Trend-cycle decomposition for Peruvian GDP: application of an alternative method


  • Ángel Guille´n Pontificia Universidad Católica del Peru
  • Gabriel Rodríguez Pontificia Universidad Católica del Peru



Trend, Cycle, Mixture of Normals, Asymmetries, Non-linearities, Recessions, Filters


Perron and Wada (J Monet Econ 56:749–765, 2009) propose a new method of decomposition of the GDP in its trend and cycle components, which overcomes the identification problems of models of unobserved components (UC) and ARIMA models and at the same time, admits non-linearities and asymmetries in cycles. The method assumes that output can be represented by a non-linear model of unobserved components, where disturbances consist of a mixture of normal distributions. In this document, we apply thisalgorithm to Peruvian GDP using quarterly data from 1980 until 2011. As a result of this analysis, we choose the UC-CN model, which presents a mixture of normals in the disturbances of the trend and cycle component of output. The obtained trend clearly reflects the structural change undergone in the early 1990s. After a steep decrease of the trend or potential GDP as a result of drastic adjustment measures, output grew in a more stable way in the following years. In the same way, one can observe an increase in the growth rate of potential GDP from 2002 onwards, which coincides with the monetary reforms that took place at the time. Finally, the obtained cycles are consistent with the evolution of the Peruvian economy and of recession periods that have been traditionally identified. A comparison with other methods of decomposition is also provided.


Aguiar M, Gopinath G (2007) Emerging market business cycles: the cycle is the trend. J Polit Econ 115:69–102

Andrews D, Ploberger W (1994) Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62:1383–1414

Apel M, Jansson P (1999) A theory-consistent system approach for estimating potential output and the NAIRU. Econ Lett 64:271–75

Basistha A (2007) Trend-cycle correlation, drift break and the estimation of trend and cycle in Canadian GDP. Can J Econ 40:584–606

Basistha A, Nelson CR (2007) New measures of the output gap based on the forward-looking new Keynesian Phillips curve. J Monet Econ 54:498–511

Baxter M, King RG (1999) Measuring business cycles: approximate band-pass filter for economic time series. Rev Econ Stat 79:551–563

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

Blanchard OJ, Quah D (1989) The dynamic effects of aggregate demand and supply disturbances. Am Econ Rev 79:655–673

Box GEP, Jenkins GM (1976) Time series analysis forecasting and control. Holden-Day, San Francisco

Burns AF, Mitchell WC (1946) Measuring business cycles. National Bureau of Economic Research, New York

Cabredo p, Valdivia L (1999) Estimación del PBI Potencial: Perú 1950 - 1997. Revista de Estudios Económicos 5

Canova F (1998) Detrending and business cycle facts. J Monet Econ 41:475–512

Campbell JY, Mankiw NG (1987) Are output fluctuations transitory?. Q J Econ 102:857–880

Castillo P, Montoro C, Tuesta F (2007) Hechos Estilizados de la Economı´a Peruana. Revista de Estudios Económicos 14:33–75

Christiano LJ, Fitzgerald TJ (2003) The band pass filter. Int Econ Rev 44:435–465

Clark PK (1987) The cyclical component of U.S. economic activity. Q J Econ 102:797–814

Cochrane J (1988) How big is the random walk in GNP?. J Polit Econ 96:893–920

Dancourt O, Mendoza W, Vilcapoma L (1997) Fluctuaciones económicas y shocks externos, Perú 1950-1996. Documento de Trabajo PUCP 135

Dancourt O, Mendoza W (2009) Perú 2008-2009: del auge a la recesión: choque externo y espuestas de políticas macroeconómicas,’’ en Crisis internacional: Impactos and respuestas de política económica en el Perú., ed. Dancourt, O., F. Jimenez, Fondo Editorial PUCP, Lima

Davies RB (1987) Hypothesis testing when a nuisance parameter is present only under the alternative. Biometrika 74:33–43

Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Stat Assoc 74:427–431

Diebold FX, Rudebusch GD (1990) A nonparametric investigation of duration dependence in the American business cycle. J Polit Econ 98:596–616

Diebold FX, Rudebusch GDSichel D (1993) Further evidence on business-cycle duration dependence. Business cycles, indicators and forecasting, University of Chicago Press, Chicago

Dome´nech R, Go´mez V (2006) Estimating potential output, core inflation, and the NAIRU as latent variables. J Bus Econ Stat 24(3):354–365

Elliott G, Rothenberg TJ, Stock JH (1996) Efficient tests for an autoregressive unit root. Econometrica 64:813–836

Fellner W (1956) Trends and cycles in economic activity. Henry Holt, New York

Friedman M (1957) A theory of the consumption function. Princeton University Press, Princeton

Friedman M (1964) Monetary studies of the National Bureau. The National Bureau enters its 45th year, 44th Annual Report, 7-25

Friedman M (1993) The ‘plucking model’ of business fluctuations revisited. Econ Inq 31(2):171–177

Garcia R, Perron P (1996) An analysis of the real interest rate under regime shifts. Rev Econ Stat 78:111–125

Goodwin TH (1993) Business-cycle analysis with a Markov-switching model. J Bus Econ Stat 11:331–339

Guillén Á, Rodríguez G (2013) Trend-cycle decomposition for Peruvian GDP: application of an alternative method. Working Paper, Department of Economics, Pontificia Universidad Católica del Perú

Haggan V, Ozaki T (1981) Modeling nonlinear random vibrations using an amplitude-dependent autoregressive time series model. Biometrika 68:189–196

Hamilton JD (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57:357–384

Hamilton JD, Waggoner DF, Zha T (2004) Normalization in econometrics. Econ Rev 26:221–252

Harrison PJ, Stevens CF (1976) Bayesian forecasting. J R Stat Soc Ser B 38:205–247

Harvey AC (1989) Forecasting, structural time series models and the Kalman filter. Cambridge University Press, Cambridge

Harvey AC, Jaeger A (1993) Detrending, stylized facts and the business cycle. J Appl Econ 8:231–241

Harvey AC, Phillips GDA (1979) The estimation of regression models with autoregressive-moving average disturbances. Biometrika 66:49–58

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

Hodrick R, Prescott E (1997) Postwar US business cycles: an empirical investigation. J Money Credit Bank 29:1–16

Kim CJ, Nelson CR (1999a) Friedman’s plucking model of business fluctuations: tests and estimates of permanent and transitory components. J Money Credit Bank 31:317–334

Kim CJ, Nelson C (1999b) State-space models with regime switching. MIT Press, Cambridge

King RG, Plosser CI, Stock JH, Watson MW (1991) Stochastic trends and economic fluctuations. Am Econ Rev 81:819–840

Kitagawa G (1987) Non-Gaussian state-space modeling of nonstationary time series. J Am Stat Assoc 82:1032–1063

Krolzig HM (1997) Markov-switching vector autoregressions. Modelling, statistical inference, and application to business cycle analysis. Lecture notes in economics and mathematical systems, vol 454. Springer, Berlin

Kuttner NK (1994) Estimating potential output as a latent variable. J Bus Econ Stat 12:361–368

Laubach T (2001) Measuring the NAIRU: evidence from seven economies. Rev Econ Stat 83(2):218–231

Marfa´n M, Artiagoitia P (1989) Estimación del PGB potencial: Chile 1960-1988. Colección de Estudios Cieplan, Diciembre 1989

Miller S (2003) Me´todos Alternativos para la Estimación del PBI potencial: Una aplicación para el caso de Perú. Revista de Estudios Económicos 10

Mills TC, Wang P (2002) Plucking models of business cycle fluctuations: evidence from the G-7 countries. Empir Econ 25:225–276

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

Murray CJ (2003) Cyclical properties of Baxter–King filtered time series. Rev Econ Stat 85:472–476

Muth JF (1960) Optimal properties of exponentially weighted forecasts. J Am Stat Assoc 55:299–306

Nelson CR, Plosser CI (1982) Trends and random walks in macroeconomic time series. J Monet Econ 10:139–162

Neftci SN (1984) Are economic time series asymmetric over the business cycles?. J Polit Econ 92(2):307–328

Ochoa E, Llado´ J (2003) Modelos de indicadores lı´deres de actividad económica para el Perú. Revista de Estudios Económicos 10

Oh K, Zivot E (2006) The Clark model with correlated components. Manuscrito no publicado

Perron P (1989) The great crash, the oil price shock and the unit root hypothesis. Econometrica 57:1361–1401

Perron P, Wada T (2009) Let’s take a break: trends and cycles in US real GDP. J Monet Econ 56:749–765

Rodrı´guez G (2010a) Application of three non-linear econometric approaches to identify business cycles in Peru. OECD J J Bus Cycle Meas Anal 2:1–25

Rodríguez G (2010b) Using a forward-looking Phillips curve to estimate the output gap in Peru. Rev Appl Econ 10:149–160

Rodríguez G (2010c) Estimating output gap, core inflatión, and the NAIRU for Peru, 1979–2007. Appl Econ Int Dev 10:149–160

Said S, Dickey D (1984) Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika 71:599–607

Seminario B, Rodríguez M, Zuloeta J (2007) Me´todos Alternativos para la Estimación del PBI Potencial 1950-2007. Documento de Discusión DD/07/20 UP

Sichel DE (1991) Business cycle duration dependence: a parametric approach. Rev Econ Stat 73:254–260

Sichel DE (1993) Business cycle asymmetry: a deeper look. Econ Inq 31(2):224–236

Stock JH, Watson MW (1988) Variable trends in economic time series. J Econ Perspect 2:147–174

Tsay R (1989) Testing and modeling threshold autoregressive processes. J Am Stat Assoc 84:231–240

Tera¨svirta T, Anderson HM (1992) Characterizing nonlinearities in business cycles using smooth transition autoregressive models. J Appl Econom 7:S119–S136

Tera¨svirta T (1994) Specification, estimation, and evaluation of smooth transition autoregressive models. J Am Stat Assoc 89:208–218

Wada T, Perron P (2006) An alternative trend-cycle decomposition using a state space model with mixtures of normals: specifications and applications to international data. Boston University

Working Paper 2005-44 Versión Septiembre 2006

Watson MW (1986) Univariate detrending methods with stochastic trends. J Monet Econ 18:49–75

Zamowitz V, Boschan C (1977) Cyclical indicators. National Bureau of Economic Research 57th Annual Report, pp 34–38






Regular articles

How to Cite

Trend-cycle decomposition for Peruvian GDP: application of an alternative method. (2024). Latin American Economic Review, 23.

Similar Articles

You may also start an advanced similarity search for this article.