Proietti, Tommaso (2010): Seasonality, Forecast Extensions and Business Cycle Uncertainty.
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Seasonality is one of the most important features of economic time series. The possibility to abstract from seasonality for the assessment of economic conditions is a widely debated issue. In this paper we propose a strategy for assessing the role of seasonal adjustment on business cycle measurement. In particular, we provide a method for quantifying the contribution to the unreliability of the estimated cycles extracted by popular filters, such as Baxter and King and Hodrick-Prescott. The main conclusion is that the contribution is larger around the turning points of the series and at the extremes of the sample period; moreover, it much more sizeable for highpass filters, like the Hodrick-Prescott filter, which retain to a great extent the high frequency fluctuations in a time series, the latter being the ones that are more affected by seasonal adjustment. If a bandpass component is considered, the effect has reduced size. Finally, we discuss the role of forecast extensions and the prediction of the cycle. For the time series of industrial production considered in the illustration, it is not possible to provide a reliable estimate of the cycle at the end of the sample.
|Item Type:||MPRA Paper|
|Original Title:||Seasonality, Forecast Extensions and Business Cycle Uncertainty|
|Keywords:||Linear filters; Unobserved Components; Seasonal Adjustment; Reliability.|
|Subjects:||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
|Depositing User:||Tommaso Proietti|
|Date Deposited:||22. Feb 2010 14:44|
|Last Modified:||13. Feb 2013 11:13|
Baxter, M., and King, R.G. (1999). Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series. The Review of Economics and Statistics, 81, 575–593.
Bell W. R. and Martin D.E.K. (2004). Computation of asymmetric signal extraction filters and mean squared error for ARIMA component models. Journal of Time Series Analysis, 25, 603–623.
Bell W. R. and Hillmer S.C. (1984). Issues involved with the seasonal adjustment of economic time series, Journal of Business and Economic Statistics, 2, 291320.
Caporello, G. and Maravall, A. (2004). Program TSW. Revised Manual Version May 2004. Documentos Occasionales N8 0408, Madrid: Banco de Espana.
Cleveland, W.P. and Tiao, G. C. (1976) Decomposition of Seasonal Time Series A Model for the Census X-11 Program, Journal of the American Statistical Association, 71, 581-587
Cleveland, W.S. (1983), Seasonal and Calendar Adjustment, D. R. Brillinger and P. R. Krishnaiah, eds., Handbook of Statistics, Vol. 3, Elsevier Science Publishers B.V. 0983) 39-72
Christiano L.J., Fitzgerald T.J., (2003), The band pass filter, International Economic Review, 44, 435-465.
Doornik, J.A. (2001). Ox 3.0 - An Object-Oriented Matrix Programming Language, Timberlake Consultants Ltd: London.
Durbin J., and Koopman, S.J. (2001). Time Series Analysis by State Space Methods, Oxford University Press: New York.
Durbin, J., and S.J. Koopman (2002). A simple and efficient simulation smoother for state space time series analysis. Biometrika, 89, 603-615.
Findley, D. F. (2005), Some Recent Developments and Directions in Seasonal Adjustment, Journal of Official Statistics, Vol. 21, No. 2
Findley, D. F., Monsell, B. C., Bell, W. R., Otto, M. C. and Chen, B. (1998), ‘New capabilities and methods of the X-12-ARIMA seasonal adjustment program’, Journal of Business and Economic Statistics 16, 127-177.
Gomez, V., Maravall, A. (1996), Programs TRAMO and SEATS, Banco de Espana, Servicios de Estudios, Documento de trabajo n. 9628.
Harvey, A.C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press: Cambridge.
Hillmer, S.C. and G.C. Tiao (1982), An ARIMA-Model- Based Approach to Seasonal Adjustment, Journal of the American Statistical Association, 77, 63–70.
Hodrick R.J., and Prescott, E.C. (1997). Postwar U.S. Business Cycles: an Empirical Investigation. Journal of Money, Credit and Banking, 29, 1-16.
Kaiser, R. Maravall A., 2001. Measuring Business Cycles in Economic Time Series, Lecture Notes in Statistics, 154, Springer-Verlag, New York.
Kaiser, R. Maravall A., (2005). Combining filter design with model-based filtering (with an application to business-cycle estimation). International Journal of Forecasting, 21, 691–710.
King, R. G., and Rebelo, S. T. (1993). Low frequency filtering and real business cycles. Journal of Economic Dynamics and Control, 17, 207-233.
Koopman S.J., Shepard, N., and Doornik, J.A. (1999), Statistical algorithms for models in state space using SsfPack 2.2, Econometrics Journal, 2, 113- 166.
Maravall, A. (2005). Brief description of the programs. Madrid. Banco de Espana.
Nerlove, M., Grether, D.M. and Carvalho, J.L. (1979), Analysis of Economic Time Series: A Synthesis, New York: Academic Press.
Orphanides A, van Norden S (2002) The Unreliability of Output Gap Estimates in Real Time. The Review of Economics and Statistics, 84, 569-583
Percival D., Walden A. (1993). Spectral Analysis for Physical Applications. Cambridge University Press.
Pollock, D. S. G. (2000). Trend estimation and de-trending via rational square wave filters. Journal of Econometrics, 99, 317 334.
Pollock, D. S. G. (2003). Improved frequency selective filters. Computational Statistics and Data Analysis, 42, 279 297.
Proietti, T. (2000), Comparing seasonal components for structural time series models, International Journal of Forecasting, 16, 247-260.
Proietti T. (2009), On the Model Based Interpretation of Filters and the Reliability of Trend-Cycle Estimates, Econometric Reviews, vol. 28, 186208.
Ravn, M.O. and Uhlig, H. (2002). On adjusting the Hodrick - Prescott filter for the frequency of observations. The Review of Economics and Statistics, 84, 371376.
West, M., Harrison, J. (1997), Bayesian Forecasting and Dynamic Models, 2nd edition, New York, Springer-Verlag.
Whittle P. (1983) Prediction and Regulation by Linear Least Squares Methods, Second edition. Basil Blackwell, Oxford.