Skip to main content

Trends, Cycles, and Structural Breaks in Cliometrics

  • Living reference work entry
  • First Online:
Handbook of Cliometrics
  • 385 Accesses

Abstract

The calculation of trends and their growth rates, along with the related calculation of cycles, is an important area of cliometrics. The methods traditionally employed to estimate trend were either the estimation of regressions containing simple functions of time, typically in conjunction with a method to deal with regime shifts or structural breaks, or simple unweighted moving averages. In both cases the cycle was determined by residual and, because the trend was, possibly locally, deterministic, the cyclical component took up most of the fluctuations in the observed series. The last 25 years or so, however, have seen major developments in both macroeconomics and time series econometrics and statistics on the modelling of trends and cycles that allow all components to be stochastic and perhaps determined by the statistical properties of the observed time series. This chapter provides a survey of these developments.

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

Access this chapter

Institutional subscriptions

References

  • Aldcroft DH, Fearon P (1972) Introduction. In: Aldcroft DH, Fearon P (eds) British economic fluctuations, 1790–1939. Macmillan, London, pp 1–73

    Google Scholar 

  • Bai J (1997) Estimating multiple breaks one at a time. Econom Theory 13:315–352

    Article  Google Scholar 

  • Bai J, Perron P (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66:47–78

    Article  Google Scholar 

  • Bai J, Perron P (2003a) Computation and analysis of multiple structural change models. J Appl Econom 18:1–22

    Article  Google Scholar 

  • Bai J, Perron P (2003b) Critical values for multiple structural change tests. Econom J 6:72–78

    Article  Google Scholar 

  • Baxter M, King RG (1999) Measuring business cycles: approximate band-pass filters for economic time series. Rev Econ Stat 81:575–593

    Article  Google Scholar 

  • Beveridge S, Nelson CR (1981) A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the “business cycle”. J Monet Econ 7:151–174

    Article  Google Scholar 

  • Broadberry S, Campbell B, Klein A, Overton M, van Leeuwn B (2011) British economic growth, 1270–1870: an output based approach. LSE, London

    Google Scholar 

  • Carvalho V, Harvey AC (2005) Growth, cycles and convergence in US regional time series. Int J Forecast 21:667–686

    Article  Google Scholar 

  • Carvalho V, Harvey AC, Trimbur TM (2007) A note on common cycles, common trends and convergence. J Bus Econ Stat 25:12–20

    Article  Google Scholar 

  • Christiano L, Fitzgerald T (2003) The band pass filter. Int Econ Rev 44:435–465

    Article  Google Scholar 

  • Cox DR (1961) Prediction by exponentially weighted moving averages and related methods. J R Stat Soc Ser B 23:414–422

    Google Scholar 

  • Crafts NFR, Mills TC (1994a) The industrial revolution as a macroeconomic epoch: an alternative view. Econ Hist Rev 47:769–775

    Article  Google Scholar 

  • Crafts NFR, Mills TC (1994b) Trends in real wages in Britain, 1750–1913. Explor Econ Hist 31:176–194

    Article  Google Scholar 

  • Crafts NFR, Mills TC (1996) Europe’s golden age: an econometric investigation of changing trend rates of growth. In: van Ark B, Crafts NFR (eds) Quantitative aspects of Europe’s postwar growth. Cambridge University Press, Cambridge, pp 415–431

    Google Scholar 

  • Crafts NFR, Mills TC (1997) Endogenous innovation, trend growth and the British industrial revolution. J Econ Hist 57:950–956

    Article  Google Scholar 

  • Crafts NFR, Mills TC (2004) After the industrial revolution: the climacteric revisited. Explor Econ Hist 41:156–171

    Article  Google Scholar 

  • Crafts NFR, Leybourne SJ, Mills TC (1989a) Trends and cycles in U.K. industrial production: 1700–1913. J R Stat Soc Ser A 152:43–60

    Article  Google Scholar 

  • Crafts NFR, Leybourne SJ, Mills TC (1989b) The climacteric in late victorian Britain and France: a reappraisal of the evidence. J Appl Econom 4:103–117

    Article  Google Scholar 

  • Feinstein CH, Matthews RCO, Odling-Smee JC (1982) The timing of the climacteric and its sectoral incidence in the UK. In: Kindleberger, CP, di Tella, G (eds) Economics of the Long View, volume 2, part 1, Clarendon Press, Oxford, pp 168–185

    Google Scholar 

  • Ford AG (1969) British economic fluctuations, 1870–1914. Manch Sch 37:99–129

    Article  Google Scholar 

  • Ford AG (1981) The trade cycle in Britain 1860–1914. In: Floud RC, McCloskey DN (eds) The economic history of Britain since 1700. Cambridge University Press, Cambridge, pp 27–49

    Google Scholar 

  • Frickey E (1947) Production in the USA, 1860–1914. Harvard University Press, Cambridge, MA

    Google Scholar 

  • Gómez V (2001) The use of Butterworth filters for trend and cycle estimation in economic time series. J Bus Econ Stat 19:365–373

    Article  Google Scholar 

  • Harris D, Harvey DI, Leybourne SJ, Taylor AMR (2009) Testing for a unit root in the presence of a possible break in trend. Econom Theory 25:1545–1588

    Article  Google Scholar 

  • Harvey AC, De Rossi P (2006) Signal extraction. In: Mills TC, Patterson K (eds) Palgrave handbook of econometrics: volume 1, econometric theory, 970–1000, Palgrave Macmillan, Basingstoke, pp 970–1000

    Google Scholar 

  • Harvey AC, Trimbur TM (2003) General model-based filters for extracting cycles and trends in economic time series. Rev Econ Stat 85:244–255

    Article  Google Scholar 

  • Harvey AC, Trimbur TM, van Dijk HK (2007) Trends and cycles in economic time series: a Bayesian approach. J Econom 140:618–649

    Article  Google Scholar 

  • Hendry DF, Massmann M (2007) Co-breaking: recent advances and a synopsis of the literature. J Bus Econ Stat 25:33–51

    Article  Google Scholar 

  • Hodrick RJ, Prescott EC (1997) Postwar U.S. business cycles: an empirical investigation. J Money Credit Bank 29:1–16

    Article  Google Scholar 

  • Hoffman WG (1955) British industry, 1700–1950. Blackwell, Oxford

    Google Scholar 

  • Hooker RH (1901) Correlation of the marriage rate with trade. J R Stat Soc 64:485–492

    Google Scholar 

  • Janossy F (1969) The end of the economic miracle. IASP, White Plains

    Google Scholar 

  • Kaiser R, Maravall A (2005) Combining filter design with model-based filtering (with an application to business cycle estimation). Int J Forecast 21:691–710

    Article  Google Scholar 

  • Kalman RE (1960) A new approach to linear filtering and prediction theory. J Basic Eng Trans ASME Ser D 82:35–45

    Article  Google Scholar 

  • Kalman RE, Bucy RE (1961) New results in linear filtering and prediction theory. J Basic Eng Trans ASME Ser D 83:95–108

    Article  Google Scholar 

  • Kim D, Perron P (2009) Unit root tests allowing for a break in the trend function at an unknown time under both the null and alternative hypotheses. J Econom 148:1–13

    Article  Google Scholar 

  • Klein JL (1997) Statistical visions in time. A history of time series analysis, 1662–1938. Cambridge University Press, Cambridge

    Google Scholar 

  • Klein LR, Kosobud RF (1961) Some econometrics of growth: great ratios in economics. Quart J Econ 75:173–198

    Article  Google Scholar 

  • Koopman SJ, Harvey AC, Doornik JA, Shephard N (2009) STAMP™ 8: structural time series analysis and predictor. Timberlake Consultants, London

    Google Scholar 

  • Kozicki S (1999) Multivariate detrending under common trend restrictions: implications for business cycle research. J Econ Dyn Control 23:997–1028

    Article  Google Scholar 

  • Leser CEV (1961) A simple method of trend construction. J R Stat Soc Ser B 23:91–107

    Google Scholar 

  • Maravall A, del Rio A (2007) Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter. Comput Stat Data Anal 52:975–998

    Article  Google Scholar 

  • Matthews RCO, Feinstein CH, Odling-Smee JC (1982) British economic growth, 1856–1973. Stanford University Press, Stanford

    Google Scholar 

  • Mills TC (1992) An economic historians’ introduction to modern time series techniques in econometrics. In: Crafts NFR, Broadberry SN (eds) Britain in the international economy 1870–1939. Cambridge University Press, Cambridge, pp 28–46

    Google Scholar 

  • Mills TC (1996) Unit roots, shocks and VARs and their place in history: an introductory guide. In: Bayoumi T, Eichengreen B, Taylor MP (eds) Modern perspectives on the gold standard. Cambridge University Press, Cambridge, pp 17–51

    Google Scholar 

  • Mills TC (2000) Recent developments in modelling trends and cycles in economic time series and their relevance to quantitative economic history. In: Wrigley C (ed) The first world war and the international economy. Edward Elgar, Cheltenham, pp 34–51

    Google Scholar 

  • Mills TC (2009a) Modelling trends and cycles in economic time series: historical perspective and future developments. Cliometrica 3:221–244

    Article  Google Scholar 

  • Mills TC (2009b) Klein and Kosobud’s great ratios revisited. Quant Qual Anal Soc Sci 3:12–42

    Google Scholar 

  • Mills TC (2011) The foundations of modern time series analysis. Palgrave Macmillan, Basingstoke

    Book  Google Scholar 

  • Mills TC, Crafts NFR (1996a) Modelling trends and cycles in economic history. Statistician (J Roy Stat Soc Ser D) 45:153–159

    Google Scholar 

  • Mills TC, Crafts NFR (1996b) Trend growth in British industrial output, 1700–1913: a reappraisal. Explor Econ Hist 33(277–295):1996

    Google Scholar 

  • Mills TC, Crafts NFR (2000) After the golden age: a long run perspective on growth rates that speeded up, slowed down and still differ. Manch Sch 68:68–91

    Article  Google Scholar 

  • Mills TC, Crafts NFR (2004) Sectoral output trends and cycles in Victorian Britain. Econ Model 21:217–232

    Article  Google Scholar 

  • Morgan MS (1990) The history of econometric ideas. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Morley JC, Nelson CR, Zivot E (2003) Why are Beveridge-Nelson and unobserved-component decompositions of GDP so different? Rev Econ Stat 85:235–243

    Article  Google Scholar 

  • Newey WK, West KD (1987) A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55:703–708

    Article  Google Scholar 

  • Percival DB, Walden AT (1999) Wavelet methods for time series analysis. Cambridge University Press, Cambridge

    Google Scholar 

  • Perron P (2006) Dealing with structural breaks. In: Mills TC, Patterson K (eds) Palgrave handbook of econometrics: volume 1, econometric theory, vol 1. Palgrave Macmillan, Basingstoke, pp 278–352

    Google Scholar 

  • Phillips PCB (2005) Challenges of trending time series econometrics. Math Comput Simul 68:401–416

    Article  Google Scholar 

  • Pollock DSG (2009) Investigating economic trends and cycles. In: Mills TC, Patterson K (eds) Palgrave handbook of econometrics: volume 2, applied econometrics. Palgrave Macmillan, Basingstoke, pp 243–307

    Google Scholar 

  • Proietti T (2009a) Structural time series models for business cycle analysis. In: Mills TC, Patterson K (eds) Palgrave handbook of econometrics: volume 2, applied econometrics. Macmillan Palgrave, Basingstoke, pp 385–433

    Google Scholar 

  • Proietti T (2009b) On the model based interpretation of filters and the reliability of trend-cycle filters. Econom Rev 28:186–208

    Article  Google Scholar 

  • Proietti T, Harvey AC (2000) A Beveridge-Nelson smoother. Econ Letts 67:139–146

    Google Scholar 

  • Ravn MO, Uhlig H (2002) On adjusting the Hodrick-Prescott filter for the frequency of observation. Rev Econ Stat 84:371–376

    Article  Google Scholar 

  • Trimbur TM (2006) Properties of higher order stochastic cycles. J Time Ser Anal 27:1–17

    Article  Google Scholar 

  • White H, Granger CWJ (2011) Consideration of trends in time series. J Time Ser Econom 3(Article 2):1–40

    Google Scholar 

  • Young PC (2011) Gauss, Kalman and advances in recursive parameter estimation. J Forecast 30:104–146

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Terence C. Mills .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag Berlin Heidelberg

About this entry

Cite this entry

Mills, T.C. (2014). Trends, Cycles, and Structural Breaks in Cliometrics. In: Diebolt, C., Haupert, M. (eds) Handbook of Cliometrics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40458-0_21-1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40458-0_21-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Online ISBN: 978-3-642-40458-0

  • eBook Packages: Springer Reference Economics and FinanceReference Module Humanities and Social SciencesReference Module Business, Economics and Social Sciences

Publish with us

Policies and ethics