Abstract
This paper presents a new method for detecting turning points in business cycles using the discrete wavelet transform. A methodology is proposed to select the ideal wavelet function and optimize the identification method. We illustrate the method by analyzing the 1957–2021 United States business cycle. We compare the effectiveness of wavelet functions with the classical detection technique usually employed for this type of analysis.
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References
Addo, P. M., Billio, M., & Guégan, D. (2014). Nonlinear dynamics and wavelets for business cycle analysis. In M. Gallegati & W. Semmler (Eds.), Wavelet applications in economics and finance. Dynamic modeling and econometrics in economics and finance (Vol. 20, pp. 73–100). Springer.
Aguiar-Conraria, L., Martins, M. M. F., & Soares, M. J. (2020). Okun’s Law across time and frequencies. Journal of Economic Dynamics and Control, 116, 103897. https://doi.org/10.1016/j.jedc.2020.103897
Aguiar-Conraria, L., & Soares, M. J. (2011). Oil and the macroeconomy: Using wavelets to analyze old issues. Empirical Economics, 40(3), 645–655. https://doi.org/10.1007/s00181-010-0371-x
Ardila, D., & Sornette, D. (2016). Dating the financial cycle with uncertainty estimates: A wavelet proposition. Finance Research Letters, 19, 298–304. https://doi.org/10.1016/j.frl.2016.09.004
Boldin, M. D. (1994). Dating turning points in the business cycle. Journal of Business, 67(1), 97–131.
Bry, G., & Boschan, C. (1971). Cyclical analysis of time series : Selected procedures and computer programs. NBER Technical Paper (Vol. 20). Retrieved from http://www.nber.org/chapters/c2145.pdf
Burns, A. F., & Mitchell, W. C. (1946). Measuring business cycles. NBER Books (Vol. I). Retrieved from http://econpapers.repec.org/bookchap/nbrnberbk/burn46-1.htm
Camacho, M. (2005). Markov-switching stochastic trends and economic fluctuations. Journal of Economic Dynamics and Control, 29(1–2), 135–158. https://doi.org/10.1016/j.jedc.2003.07.002
Camacho, M. (2011). Markov-switching models and the unit root hypothesis in real US GDP. Economics Letters, 112(2), 161–164. https://doi.org/10.1016/j.econlet.2011.03.019
Camacho, M., Gadea, M. D., & Loscos, A. G. (2020). A new approach to dating the reference cycle. Journal of Business and Economic Statistics. https://doi.org/10.1080/07350015.2020.1773834
Camacho, M., & Palmieri, G. (2021). Evaluating the OECD’s main economic indicators at anticipating recessions*. Journal of Forecasting, 40(1), 80–93. https://doi.org/10.1002/for.2709
Canova, F. (1994). Detrending and turning points. European Economic Review, 38(3–4), 614–623. https://doi.org/10.1016/0014-2921(94)90097-3
Canova, F. (1998). Detrending and business cycle facts: A user’s guide. Journal of Monetary Economics, 41(3), 533–540. https://doi.org/10.1016/S0304-3932(98)00008-7
Chen, S.-W. (2006). Simultaneously modeling the volatility of the growth rate of real GDP and determining business cycle turning points: Evidence from the U.S., Canada and the UK. Mathematics and Computers in Simulation, 71(2), 87–102. https://doi.org/10.1016/j.matcom.2005.11.015
Crowley, P. M. (2007). A guide to wavelets for economists. Journal of Economic Surveys, 21(2), 207–267. https://doi.org/10.1111/j.1467-6419.2006.00502.x
Daubechies, I. (1992). Ten lectures on wavelets. Ten lectures on wavelets. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611970104
Debnath, L. (2002). Multiresolution analysis and construction of wavelets. Wavelet transforms and their applications (pp. 403–474). Birkhäuser.
Fawcett, T. (2006). An introduction to ROC analysis. Pattern Recognition Letters, 27(8), 861–874. https://doi.org/10.1016/j.patrec.2005.10.010
FRED | St. Louis Fed. (2020). Real gross domestic product. Retrieved May 15, 2021, from https://fred.stlouisfed.org/series/GDPC1
Gao, R. X., & Yan, R. (2011). Wavelets: Theory and applications for manufacturing. Wavelets: Theory and Applications for Manufacturing. https://doi.org/10.1007/978-1-4419-1545-0
Goupillaud, P., Grossmann, A., & Morlet, J. (1984). Cycle-octave and related transforms in seismic signal analysis. Geoexploration, 23(1), 85–102. https://doi.org/10.1016/0016-7142(84)90025-5
Hamilton, J. D. (1989). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica, 57(2), 357. https://doi.org/10.2307/1912559
Harding, D., & Pagan, A. (2002). Dissecting the cycle: A methodological investigation. Journal of Monetary Economics, 49(2), 365–381. https://doi.org/10.1016/S0304-3932(01)00108-8
Harding, D., & Pagan, A. (2016). The econometric analysis of recurrent events in macroeconomics and finance. The Econometric Analysis of Recurrent Events in Macroeconomics and Finance. https://doi.org/10.23943/princeton/9780691167084.001.0001
Layton, A. P. (1996). Dating and predicting phase changes in the U.S. business cycle. International Journal of Forecasting, 12(3), 417–428. https://doi.org/10.1016/0169-2070(95)00663-X
Lera, C. S., & Sornette, D. (2017). Evidence of a bimodal US GDP growth rate distribution: A wavelet approach. Quantitative Finance and Economics, 1(1), 26–43. https://doi.org/10.3934/qfe.2017.1.26
Mallat, S. G. (1989). A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(7), 674–693. https://doi.org/10.1109/34.192463
Mondaca, C. M. (2012). Estudio de sincronismos entre ciclos económicos mediante la transformada wavelet: Análisis del caso Chile y Mercosur. University of Valladolid. https://doi.org/10.35376/10324/1780
Morley, J., & Piger, J. (2012). The asymmetric business cycle. Review of Economics and Statistics, 94(1), 208–221. https://doi.org/10.1162/REST_a_00169
Nguyen, T., & He, T.-X. (2015). Wavelet applications in economics and finance. Journal of Statistics and Mathematical Sciences. https://doi.org/10.1007/978-3-319-07061-2
Okun, A. M. (1962). Potential GNP: its measurement and significance. In Proceedings of the Business and Economic Statistics Section of the American Statistical Association (pp. 89–104). Alexandria: VA American Statistical Association.
Percival, D. B., & Walden, A. T. (2000). Wavelet methods for time series analysis. Cambridge University Press.
Ramsey, J. B. (1999). The contribution of wavelets to the analysis of economic and financial data. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 357(1760). Retrieved from http://rsta.royalsocietypublishing.org/content/357/1760/2593
Ramsey, J. B. (2002). Wavelets in economics and finance: Past and future. Studies in Nonlinear Dynamics and Econometrics. https://doi.org/10.2202/1558-3708.1090
Ramsey, J. B., & Lampart, C. (1998). Decomposition of economic relationships by timescale using wavelets: Money and income. Macroeconomic Dynamics, 2(1), 49–71. https://doi.org/10.1017/s1365100598006038
Schleicher, C. (2002). An introduction to wavelets for economists (No. 3). Bank of Canada (Vol. 2002). Retrieved from https://pdfs.semanticscholar.org/658c/0cfb2d72937295d148466adeac8954d3ad6c.pdf
Si, D. K., Liu, X. H., & Kong, X. (2019). The comovement and causality between stock market cycle and business cycle in China: Evidence from a wavelet analysis. Economic Modelling, 83, 17–30. https://doi.org/10.1016/j.econmod.2019.10.003
Tsay, R. S., & Chen, R. (2018). Nonlinear time series analysis. Nonlinear Time Series Analysis. https://doi.org/10.1002/9781119514312
Verona, F. (2016a). Time-frequency characterization of the U.S financial cycle. Economics Letters, 144, 75–79. https://doi.org/10.1016/j.econlet.2016.04.024
Verona, F. (2016b). Time-frequency characterization of the U.S. financial cycle. Economics Letters, 144, 75–79. https://doi.org/10.1016/j.econlet.2016.04.024
Wecker, W. E. (1979). Predicting the turning points of a time series. The Journal of Business, 52(1), 35. https://doi.org/10.1086/296032
Zarnowitz, V. (1992). What is a business cycle? The business cycle: Theories and evidence (pp. 3–83). Springer.
Zarnowitz, V., & Ozyildirim, A. (2006). Time series decomposition and measurement of business cycles, trends and growth cycles. Journal of Monetary Economics, 53(7), 1717–1739. https://doi.org/10.1016/j.jmoneco.2005.03.015
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Colther, C., Rojo, J.L. & Hornero, R. A Wavelet Method for Detecting Turning Points in the Business Cycle. J Bus Cycle Res 18, 171–187 (2022). https://doi.org/10.1007/s41549-022-00072-y
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DOI: https://doi.org/10.1007/s41549-022-00072-y