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A Diagnostic for Seasonality Based Upon Polynomial Roots of ARMA Models

   | Jun 22, 2021
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Journal of Official Statistics
Special Issue on New Techniques and Technologies for Statistics

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Ansley, C., and W. Wecker. 1984. “Issues involved with the seasonal adjustment of economic time series, comment: on dips in the spectrum of a seasonally adjusted time series.” Journal of Business and Economics Statistics 2(4): 323–324. DOI: https://doi.org/10.1080/07350015.1984.10509400.10.1080/07350015.1984.10509400Search in Google Scholar

Bell, W.R. 1984. “Signal extraction for nonstationary time series.” Annals of Statistics 12(2): 646–664. DOI: https://doi.org/10.1214/aos/1176346512.10.1214/aos/1176346512Search in Google Scholar

Bell, W.R., and S. Hillmer. 1984. “Issues involved with the seasonal adjustment of economic time series.” Journal of Business and Economics Statistics 2(4): 291–320. DOI: https://doi.org/10.1080/07350015.1984.10509398.10.1080/07350015.1984.10509398Search in Google Scholar

Blakely, C., and T.S. McElroy. 2017. “Signal extraction goodness-of-fit diagnostic tests under model parameter uncertainty: formulations and empirical evaluation.” Econometric Reviews 36(4): 447–467. DOI: https://doi.org/10.1080/07474938.2016.1140277.10.1080/07474938.2016.1140277Search in Google Scholar

Busetti, F., and A. Harvey. 2003. “Seasonality tests.” Journal of Business and Economic Statistics 21(3): 420–436. DOI: https://doi.org/10.1198/073500103288619061.10.1198/073500103288619061Search in Google Scholar

Canova, F., and B.E. Hansen. 1995. “Are seasonal patterns constant over time? A test for seasonal stability.” Journal of Business and Economic Statistics 13(3): 237–252. DOI: https://doi.org/10.1080/07350015.1995.10524598.10.1080/07350015.1995.10524598Search in Google Scholar

Chiu, S.T. 1988. “Weighted least squares estimators on the frequency domain for the parameters of a time series.” The Annals of Statistics 16(3): 1315–1326. DOI: https://doi.org/10.1214/aos/1176350963.10.1214/aos/1176350963Search in Google Scholar

Den Butter, F., and M. Fase. 1991. Seasonal Adjustment as a Practical Problem, (Vol. 1991. Amsterdam: North Holland.Search in Google Scholar

Deo, R.S., and W.W. Chen. 2000. “On the integral of the squared periodogram.” Stochastic processes and their applications 85(1): 159–176. DOI: https://doi.org/doi.org/10.1016/S0304-4149(99)00071-X.10.1016/S0304-4149(99)00071-XSearch in Google Scholar

Fase, M., J. Koning, and A. Volgenant. 1973. “An experimental look at seasonal adjustment: a comparative analysis of nine adjustment methods.” De Economist 121: 177–180. DOI: https://doi.org/doi.org/10.1007/BF01712804.10.1007/BF01712804Search in Google Scholar

Findley, D.F., D.P. Lytras, and T.S. McElroy. 2017. Detecting seasonality in seasonally adjusted monthly time series. Census Bureau research report. Available at: www. census.gov/ts/papers/rrs2017-03.pdf (accessed May 2021).Search in Google Scholar

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: 127–177. DOI: https://doi.org/doi.org/10.1080/07350015.1998.10524743.10.2307/1392565Search in Google Scholar

Franses, P.H. 1994. “A multivariate approach to modeling univariate seasonal time series.” Journal of Econometrics: 133–151. DOI: https://doi.org/doi.org/10.1016/0304-4076(93)01563-2.Search in Google Scholar

Furman, J. 2015. “Second estimate of GDP for the first quarter of 2015.” Council of Economic Advisers Blog, May 29, 2015. Available at: https://obamawhitehouse.archives.gov/-blog/2015/05/29/second-estimate-gdp-first-quarter-2015 (accessed May 2021).Search in Google Scholar

Gilbert, C.E., N.J. Morin, A.D. Paciorek, and C.R. Sahm. 2015. “Residual seasonality in GDP.” FEDS Notes. Washington: Board of Governors of the Federal Reserve System, May 14, 2015. DOI: https://doi.org/10.17016/2380-7172.1538.10.17016/2380-7172.1538Search in Google Scholar

Granger, C. 1978. “Seasonality: causation, interpretation, and implications.” In Seasonal Analysis of Economic Time Series, edited by A. Zellner: 33–46. Cambridge, MA: NBER.Search in Google Scholar

Groen, J., and Russo. 2015. “The myth of first-quarter residual seasonality.” Liberty Street Economics. June 8, 2015. Available at: https://libertystreeteconomics.newyorkfed.org/2015/06/the-myth-of-first-quarter-residual-seasonality.html (accessed May 2021).Search in Google Scholar

Hylleberg, S. 1986. Seasonality in Regression, Orlando, Florida: Academic Press.Search in Google Scholar

Hylleberg, S., R.F. Engle, C.W. Granger, and B.S. Yoo. 1990. “Seasonal integration and cointegration.” Journal of econometrics 44(1–2): 215–238. DOI: https://doi.org/10.1016/0304-4076(90)90080-D.10.1016/0304-4076(90)90080-DSearch in Google Scholar

Lengermann, P., N. Morin, A. Paciorek, E. Pinto, and C. Sahm. 2017. “Another Look at Residual Seasonality in GDP.” FEDS Notes. Washington: Board of Governors of the Federal Reserve System, July 28, 2017. DOI: https://doi.org/10.17016/2380-7172.2031.10.17016/2380-7172.2031Search in Google Scholar

Lin, W., J. Huang, and T. McElroy. 2019. “Time series seasonal adjustment methods using regularized singular value decomposition.” Published online. Journal of Business and Economics Statistics: 1–23. DOI: https://doi.org/10.1080/07350015.2018.1515081.10.1080/07350015.2018.1515081Search in Google Scholar

Lunsford, K.G. 2017. Lingering residual seasonality in GDP growth. Economic Commentary, Federal Reserve Bank of Cleveland, March 28, 2017.Search in Google Scholar

Lytras, D.P., R.M. Feldpausch, and W.R. Bell. 2007. “Determining seasonality: a comparison of diagnostics from X-12-ARIMA.” In Proceedings of the Third International Conference on Establishment Surveys (ICES-III June 18–21, 2007, Montreal, Canada. Available at: www.census.gov/ts/papers/ices2007dpl.pdf (accessed May 2021).Search in Google Scholar

Maravall, A. 2003. “A class of diagnostics in the ARIMA-model-based decomposition of a time series.” In Seasonal Adjustment, edited by M. Manna and R. Peronaci: pp. 23–36. Frankfurt am Main: European Central Bank.Search in Google Scholar

McCulla, S.H., and S. Smith. 2015. “Preview of the 2015 annual revision of the national income and product accounts.” Survey of Current Business 95(6): 1–8. Available at: https://apps.bea.gov/scb/pdf/2015/06%20June/0615_preview_of_2015_annual_revision_of_national_income_and_product_accounts.pdf (accessed May 2021).Search in Google Scholar

McElroy, T.S. 2008. “Statistical properties of model-based signal extraction diagnostic tests.” Communications in Statistics, Theory and Methods 37: 591–616. DOI: https://doi.org/10.1080/03610920701669785.10.1080/03610920701669785Search in Google Scholar

McElroy, T.S. 2012. “An alternative model-based seasonal adjustment that reduces over-adjustment.” Taiwan Economic Forecast and Policy 43: 33–70. Available at: http://www.econ.sinica.edu.tw/UpFiles/2013092817175327692/Periodicals_Pdf2013093010104847832/EC431-02.pdf (accessed May 2021).Search in Google Scholar

McElroy, T., and Jach, A. 2019. “Testing collinearity of vector time series.” The Econometrics Journal 22(2): 97–116. DOI: https://doi.org/10.1093/ectj/uty002.10.1093/ectj/uty002Search in Google Scholar

McElroy, T.S., B.C. Monsell, and R.J. Hutchinson. 2018. Modeling of holiday effects and seasonality in daily time series. Census Bureau research report 2018-01. Available at: www.censusgov/srd/papers/pdf/RRS2018-01.pdf (accessed May 2021).Search in Google Scholar

McElroy, T., and D. Politis. 2020. Time Series: a First Course with Bootstrap Starter. New York: Chapman and Hall.10.1201/9780429109553Search in Google Scholar

McElroy, T.S. and A. Roy. 2017. Detection of seasonality in the frequency domain. Census Bureau research report, 2017–01. Available at: www.census.gov/ts/papers/rrs2017-01.pdf (accessed May 2021).Search in Google Scholar

McElroy, T., and A. Roy. 2018. “The inverse Kullback Leibler method for fitting vector moving averages.” Journal of Time Series Analysis 39: 172–191. DOI: https://doi.org/10.1111/jtsa.12276.10.1111/jtsa.12276Search in Google Scholar

Moulton, B.R., and B.D. Cowan. 2016. “Residual seasonality in GDP and GDI: findings and next steps.” Survey of Current Business 96(7): 1–6. Available at: https://apps.bea.gov/scb/pdf/2016/07%20July/0716_residual_seasonality_in_gdp_and_gdi.pdf (accessed May 2021).Search in Google Scholar

Nerlove, M. 1964. “Spectral analysis of seasonal adjustment procedures.” Econometrica 32: 241–286. DOI: https://doi.org/10.2307/1913037.10.2307/1913037Search in Google Scholar

Phillips, K., and J. Wang. 2016. “Residual seasonality in U.S. GDP data.” FRB of Dallas Working Paper No. 1608. DOI: https://doi.org/10.24149/wp1608.10.24149/wp1608Search in Google Scholar

Proietti, T. 1996. “Persistence of shocks on seasonal processes.” Journal of Applied Econometrics 11(4): 383–398. DOI: https://doi.org/10.1002/(SICI)1099-1255(199607)11:4¡383:AID-JAE403¿3.0.CO;2-3.Search in Google Scholar

Rudebusch, G.D., D. Wilson, and T. Mahedy. 2015. “The puzzle of weak first-quarter GDP growth.” FRBSF Economic Letter, May 18, 2015. Available at: https://www.frbsf.org/economic-research/publications/economic-letter/2015/may/weak-first-quarter-gdp-residual-seasonality-adjustment/ (accessed May 2021).Search in Google Scholar

Sims, C. 1978. “Comments on ‘Seasonality: causation, interpretation, and implications’ by Clive W.J. Granger.” In Seasonal Analysis of Economic Time Series, edited by A. Zellner: 47–49. Cambridge, MA: NBER.Search in Google Scholar

Soukup, R., and D. Findley. 1999. “On the spectrum diagnostics used by X-12-ARIMA to indicate the presence of trading day effects after modeling or adjustment.” In 1999 Proceedings American Statistical Association: Alexandria. August 8–12, 1999, Baltimore, Maryland, USA. Available at: www.census.gov/ts/papers/rr9903s.pdf (accessed May 2021).Search in Google Scholar

Stark, T. 2015. “First quarter in the national income and product accounts.” Research Rap, Federal Reserve Bank of Philadelphia, May 14, 2015. Available at: https://www.philadelphiafed.org/-/media/frbp/assets/economy/reports/research-rap/2015/first_quarters_national_income_product_accounts.pdf (accessed May 2021).Search in Google Scholar

Tanaka, K. 1996. Time series analysis: nonstationary and noninvertible distribution theory. New York: John Wiley and Sons.Search in Google Scholar

Tukey, J. 1978. “Comments on ‘Seasonality: causation, interpretation, and implications’ by Clive W.J. Granger.” In Seasonal Analysis of Economic Time Series, edited by A. Zellner: 50–54. Cambridge, MA: NBER.Search in Google Scholar

U.S Census Bureau. 2015. X-13ARIMA-SEATS reference manual. U.S. Census Bureau, Washington D.C., USA. Available at: www.census.gov/ts/x13as/docX13AS.pdf (accessed date May 2021).Search in Google Scholar

Wright, J.H. 2018. “Seasonal adjustment of NIPA data.” NBER working paper, 24895, August 2018. DOI: https://doi.org/10.3386/w24895.10.3386/w24895Search in Google Scholar

eISSN:
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Language:
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