Detection of the industrial business cycle using SETAR models

Ferrara, Laurent and Guégan, Dominique (2005): Detection of the industrial business cycle using SETAR models. Published in: Journal of Business Cycle Measurement and Analysis , Vol. 2, No. 3 (2005): pp. 353-372.

Abstract

In this paper, we consider a threshold time series model in order to take into account certain stylized facts of the industrial business cycle, such as asymmetries in the phases of the cycle. Our aim is to point out some thresholds under (over) which a signal of turning point could be given. First, we introduce the various threshold models and we discuss both their statistical theoretical and empirical properties. Especially, we review the classical techniques to estimate the number of regimes, the threshold, the delay and the parameters of the model. Then, we apply these models to the Euro-zone industrial production index to detect, through a dynamic simulation approach, the dates of peaks and troughs in the business cycle.

• Item Type: MPRA Paper
• Language: English
• Keywords: Economic cycle; turning point detection; Threshold model; Euro-zone IPI
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation; E - Macroeconomics and Monetary Economics > E3 - Prices, Business Fluctuations, and Cycles > E32 - Business Fluctuations ; Cycles; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Akaike, H. (1974), "A New Look of Statistical Model Identification", IEEE Transactions on Automatic Control, 19, 716-722.

Anas, J., Billio, M., Ferrara, L., and LoDuca, M. (2003), "A Turning Point Chronology for the Euro-zone Classical and Growth Cycles", Eurostat Working Paper, presented at the 4th Eurostat Colloquium on Modern Tools for Business Cycle Analysis, Luxembourg, October 2003.

Anas, J., and Ferrara, L. (2004a), "A Comparative Assessment of Parametric and Non-Parametric Turning Points Methods: The Case of the Euro-zone Economy", in Monographs of Official Statistics : Statistical Methods and Business Cycle Analysis of the Euro zone, G.L. Mazzi and G. Savio (eds.), Eurostat, 86-121.

Anas, J., and Ferrara, L. (2004b), "Detecting cyclical turning points: The ABCD approach and two probabilistic indicators", Journal of Business Cycle Measurement and Analysis, 1, 2, 1-36.

Artis, M., Krolzig, H.M., and Toro, J. (2003), "The European Business Cycle", Oxford Economic Papers, 56, 1-44.

Bry, G., and Boschan, C. (1971), Cyclical Analysis of Time Series: Selected Procedures and Computer Programs, NBER, New York.

Chan, K.S. (1993), "Consistency and Limiting Distribution of the Least Squares Estimator of a Threshold Autoregressive Model", Annals of Statistics, 21, 520-533.

Chen, R. (1995), "Threshold Variable Selection in Open-Loop Threshold Autoregressive Models", Journal of Time Series Analysis, 16, 461-481.

Chauvet, M., and Piger, J.M. (2003), "Identifying Business Cycle Turning Points in Real Time", Review of the Federal Reserve Bank of St. Louis, March/April, 47-61.

Clements, M.P., and Smith, J. (2001), "Evaluating Forecasts from SETAR Models of Exchange Rates", Journal of International Money and Finance, 20, 133-148.

Clements, M.P., and Krolzig, H.M. (2003), "Business Cycle Asymmetries: Characterization and Testing Based on Markov-Switching Autoregressions", Journal of Business and Economic Statistics, 21, 1, 196-211.

Coakley, J., Fuertes, A.M., and P\'erez, M.T. (2003), "Numerical Issues in Threshold Autoregressive Modeling of Time Series", Journal of Economic Dynamics and Control, forthcoming.

van Dijk, D., Franses, P.H., and Paap, R. (2002), "A Nonlinear Long Memory Model to US Unemployment", Journal of Econometrics, 110, 135-165.

van Dijk, D., Terasvirta, T., and Franses, P.H. (2002), "Smooth Transition Autoregressive Models - A Survey of Recent Developments", Econometric Reviews, 21, 1-47.

Dufrénot, G., Guégan, D., and Peguin-Feissolle, A. (2005 a), "Long memory dynamics in a SETAR model: Applications to stock markets", Journal of International Financial markets, Institutions and Money, 15, 5.

Dufrénot, G., Guégan, D., and Peguin-Feissolle, A. (2005 b), "Modelling squares returns using a SETAR model with long memory dynamics", Economics Letters, 86, 237 - 243.

Estrella, A., and Mishkin, F.S. (1998), "Predicting US Recessions: Financial Variables as Leading Indicators", Review of Economics and Statistics, 80, 45-61.

Ferrara, L. (2003), "A Three-Regime Real-Time Indicator for the US Economy", Economics Letters, 81, 3, 373 - 378.

Franses, P.H. and D. van Dijk (2000), Non-Linear Time Series Models in Empirical Finance, Cambridge University Press, Cambridge.

Gonzalo, J., and Pitarakis, J.Y. (2002), "Estimation and Model Selection Based Inference in Single and Multiple Threshold Models", Journal of Econometrics, 110, 319 - 352.

de Goojier, J.G., and de Bruin, P.T. (1999), "On Forecasting SETAR Processes", Statistics and Probability Letters, 37, 7 - 14.

Guégan, D. (2003), "Point de Vue Personnel sur le Problème de Contagion en Economie et l'Interaction entre Cycle Réel et Cycle Financier", Note de Recherche MORA-IDHE 06-2003, Ecole Normale Supérieure, Cachan, France.

Hamilton, J.D. (1989), "A New Approach to the Economic Analysis of Non-stationary Time Series and the Business Cycle", Econometrica, 57, 357-384.

Hansen, B.E. (1997), "Inference in TAR Models", Studies in Nonlinear Dynamics and Econometrics, 2, 1-14.

Hansen, B.E. (2000), "Sample splitting and threshold estimation", Econometrica, 68, 575-603.

Harding, D., and Pagan, A. (2001), "A comparison of two business cycle dating methods", unpublished manuscript, University of Melbourne.

Jones, D.A. (1978), "Nonlinear Autoregressive Processes", Proceedings of the Royal Society, A, 360, 71-95.

Krolzig, H.M. (2001), "Markov-Switching Procedures for Dating the Euro-zone Business Cycle", Quarterly Journal of Economic Research, 3, 339-351.

Krolzig, H.M. (2004), "Constructing Turning Point Chronologies with Markov-Switching Vector Autoregressive Models: the Euro-zone Business Cycle", in Monographs of Official Statistics : Statistical Methods and Business Cycle Analysis of the Euro zone, G.L. Mazzi and G. Savio (eds.), Eurostat, 147-190.

Krolzig, H.M., and Toro, J. (2001), "Classical and Modern Business Cycle Measurement: The European Case", Discussion Paper in Economics 60, University of Oxford.

Lahiri, K., and Wang, J.G. (1994), "Predicting Cyclical Turning Points with Leading Index in a Markov-Switching Model", Journal of Forecasting, 13, 245-263.

Lahiri, K., Yao, W., and Young, P. (2004), "Cycles in the Transportation Sector and the Aggregate Economy", Transportation Research Record, National Academies, 103-111.

Maravall, A. and Planas, C.(1999), "Estimation Error and the Specification of Unobserved Component Models", Journal of Econometrics, 92, 325-353.

Pemberton, J. (1985), "Contributions to the Theory of Nonlinear Time Series Models", unpublished Ph.D. Thesis, University of Manchester.

Pfann, G.A., Schotman, P.C., and Tchernig, R. (1996), "Nonlinear Interest Rate Dynamics and Implication for the Term Structure", Journal of Econometrics, 74, 149 - 176.

Potter, S.M. (1995), "A Nonlinear Approach to US GNP", Journal of Applied Econometrics, 10, 109-125.

Potter, S.M. (1999), "Nonlinear Time Series Modelling: An Introduction", Journal of Economic Surveys, 13, 505-528.

Proietti, T. (1998), "Characterizing Asymmetries in Business Cycles Using Smooth-Transition Structural Times Series Models", Studies in Nonlinear Dynamics and Econometrics, 3, 141-156.

Sichel, D.E. (1994), "Inventories and the three phases of the business cycles", Journal of Business and Economic Statistics, 12, 269 - 277.

So, M.K.P., and Chen, C.W.S. (2003), "Subset Threshold Autoregression", Journal of Forecasting, 22, 49-66.

Terasvirta, T., and Anderson, H.M. (1992), "Characterising Nonlinearities in Business Cycles using Smooth Transition Autoregressive Models", Journal of Applied Econometrics, 7, S119 - S136.

Tiao, G.C., and Tsay, R.S. (1994), "Some Advances in Non-Linear and Adaptive Modelling in Time-Series", Journal of Forecasting, 13, 109 - 131.

Tong, H., and Lim, K.S. (1980), "Threshold Autoregression, Limit Cycles and Cyclical Data", Journal of the Royal Statistical Society, B, 42, 245-292.

Tong, H. (1990), Non-linear Time Series: A Dynamical Approach, Oxford Scientific Publications, Oxford.

Tsay, R.S. (1989), "Testing and Modeling Threshold Autoregressive Processes", Journal of the American Statistical Association, 84, 231-240.

Zakoian, J.M. (1994), "Threshold Heteroskedastic Models", Journal of Economic Dynamics and Control, 18, 931-955.