IDEAS home Printed from https://ideas.repec.org/a/bpj/jtsmet/v3y2011i1n2.html
   My bibliography  Save this article

Consideration of Trends in Time Series

Author

Listed:
  • White Halbert

    (University of California, San Diego)

  • Granger Clive W.J.

    (University of California, San Diego)

Abstract

Even though the trend components of economic time series were among the first to be distinguished, even today the trend remains relatively little understood. As Phillips (2005) notes, no one understands trends, but everyone sees them in the data. Economists and econometricians can give plenty of examples of trends, such as straight lines, exponentials or polynomials in time, and also forms of random walks, but these are merely examples. Individuals or groups do have their own personal definitions, but these diverse approaches illustrate the lack of a generally accepted definition of a trend. They also suggest a richness of alternatives to consider, both individually and jointly. Here, we make a variety of observations about trends, and based on these, we offer working definitions of various kinds of trends. We emphasize that these are working definitions, as our purpose here is to invite discussion, not to settle matters once and for all. Our hope is that our discussion here may facilitate development of increasingly better methods for prediction, estimation and hypothesis testing for non-stationary time-series data, and ultimately may enable decision makers to make more informed decisions.

Suggested Citation

  • White Halbert & Granger Clive W.J., 2011. "Consideration of Trends in Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-40, February.
  • Handle: RePEc:bpj:jtsmet:v:3:y:2011:i:1:n:2
    DOI: 10.2202/1941-1928.1092
    as

    Download full text from publisher

    File URL: https://doi.org/10.2202/1941-1928.1092
    Download Restriction: For access to full text, subscription to the journal or payment for the individual article is required.

    File URL: https://libkey.io/10.2202/1941-1928.1092?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    2. Vahid, F & Engle, Robert F, 1993. "Common Trends and Common Cycles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(4), pages 341-360, Oct.-Dec..
    3. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    4. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 401-416.
    5. Hendry,David F. & Morgan,Mary S., 1997. "The Foundations of Econometric Analysis," Cambridge Books, Cambridge University Press, number 9780521588706, September.
    6. M. Hashem Pesaran & Davide Pettenuzzo & Allan Timmermann, 2006. "Forecasting Time Series Subject to Multiple Structural Breaks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(4), pages 1057-1084.
    7. Shiller, Robert J, 1981. "Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?," American Economic Review, American Economic Association, vol. 71(3), pages 421-436, June.
    8. KevinJ. Lansing, 2010. "Rational and Near-Rational Bubbles Without Drift," Economic Journal, Royal Economic Society, vol. 120(549), pages 1149-1174, December.
    9. Stock, James H, 1996. "VAR, Error Correction and Pretest Forecasts at Long Horizons," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 58(4), pages 685-701, November.
    10. Granger, Clive W.J. & Jeon, Yongil, 2007. "Long-term forecasting and evaluation," International Journal of Forecasting, Elsevier, vol. 23(4), pages 539-551.
    11. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    12. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    13. Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, September.
    14. Hui Liu & Gabriel Rodriguez, 2003. "Human Activities and Global Warming: A Cointegration Analysis," Working Papers 0307E, University of Ottawa, Department of Economics.
    15. Mark W. French, 2001. "Estimating changes in trend growth of total factor productivity: Kalman and H-P filters versus a Markov-switching framework," Finance and Economics Discussion Series 2001-44, Board of Governors of the Federal Reserve System (U.S.).
    16. Hendry, David F., 1995. "Dynamic Econometrics," OUP Catalogue, Oxford University Press, number 9780198283164.
    17. repec:bla:jecsur:v:12:y:1998:i:5:p:423-69 is not listed on IDEAS
    18. Phillips, Peter C.B. & Magdalinos, Tassos, 2008. "Limit Theory For Explosively Cointegrated Systems," Econometric Theory, Cambridge University Press, vol. 24(4), pages 865-887, August.
    19. LeRoy, Stephen F & Porter, Richard D, 1981. "The Present-Value Relation: Tests Based on Implied Variance Bounds," Econometrica, Econometric Society, vol. 49(3), pages 555-574, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Terence C. Mills, 2013. "Trends, cycles and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 3, pages 45-60, Edward Elgar Publishing.
    2. Wulfrano Gómez & Leovardo Mata & Montserrat Reyna, 2013. "Hodrick-Prescott Filter: An Extreme-Sport Testing," Revista de Administración, Finanzas y Economía (Journal of Management, Finance and Economics), Tecnológico de Monterrey, Campus Ciudad de México, vol. 7(1), pages 1-13.
    3. Joël Cariolle & Michaël Goujon, 2015. "Measuring Macroeconomic Instability: A Critical Survey Illustrated With Exports Series," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 1-26, February.
    4. Gadea Rivas, María Dolores & Gonzalo, Jesús, 2020. "Trends in distributional characteristics: Existence of global warming," Journal of Econometrics, Elsevier, vol. 214(1), pages 153-174.
    5. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    6. Javier Hualde & Morten Ørregaard Nielsen, 2022. "Truncated sum-of-squares estimation of fractional time series models with generalized power law trend," CREATES Research Papers 2022-07, Department of Economics and Business Economics, Aarhus University.
    7. Peter C. B. Phillips & Zhentao Shi, 2021. "Boosting: Why You Can Use The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 521-570, May.
    8. Javier Hidalgo & Jungyoon Lee, 2014. "A Cusum Test of Common Trends in Large Heterogeneous Panels," STICERD - Econometrics Paper Series 576, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    9. Weshah Razzak & Elmostafa Bentour, 2012. "Do Developing Countries Benefit from Foreign Direct Investments?," EERI Research Paper Series EERI_RP_2012_07, Economics and Econometrics Research Institute (EERI), Brussels.
    10. Sosso Feindouno, 2019. "Improving the measurement of export instability in the Economic Vulnerability Index: A simple proposal," Post-Print hal-02167897, HAL.
    11. Sosso Feindouno, 2019. "Improving the measurement of export instability in the Economic Vulnerability Index: A simple proposal," Post-Print hal-02128482, HAL.
    12. Lof, Matthijs & Nyberg, Henri, 2017. "Noncausality and the commodity currency hypothesis," Energy Economics, Elsevier, vol. 65(C), pages 424-433.
    13. T. C. Mills & K. D. Patterson, 2015. "Modelling The Trend: The Historical Origins Of Some Modern Methods And Ideas," Journal of Economic Surveys, Wiley Blackwell, vol. 29(3), pages 527-548, July.
    14. repec:cep:stiecm:/2014/576 is not listed on IDEAS
    15. Gourieroux, Christian & Jasiak, Joann, 2017. "Noncausal vector autoregressive process: Representation, identification and semi-parametric estimation," Journal of Econometrics, Elsevier, vol. 200(1), pages 118-134.
    16. repec:rdg:wpaper:em-dp2013-03 is not listed on IDEAS
    17. Sosso Feindouno, 2019. "Improving the measurement of export instability in the Economic Vulnerability Index: A simple proposal," Economics Bulletin, AccessEcon, vol. 39(2), pages 1629-1638.
    18. Yonghui Zhang & Liangjun Su & Peter C. B. Phillips, 2012. "Testing for common trends in semi‐parametric panel data models with fixed effects," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 56-100, February.
    19. Peter C. B. Phillips & Sainan Jin, 2021. "Business Cycles, Trend Elimination, And The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 469-520, May.
    20. Terence Mills & Kerry Patterson, 2013. "Modelling the Trend: The Historical Origins of Some Modern Methods and Ideas," Economics Discussion Papers em-dp2013-03, Department of Economics, University of Reading.
    21. Yamada, Hiroshi & Yoon, Gawon, 2014. "When Grilli and Yang meet Prebisch and Singer: Piecewise linear trends in primary commodity prices," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 193-207.
    22. Julia Adamska & Łukasz Bielak & Joanna Janczura & Agnieszka Wyłomańska, 2022. "From Multi- to Univariate: A Product Random Variable with an Application to Electricity Market Transactions: Pareto and Student’s t -Distribution Case," Mathematics, MDPI, vol. 10(18), pages 1-29, September.
    23. Razzak Weshah A. & Bentour El M., 2013. "Do Developing Countries Benefit from Foreign Direct Investments? An Analysis of Some Arab and Asian Countries," Review of Middle East Economics and Finance, De Gruyter, vol. 9(3), pages 357-388, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Charles G. Renfro, 2009. "The Practice of Econometric Theory," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75571-5.
    2. Panagiotis Petris & George Dotsis & Panayotis Alexakis, 2022. "Bubble tests in the London housing market: A borough level analysis," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(1), pages 1044-1063, January.
    3. David Greasley & Les Oxley, 2010. "Cliometrics And Time Series Econometrics: Some Theory And Applications," Journal of Economic Surveys, Wiley Blackwell, vol. 24(5), pages 970-1042, December.
    4. Bardsen, Gunnar & Eitrheim, Oyvind & Jansen, Eilev S. & Nymoen, Ragnar, 2005. "The Econometrics of Macroeconomic Modelling," OUP Catalogue, Oxford University Press, number 9780199246502.
    5. Man Fu & Prasad V. Bidarkota, 2011. "Periodically Collapsing Bubbles in Stock Prices Cointegrated with Broad Dividends and Macroeconomic Factors," JRFM, MDPI, vol. 4(1), pages 1-36, December.
    6. Niels Haldrup & Robinson Kruse & Timo Teräsvirta & Rasmus T. Varneskov, 2013. "Unit roots, non-linearities and structural breaks," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 4, pages 61-94, Edward Elgar Publishing.
    7. Akcora, Begum & Kandemir Kocaaslan, Ozge, 2023. "Price bubbles in the European natural gas market between 2011 and 2020," Resources Policy, Elsevier, vol. 80(C).
    8. Knight, John & Satchell, Stephen & Srivastava, Nandini, 2014. "Steady state distributions for models of locally explosive regimes: Existence and econometric implications," Economic Modelling, Elsevier, vol. 41(C), pages 281-288.
    9. Domenico Giannone & Michele Lenza & Giorgio E. Primiceri, 2019. "Priors for the Long Run," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 565-580, April.
    10. Neil R. Ericsson & David F. Hendry & Kevin M. Prestwich, 1998. "The Demand for Broad Money in the United Kingdom, 1878–1993," Scandinavian Journal of Economics, Wiley Blackwell, vol. 100(1), pages 289-324, March.
    11. Bond, Derek & Gallagher, Emer & Ramsey, Elaine, 2012. "A preliminary investigation of northern Ireland's housing market dynamics," MPRA Paper 39806, University Library of Munich, Germany.
    12. Dettoni, Robinson & Gil-Alana, Luis A. & Yaya, OlaOluwa S., 2024. "Stock market prices and Dividends in the US: Bubbles or Long-run equilibria relationships?," International Review of Financial Analysis, Elsevier, vol. 94(C).
    13. Paulo M.M. Rodrigues & Rita Fradique Lourenço, 2015. "House prices: bubbles, exuberance or something else? Evidence from euro area countries," Working Papers w201517, Banco de Portugal, Economics and Research Department.
    14. Escobari, Diego & Garcia, Sergio & Mellado, Cristhian, 2017. "Identifying bubbles in Latin American equity markets: Phillips-Perron-based tests and linkages," Emerging Markets Review, Elsevier, vol. 33(C), pages 90-101.
    15. Horváth, Lajos & Li, Hemei & Liu, Zhenya, 2022. "How to identify the different phases of stock market bubbles statistically?," Finance Research Letters, Elsevier, vol. 46(PA).
    16. Lüders, Erik & Lüders-Amann, Inge & Schröder, Michael, 2004. "The Power Law and Dividend Yields," ZEW Discussion Papers 04-51, ZEW - Leibniz Centre for European Economic Research.
    17. Eric Ghysels & J. Isaac Miller, 2014. "On the Size Distortion from Linearly Interpolating Low-frequency Series for Cointegration Tests," Advances in Econometrics, in: Essays in Honor of Peter C. B. Phillips, volume 14, pages 93-122, Emerald Group Publishing Limited.
    18. David F. Hendry & Grayham E. Mizon, 2016. "Improving the teaching of econometrics," Cogent Economics & Finance, Taylor & Francis Journals, vol. 4(1), pages 1170096-117, December.
    19. Chen, Li & Gao, Jiti & Vahid, Farshid, 2022. "Global temperatures and greenhouse gases: A common features approach," Journal of Econometrics, Elsevier, vol. 230(2), pages 240-254.
    20. Geweke, J. & Joel Horowitz & Pesaran, M.H., 2006. "Econometrics: A Bird’s Eye View," Cambridge Working Papers in Economics 0655, Faculty of Economics, University of Cambridge.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bpj:jtsmet:v:3:y:2011:i:1:n:2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.