New York: Wiley.

    Google Scholar 

  • Durbin, J., and S. Koopman. 2001. Time series analysis by state space methods. Oxford: Oxford University Press.

    Google Scholar 

  • Durlauf, S., and P. Phillips. 1988. Trends versus random walks in time series analysis. Econometrica 56: 1333–1354.

    Article  Google Scholar 

  • Elliott, G. 1998. The robustness of co-integration methods when regressors almost have unit roots. Econometrica 66: 49–58.

    Article  Google Scholar 

  • Engle, R. 1982. Autoregressive conditional heteroskedasticity with estimates of the variance of UK inflation. Econometrica 50: 987–1008.

    Article  Google Scholar 

  • Engle, R., and C. Granger. 1987. Co-integration and error correction: Representation, estimation and testing. Econometrica 55: 251–276.

    Article  Google Scholar 

  • Engle, R., and C. Granger. 1991. Long run economic relations: Readings in co-integration. Oxford: Oxford University Press.

    Google Scholar 

  • Faust, J. 1998. The robustness of identified VAR conclusions about money. Carnegie-Rochester Conference Series on Public Policy 49: 207–244.

    Article  Google Scholar 

  • Faust, J., E. Swanson, and J. Wright. 2004. Identifying VARs based on high frequency futures data. Journal of Monetary Economics 51: 1107–1131.

    Article  Google Scholar 

  • Fishman, G. 1969. Spectral methods in econometrics. Cambridge: Harvard University Press.

    Book  Google Scholar 

  • Franses, P. 1996. Periodicity and stochastic trends in economic time series. Oxford: Oxford University Press.

    Google Scholar 

  • Fuller, W. 1976. Introduction to statistical time series. New York: Wiley.

    Google Scholar 

  • Geweke, J., and S. Porter-Hudak. 1983. The estimation and application of long memory series models. Journal of Time Series Analysis 4: 221–238.

    Article  Google Scholar 

  • Ghysels, E., and D. Osborn. 2001. The econometric analysis of seasonal time series. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Granger, C. 1966. The typical spectral shape of an economic variable. Econometrica 34: 150–161.

    Article  Google Scholar 

  • Granger, C. 1969. Prediction with a generalized cost of error function. Operations Research Quarterly 20: 199–207.

    Article  Google Scholar 

  • Granger, C. 1980. Long memory relationships and the aggregation of dynamic models. Journal of Econometrics 14: 227–238.

    Article  Google Scholar 

  • Granger, C. 1981. Some properties of time series data and their use in econometric model specification. Journal of Econometrics 16: 121–130.

    Article  Google Scholar 

  • Granger, C., and P. Newbold. 1974. Spurious regressions in econometrics. Journal of Econometrics 2: 111–120.

    Article  Google Scholar 

  • Granger, C., and P. Newbold. 1977. Forecasting economic time series. New York: Academic Press.

    Google Scholar 

  • Granger, C., and T. Teräsvirta. 1993. Modelling nonlinear economic relationships. Oxford: Oxford University Press.

    Google Scholar 

  • Grether, D., and M. Nerlove. 1970. Some properties of ‘optimal’ seasonal adjustment. Econometrica 38: 682–703.

    Article  Google Scholar 

  • Hamilton, J. 1989. A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57: 357–384.

    Article  Google Scholar 

  • Hannan, E. 1960. Time series analysis. London: Methuen.

    Google Scholar 

  • Hannan, E. 1969. The estimation of mixed moving average autoregressive systems. Biometrika 56: 223–225.

    Google Scholar 

  • Hannan, E. 1970. Multiple time series. New York: Wiley.

    Book  Google Scholar 

  • Hannan, E. 1971. The identification problem for multiple equation systems with moving average errors. Econometrica 39: 751–765.

    Article  Google Scholar 

  • Hannan, E. 1976. The identification and parameterization of ARMAX and state space forms. Econometrica 44: 713–723.

    Article  Google Scholar 

  • Hannan, E. 1979. The statistical theory of linear systems. In Developments in statistics, ed. P. Krishnaiah. New York: Academic Press.

    Google Scholar 

  • Harvey, A. 1981. Time series models. Oxford: Allan.

    Google Scholar 

  • Harvey, A. 1984. A unified view of statistical forecasting procedures. Journal of Forecasting 3: 245–275.

    Article  Google Scholar 

  • Harvey, A. 1989. Forecasting. Structural time series models and the Kalman filter. Cambridge: Cambridge University Press.

    Google Scholar 

  • Harvey, A., and S. Peters. 1990. Estimation procedures for structural time series models. Journal of Forecasting 9: 89–108.

    Article  Google Scholar 

  • Harvey, A., and P. Todd. 1984. Forecasting economic time series with structural and Box–Jenkins models: A case study (with discussion). Journal of Business and Economic Statistics 1: 299–315.

    Google Scholar 

  • Hatanaka, M. 1975. On the global identification of the dynamic simultaneous equations model with stationary disturbances. International Economic Review 16: 545–554.

    Article  Google Scholar 

  • Hillmer, S., and G. Tiao. 1982. An ARIMA-model-based approach to seasonal adjustment. Journal of the American Statistical Association 77: 63–70.

    Article  Google Scholar 

  • Hillmer, S., W. Bell, and G. Tiao. 1983. Modeling considerations in the seasonal analysis of economic time series. In Applied time series analysis of economic data, ed. A. Zellner. Washington, DC: Bureau of the Census, Department of Commerce.

    Google Scholar 

  • Hodrick, R., and E. Prescott. 1997. Postwar US business cycles: An empirical investigation. Journal of Money, Credit and Banking 29: 1–16.

    Article  Google Scholar 

  • Holt, C. 1957. Forecasting seasonals and trends by exponentially weighted moving averages. ONR Research Memorandum No. 52, Carnegie Institute of Technology.

    Google Scholar 

  • Hylleberg, S. 1992. Modelling seasonality. Oxford: Oxford University Press.

    Google Scholar 

  • Jevons, W. 1884. Investigations in currency and finance. London: Macmillan.

    Google Scholar 

  • Johansen, S. 1995. Likelihood-based inference in cointegrated vector autoregressive models. Oxford: Oxford University Press.

    Book  Google Scholar 

  • Kalman, R. 1960. A new approach to linear filtering and prediction problems. Transactions of the American Society of Mechanical Engineers – Journal of Basic Engineering 82 (Series D): 35–45.

    Google Scholar 

  • King, R., C. Plosser, J. Stock, and M. Watson. 1991. Stochastic trends and economic fluctuations. American Economic Review 81: 819–840.

    Google Scholar 

  • Kolmogorov, A. 1941. Interpolation und Extrapolation von stationären zufälligen Folgen. Bulletin of the Academy Science (Nauk), USSR, Mathematical Series 5: 3–14.

    Google Scholar 

  • Koopmans, L. 1974. The spectral analysis of time series. New York: Academic Press.

    Google Scholar 

  • Kuznets, S. 1961. Capital and the American economy: Its formation and financing. New York: Princeton University Press for the National Bureau of Economic Research.

    Google Scholar 

  • Maravall, A. 1981. Desestacionalization y Politica Monetaria. Economic studies no. 19. Madrid: Bank of Spain.

    Google Scholar 

  • Maravall, A. 1984. Model-based treatment of a manic depressive series. Working paper, Bank of Spain.

    Google Scholar 

  • Muth, J. 1960. Optimal properties of exponentially weighted forecasts. Journal of the American Statistical Association 55: 299–305.

    Article  Google Scholar 

  • Nelson, C., and H. Kang. 1981. Spurious periodicity in inappropriately detrended time series. Econometrica 49: 741–752.

    Article  Google Scholar 

  • Nelson, C., and C. Plosser. 1982. Trends and random walks in macroeconomic time series: Some evidence and implications. Journal of Monetary Economics 10: 139–162.

    Article  Google Scholar 

  • Nerlove, M. 1964. Spectral analysis of seasonal adjustment procedures. Econometrica 32: 241–286.

    Article  Google Scholar 

  • Nerlove, M. 1965. A comparison of a modified Hannan and the BLS seasonal adjustment filters. Journal of the American Statistical Association 60: 442–491.

    Google Scholar 

  • Nerlove, M. 1967. Distributed lags and unobserved components in economic time nseries. In Ten economic essays in the tradition of Irving Fisher, ed. W. Fellner et al. New York: Wiley.

    Google Scholar 

  • Nerlove, M., and S. Wage. 1964. On the optimality of adaptive forecasting. Management Science 10: 207–224.

    Article  Google Scholar 

  • Nerlove, M., D. Grether, and J. Carvalho. 1979. Analysis of economic time series. New York: Academic Press.

    Google Scholar 

  • Newbold, P. 1974. The exact likelihood function for a mixed autoregressive-moving average process. Biometrika 61: 423–426.

    Article  Google Scholar 

  • Parzen, E. 1961. An approach to time series analysis. Annals of Mathematical Statistics 32: 951–989.

    Article  Google Scholar 

  • Phillips, P. 1986. Understanding spurious regressions in econometrics. Journal of Econometrics 33: 311–340.

    Article  Google Scholar 

  • Phillips, P., and S. Durlauf. 1986. Multiple time series regression with integrated processes. Review of Economic Studies 53: 473–495.

    Article  Google Scholar 

  • Phillips, P., and B. Hansen. 1990. Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies 57: 99–125.

    Article  Google Scholar 

  • Pierce, D. 1978. Seasonal adjustment when both deterministic and stochastic seasonality are present. In Seasonal analysis of economic time series, ed. A. Zellner. Washington, DC: Bureau of the Census, Department of Commerce.

    Google Scholar 

  • Pierce, D. 1979. Signal extraction error in nonstationary time series. Annals of Statistics 7: 1303–1320.

    Article  Google Scholar 

  • Priestley, M. 1981. Spectral analysis and time series. New York: Academic Press.

    Google Scholar 

  • Raftery, A., D. Madigan, and J. Hoeting. 1997. Bayesian model averaging for linear regression models. Journal of the American Statistical Association 92: 179–191.

    Article  Google Scholar 

  • Ravn, M., and H. Uhlig. 2002. On adjusting the HP-filter for the frequency of observations. Review of Economics and Statistics 84: 371–376.

    Article  Google Scholar 

  • Rigobon, R. 2003. Identification through heteroskedasticity. Review of Economics and Statistics 85: 777–792.

    Article  Google Scholar 

  • Rudebusch, G. 1993. The uncertain unit root in real GNP. American Economic Review 83: 264–272.

    Google Scholar 

  • Sargan, J., and A. Bhargava. 1983. Maximum likelihood estimation of regression models with moving average errors when the root lies on the unit circle. Econometrica 51: 799–820.

    Article  Google Scholar 

  • Schuster, A. 1898. On the investigation of hidden periodicities with application to the supposed 26-day period of meteorological phenomena. Terrestrial Magnetism and Atmospheric Electricity [now Journal of Geophysical Research] 3: 13–41.

    Google Scholar 

  • Schwarz, G. 1978. Estimating the dimension of a model. Annals of Statistics 6: 461–464.

    Article  Google Scholar 

  • Schweppe, F. 1965. Evaluation of likelihood functions for Gaussian signals. IEEE Transactions on Information Theory 11: 61–70.

    Article  Google Scholar 

  • Shapiro, M., and M. Watson. 1988. Sources of business cycle fluctuations. NBER Macroeconomics Annual 3: 111–156.

    Article  Google Scholar 

  • Shephard, N. 2005. Stochastic volatility: Selected readings. Oxford: Oxford University Press.

    Google Scholar 

  • Sims, C. 1980. Macroeconomics and reality. Econometrica 48: 1–48.

    Article  Google Scholar 

  • Sims, C. 1986. Are forecasting models usable for policy analysis? Quarterly Review, Federal Reserve Bank of Minneapolis 10: 2–16.

    Google Scholar 

  • Sims, C., J. Stock, and M. Watson. 1991. Inference in linear time series models with some unit roots. Econometrica 58: 113–144.

    Article  Google Scholar 

  • Slutsky, E. 1927. The summation of random causes as the source of cyclic processes. Econometrica 5 (April 1937): 105–46.

    Google Scholar 

  • Sowell, F. 1992. Maximum likelihood estimation of stationary univariate fractionally integrated time series models. Journal of Econometrics 53: 165–188.

    Article  Google Scholar 

  • Stock, J. 1991. Confidence intervals for the largest autoregressive root in US economic time series. Journal of Monetary Economics 28: 435–460.

    Article  Google Scholar 

  • Stock, J., and M. Watson. 1993. A simple estimator of cointegrating vectors in higher order integrated systems. Econometrica 61: 783–820.

    Article  Google Scholar 

  • Stock, J., and M. Watson. 2002a. Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association 97: 1167–1179.

    Article  Google Scholar 

  • Stock, J., and M. Watson. 2002b. Macroeconomic forecasting using diffusion indexes. Journal of Business and Economic Statistics 20: 147–162.

    Article  Google Scholar 

  • Stokes, G. 1879. Note on searching for hidden periodicities. Proceedings of the Royal Society 29: 122–125.

    Google Scholar 

  • Theil, H., and S. Wage. 1964. Some observations on adaptive forecasting. Management Science 10: 198–206.

    Article  Google Scholar 

  • Wallis, K. 1977. Multiple time series analysis and the final form of econometric models. Econometrica 45: 1481–1497.

    Article  Google Scholar 

  • Whittle, P. 1963. Prediction and regulation by linear least-squares methods. London: English Universities Press.

    Google Scholar 

  • Wiener, N. 1949. The extrapolation, interpolation and smoothing of stationary time series with engineering applications. New York: Wiley.

    Google Scholar 

  • Winters, P. 1960. Forecasting sales by exponentially weighted moving averages. Management Science 6: 324–342.

    Article  Google Scholar 

  • Wold, H. 1938. A study in the analysis of stationary time series. Stockholm: Almqvist and Wiksell.

    Google Scholar 

  • Yule, G. 1921. On the time-correlation problem, with special reference to the variate difference correlation method. Journal of the Royal Statistical Society 84: 497–526.

    Article  Google Scholar 

  • Yule, G. 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.

    Article  Google Scholar 

  • Yule, G. 1927. On a method of investigating periodicities in disturbed series with special reference to Wolfer’s sunspot numbers. Philosophical Transactions of the Royal Society of London A 226: 267–298.

    Article  Google Scholar 

  • Zellner, A., and F. Palm. 1974. Time series analysis and simultaneous equation econometric models. Journal of Econometrics 2: 17–54.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Copyright information

© 2018 Macmillan Publishers Ltd.

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Diebold, F.X., Kilian, L., Nerlove, M. (2018). Time Series Analysis. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_1491

Download citation

Publish with us

Policies and ethics