A Comparison Between Direct and Indirect Seasonal Adjustment of the Chilean GDP 1986-2009 with X-12-ARIMA

Medel, Carlos A. (2014): A Comparison Between Direct and Indirect Seasonal Adjustment of the Chilean GDP 1986-2009 with X-12-ARIMA.

Abstract

It is well known among practitioners that the seasonal adjustment applied to economic time series could involve several decisions to be made by the econometrician. In this paper, I assess which aggregation strategy delivers the best results for the case of the Chilean GDP 1986-2009 quarterly dataset (base year: 2003). This is done by performing an aggregate-by-disaggregate analysis under different schemes, as the fixed base year dataset allows this fair comparison. The analysis is based exclusively on seasonal adjustment diagnostics contained in X-12-ARIMA program. A detailed description of the program and its quality assessment are also provided. The results show that it is preferred, in terms of stability, to use the first block of supply-side disaggregation as well as the direct mode.

• Item Type: MPRA Paper
• Language: English
• Keywords: Seasonal adjustment; univariate time-series models; ARMA; X-12-ARIMA
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C49 - Other; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools; C - Mathematical and Quantitative Methods > C8 - Data Collection and Data Estimation Methodology ; Computer Programs > C87 - Econometric Software

References

Akaike, H. and M. Ishiguro, 1983, Comparative Study of the X-11 and BAYSEA Procedures of Seasonal Adjustment, in A. Zellner (ed.), Applied Time Series Analysis of Economic Data, Bureau of the Census, US Department of Commerce, New York, US.

Almon, S., 1965, "The Distributed Lag Between Capital Appropriations and Net Expenditures," Econometrica 33(1): 178-196.

Astolfi, R., D. Ladiray and G.L. Mazzi, 2001, Seasonal Adjustment of European Aggregates: Direct versus Indirect Approach, Working Document 14 2001, Theme 1 General Statistics, Eurostat.

Banco Central de Chile, 2010, Cuentas Nacionales de Chile 2003-2009, available at: http://www.bcentral.cl/publicaciones/estadisticas/actividad-economica-gasto/pdf/ccnn_2003_2009.pdf.

Battipaglia, P. and D. Focarelli, 1995, A Comparison of Indicators for Evaluating X-11-ARIMA Seasonal Adjustments, Technical Report, Research Department, Bank of Italy.

Bobbitt, L. and M.C. Otto, 1990, Effects of Forecasts on the Revisions of Seasonally Adjusted Values Using the X-11 Seasonal Adjustment Procedure, Proceedings of the Business and Economic Statistics Section, American Statistical Association, pp. 449-453.

Bradley, J.V., 1968, Distribution-Free Statistical Tests, Prentice Hall, Englewood Cliffs, New Jersey, US.

Clements, M.P. and D.F. Hendry, 1996, "Intercept Corrections and Structural Change," Journal of Applied Economics 11(5): 475-494.

Cleveland, W.S. and S.J. Devlin, 1980, Calendar Effects in Monthly Time Series: Detection by Spectrum Analysis and Graphical Methods, Journal of the American Statistical Association 75(371): 487-496.

Cunnyngham, J., 1963, Spectral Analysis of Economic Time Series, Working Paper 16, Bureau of the Census, US Department of Commerce, New York, US.

Dagum, E.B., 1980, The X-11-ARIMA Seasonal Adjustment Method, Statistics Canada.

Findley, D.F., 2005, "Asymptotic Stationary Properties of the Out-of-sample Forecast Errors of Misspecified RegARIMA Models and the Optimality of GLS for One-step-ahead Forecasting," Statistica Sinica 15(2): 447-476.

Findley, D.F. and B.C. Monsell, 1986, New Techniques for Determining if a Time Series can be Seasonally Adjusted Reliably, and their application to US Foreign Trade Series, in M.R. Perryman and J.R. Schmidt, Regional Econometric Modeling, Kluwer-Nijhoff, Amsterdam, The Netherlands.

Findley, D.F, B.C. Monsell, W.R. Bell, M.C. Otto and B.-C. Chen, 1998, "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business and Economic Statistics 16(2): 127-152.

Findley, D.F., B.C. Monsell, H.B. Shulman and M.G. Pugh, 1990, "Sliding Spans Diagnostics for Seasonal and Related Adjustments," Journal of the American Statistical Association 85(410): 345-355.

Gómez, V. and A. Maravall, 1997, Programs TRAMO and SEATS, Instructions for User (Beta Version: September 1996), Working Paper 9628, Bank of Spain.

Granger, C.W.J., 1966, "The Typical Spectral Shape of an Economic Variable," Econometrica 34(1): 150-161.

Granger, C.W.J., 1979, Seasonality: Causation, Interpretation, and Implications, in A. Zellner (ed.) Seasonal Analysis of Economic Time Series, National Bureau of Economic Research, US.

Granger, C.W.J. and M. Hatanaka, 1964, Spectral Analysis of Economic Time Series, Princeton University Press, New Jersey, US.

Granger, C.W.J. and O. Morgenstern, 1963, "Spectral Analysis of Stock Market Prices," Kyklos 16: 1-27.

Hamilton, J., 1994, Time Series Analysis, Princeton University Press, New Jersey, US.

Hatanaka, M., 1963, A Spectral Analysis of Business Cycle Indicators: Lead-lag in Terms of All Time Points, Econometric Research Program, Princeton Research Memorandum 53, Princeton University, US.

Henderson, R., 1916, "Note on Graduation by Adjusted Average," Transactions of the American Society of Actuaries 17: 43-48.

Hood, C.C.H., 2007, Assessment of Diagnostics for the Presence of Seasonality, Proceedings of the International Conference on Establishment Surveys III, June 2007.

Hood, C.C.H. and D.F. Findley, 2001, Comparing Direct and Indirect Seasonal Adjustments of Aggregate Series, American Statistical Association Proceedings, October 2001.

Hood, C.C.H. and Kathleen M. McDonald-Johnson, 2009, Getting Started with X-12-ARIMA Diagnostics, Catherine Hood Consulting: http://www.catherinechhood.net/papers/gsx12diag.pdf.

Kendall, M. and J.K. Ord, 1990, Time Series, Third edition, Oxford University Press, UK.

Koyck, L.M., 1954, Distributed Lags and Investment Analysis, North-Holland Publishing Co., Amsterdam, The Netherlands.

Ladiray, D., 2008, Theoretical and Real Trading-Day Frequencies, American Statistical Association Proceedings, 2008.

Ladiray, D. and B. Quenneville, 2001, Seasonal Adjustment with the X-11 Method, Lecture Notes in Statistics 158, Springer, New York, US.

Ladiray, D. and G.L. Mazzi, 2003, Seasonal Adjustment of European Aggregates: Direct versus Indirect Approach, in M. Manna and R. Peronacci (eds.) Seasonal Adjustment, European Central Bank.

Lothian, J., 1978, The Identification and Treatment of Moving Seasonality in the X-11-ARIMA Seasonal Adjustment Program, Research Paper, Seasonal Adjustment and Time Series Staff, Statistics Canada.

Lothian, J. and M. Morry, 1978, A Set of Quality Control Statistics for the X-11-ARIMA Seasonal Adjustment Method, Research Paper, Statistics Canada.

Maravall, A., 2002, "An Application of TRAMO-SEAT: Automatic Procedure and Sectoral Aggregation. The Japanese Foreign Trade Series," Documento de Trabajo 0207, Banco de España.

Maravall, A., 2005, "An Application of the TRAMO-SEATS Automatic Procedure; Direct Versus Indirect Adjustment," Documento de Trabajo 0524, Banco de España.

Medel, C.A., 2013, "How Informative are In-sample Information Criteria to Forecasting? The Case of Chilean GDP," Latin American Journal of Economics 50(1): 133-161.

Nerlove, M., 1964, "Spectral Analysis of Seasonal Adjustment Procedures," Econometrica 32(3): 241-286.

Otto, M.C., 1985, Effects of Forecasts on the Revisions of Seasonally Adjusted Data Using the X-11 Seasonal Adjustment Procedure, Proceedings of the Business and Economic Statistics Section, American Statistical Association, pp. 463-466.

Otto, M.C., W.R. Bell and J.P. Burman, 1987, An Iterative GLS Approach to Maximum Likelihood Estimation of Regression Models with ARIMA Errors, Proceedings of the Business and Economic Statistics Section, American Statistical Association, pp. 632-637.

Otranto, E. and U. Triacca, 2000, A Distance-based Method for the Choice of Direct or Indirect Seasonal Adjustment, mimeo, Istituto Nazionale di Statistica, Italy.

Peronacci, R., 2003, The Seasonal Adjustment of Euro Area Monetary Aggregates: Direct versus Indirect Approach, in M. Manna and R. Peronacci (eds.) Seasonal Adjustment, European Central Bank.

Priestley, M.B., 1981, Spectral Analysis and Time Series, Volume 1: Univariate Series, Academic Press, Massachusetts, US.

Scheiblecker, M., 2014, "Direct versus Indirect Approach in Seasonal Adjustment," Working Paper 460, Austrian Institute of Economic Research.

Shiskin, J., A.H. Young and J.C. Musgrave, 1967, The X-11 Variant of the Census Method II Seasonal Adjustment Program, Technical Paper 15, Bureau of the Census, US Department of Commerce, New York, US.

Soukup, R.J. and D.F. Findley, 1999, On the Spectrum Diagnostics used by X-12-ARIMA to Indicate the Presence of Trading Day Effects after Modeling for Adjustment, American Statistical Association Proceedings, September 1999.

Stanger, M., 2007, "Empalme del PIB y de los Componentes del Gasto: Series Anuales y Trimestrales 1986-2002, Base 2003 ," Estudio Económico Estadístico 55, Banco Central de Chile.

Wallis, W.A. and G.H. Moore, 1941, A Significance Test for Time Series, National Bureau of Economic Research, Technical Paper No. 1, US.

US Census Bureau, 2011, X-12-ARIMA Reference Manual, Version 0.3, available at http://www.census.gov/srd/www/x12/.