×

Testing for adequacy of seasonal adjustment in the frequency domain. (English) Zbl 1455.62179

Summary: Peaks in the spectral density estimates of seasonally adjusted data are indicative of an inadequate adjustment. Spectral peaks are currently assessed in the X-13ARIMA-SEATS program via the visual significance (VS) approach; this paper provides a rigorous statistical foundation for VS by defining measures of uncertainty for spectral peak measures, allowing for formal hypothesis testing, using the framework of fixed-bandwidth fraction asymptotics for taper-based spectral density estimates. The simulation results show that the test has good size and power properties for a variety of peak features.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M15 Inference from stochastic processes and spectral analysis
62G10 Nonparametric hypothesis testing
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bell, W. R.; Hillmer, S. C., Modeling time series with calendar variation, J. Amer. Statist. Assoc., 78, 526-534 (1983) · Zbl 0534.62063
[2] Berger, R. L., Uniformly more powerful tests for hypotheses concerning linear inequalities and normal means, J. Amer. Statist. Assoc., 84, 192-199 (1989) · Zbl 0683.62035
[3] Findley, D. F., Some recent developments and directions in seasonal adjustment, J. Off. Stat., 21, 343-365 (2005)
[4] Findley, D. F.; Lytras, D. P.; McElroy, T. S., Detecting Seasonality in Seasonally Adjusted Monthly Time SeriesResearch report series, Statistics 2017-03 (2017), U.S. Census Bureau
[5] Grether, D. M.; Nerlove, M., Some properties of optimal seasonal adjustment, Econometrica, 38, 682-703 (1970)
[6] Hashimzade, N.; Vogelsang, T., Fixed-b asymptotic approximation of the sampling behaviour of nonparametric spectral density estimators, J. Time Series Anal., 29, 142-162 (2008) · Zbl 1164.62061
[7] Hylleberg, S., Seasonality in Regression (1986), Academic Press: Academic Press Orlando, Florida · Zbl 0718.90021
[8] Liu, H.; Berger, R. L., Uniformly more powerful, one-sided tests for hypotheses about linear inequalities, Ann. Statist., 23, 55-72 (1995) · Zbl 0821.62011
[9] Lytras, D. P.; Feldpausch, R. M.; Bell, W. R., Determining aeasonality: a comparison of diagnostics from X-13-ARIMA, (Proceedings of the Third International Conference on Establishment Surveys (2007)), http://www.census.gov/srd/www/sapaper/sapaper.html
[10] Maravall, A., 2012. Update of seasonality tests and automatic model identification in TRAMO-SEATS. Working paper, Bank of Spain.
[11] McElroy, T.; Holan, S., A nonparametric test for residual seasonality, Surv. Meth., 35, 67-83 (2009)
[12] McElroy, T.; Politis, D., Spectral density and spectral distribution inference for long memory time series via fixed-b asymptotics, J. Econometrics, 182, 211-225 (2014) · Zbl 1311.62151
[13] McElroy, T.; Roy, A., Detection of Seasonality in the Frequency DomainResearch report series, Statistics 2017-01 (2017), U.S. Census Bureau, https://www.census.gov/srd/papers/pdf/RRS2017-03.pdf
[14] Nerlove, M., Spectral analysis of seasonal adjustment procedures, Econometrica, 32, 241-286 (1964) · Zbl 0129.33901
[15] Parzen, E., On consistent estimates of the spectrum of a stationary time series, Ann. Math. Stat., 28, 329-348 (1957) · Zbl 0081.14102
[16] Pierce, D.A., 1976. Uncertainty in seasonal adjustment procedures. In: Proceedings of the Business and Economic Statistics Section of the American Statistical Association. Washington, D.C. pp. 528-533.
[17] Pierce, D. A., Seasonal adjustment when both deterministic and stochastic seasonality are present, (Zellner, Arnold, Seasonal Analysis of Economic Time Series (1979), NBER), 242-280
[18] Priestley, M. B., Spectral Analysis and Time Series (1981), Academic Press: Academic Press New York · Zbl 0537.62075
[19] Sasabuchi, S., A test of a multivariate normal mean with composite hypotheses determined by linear inequalities, Biometrika, 67, 429-439 (1980) · Zbl 0437.62053
[20] Soukup, R., Findley, D., 1999. On the spectrum diagnostics used by X-13-ARIMA to indicate the presence of trading day effects after modeling or adjustment. In: Proceedings of the Third International Conference on Establishment Surveys (ICES-III). Montreal, Canada.
[21] Sun, Y., Let’s fix it: Fixed-b asymptotics versus small-b asymptotics in heteroskedasticity and autocorrelation robust inference, J. Econometrics, 178, 659-677 (2014) · Zbl 1293.62108
[22] X-13ARIMA-SEATS Reference Manual (2015), U.S. Census Bureau: U.S. Census Bureau Washington D.C. USA, (Available from https://www.census.gov/ts/x13as/docX13AS.pdf)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.