Abstract
We demonstrate the poor performance, with seasonal data, of existing methods for endogenously dating multiple structural breaks. Motivated by iterative nonparametric techniques, we present a new approach for estimating parametric structural break models that perform well. We suggest that iterative estimation methods are a simple but important feature of this approach when modelling seasonal data. The methodology is illustrated by simulation and then used for an analysis of monthly short-term visitor arrival time series to New Zealand, to assess the effect of the 9/11 terrorist attacks. While some historical events had a marked structural effect on trends in those arrivals, we show that 9/11 did not.
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References
Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59, 817–858.
Andrews, D. W. K., & Monahan, J. C. (1992). An improved heteroskedasticity and autocorrelation consistent covariance matrix estimator. Econometrica, 60, 953–966.
Australian Bureau of Statistics. (2003). Information paper: A guide to interpreting time series – Monitoring trends. ABS Cat. No. 1349.0. Canberra: Australian Bureau of Statistics.
Bai, J., & Perron, P. (1998). Estimating and testing linear models with multiple structural changes. Econometrica, 66, 47–78.
Bai, J., & Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of Applied Econometrics, 18, 1–22.
Box, G. E. P., & Jenkins, G. M. (1976). Time series analysis, forecasting and control (2nd ed.). Oakland: Holden-Day.
Box, G. E. P., & Tiao, G. C. (1975). Intervention analysis with applications to economic and environmental problems. Journal of the American Statistical Association, 70, 70–79.
Busetti, F., & Harvey, A. (2008). Testing for trend. Econometric Theory, 24, 72–87.
Cleveland, R. B., Cleveland, W. S., McRae, J. E., & Terpenning, I. (1990). STL: A seasonal-trend decomposition procedure based on loess. Journal of Official Statistics, 6, 3–73.
Dungey, M., Fry, R., & Martin, V. L. (2004). Currency market contagion in the Asia-Pacific region. Australian Economic Papers, 43, 379–395.
Findley, D. F., Monsell, B. C., Bell, W. R., Otto, M. C., & Chen, B. C. (1998). New capabilities and methods of the X-12-ARIMA seasonal-adjustment program. Journal of Business and Economic Statistics, 16, 127–177.
Franses, P. H. (1998). Time series models for business and economic forecasting. Cambridge: Cambridge University Press.
Hall, R., Feldstein, M., Bernanke, B., Frankel, J., Gordon, R., & Zarnowitz, V. (2001). The business-cycle peak of March 2001. Technical report, Business Cycle Dating Committee, National Bureau of Economic Research, USA. http://www.nber.org/cycles/november2001/.
Hamilton, J. D. (1994). Time series analysis. Princeton: Princeton University Press.
Harvey, A. C. (1989). Forecasting, structural time series models and the Kalman filter. Cambridge: Cambridge University Press.
Haywood, J., & Randal, J. (2004). Stochastic seasonality, New Zealand visitor arrivals, and the effects of 11 September 2001. Research Report 04-1, School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, New Zealand.
Hoaglin, D. C., Mosteller, F., & Tukey, J. W. (Eds.) (1983). Understanding robust and exploratory data analysis. New York: Wiley.
Kaminsky, G. L., & Schmukler, S. L. (1999). What triggers market jitters? A chronicle of the Asian crisis. Journal of International Money and Finance, 18, 537–560.
Macaulay, F. R. (1931). The smoothing of time series. New York: National Bureau of Economic Research.
Makridakis, S., Wheelwright, S. C., & Hyndman, R. J. (1998). Forecasting: Methods and applications (3rd ed.). New York: Wiley.
NSW Department of Education (1985, April). 1987:Â Perspectives: Looking at Education, 8(4), pp. 3.
Pearce, D. (2001). Tourism. Asia Pacific Viewpoint, 42, 75–84.
R Development Core Team (2007). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461–464.
Statistics New Zealand. (2005). Tourism satellite account 2004. Wellington: Statistics New Zealand.
US Department of State. (2004). Three years after 9/11: Mixed reviews for war on terror. http://www.globalsecurity.org/security/library/news/2004/09/wwwh40915.htm.
Zeileis, A. (2004). Econometric computing with HC and HAC covariance matrix estimators. Journal of Statistical Software, 11(10), 1–17.
Zeileis, A. (2006). Object-oriented computation of sandwich estimators. Journal of Statistical Software, 16(9), 1–16.
Zeileis, A., Kleiber, C., Krämer, W., & Hornik, K. (2003). Testing and dating of structural changes in practice. Computational Statistics and Data Analysis, 44, 109–123.
Zeileis, A., Leisch, F., Hornik, K., & Kleiber, C. (2002). Strucchange: An R package for testing for structural change in linear regression models. Journal of Statistical Software, 7(2), 1–38.
Acknowledgements
Statistics New Zealand kindly supplied the data. We thank those who commented on presentations at Statistics New Zealand, the Reserve Bank of New Zealand, Victoria Management School, the ASC/NZSA 2006 Conference, and the TSEFAR 2006 Conference. We also thank Peter Thomson for some helpful suggestions that improved the paper.
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Haywood, J., Randal, J. (2014). Modelling Seasonality and Structural Breaks: Visitors to NZ and 9/11. In: MacKenzie, G., Peng, D. (eds) Statistical Modelling in Biostatistics and Bioinformatics. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-04579-5_6
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DOI: https://doi.org/10.1007/978-3-319-04579-5_6
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