Illuminating ARIMA model-based seasonal adjustment with three fundamental seasonal models

David F. Findley (), Demetra P. Lytras () and Agustin Maravall ()
Additional contact information
David F. Findley: U.S. Census Bureau
Demetra P. Lytras: U.S. Census Bureau
Agustin Maravall: Bank of Spain

SERIEs: Journal of the Spanish Economic Association, 2016, vol. 7, issue 1, No 2, 52 pages

Abstract: Abstract Our starting place is the first order seasonal autoregressive model. Its series are shown to have canonical model-based decompositions whose finite-sample estimates, filters, and error covariances have simple revealing formulas from basic linear regression. We obtain analogous formulas for seasonal random walks, extending some of the results of Maravall and Pierce (J Time Series Anal, 8:177–293, 1987). The seasonal decomposition filters of the biannual seasonal random walk have formulas that explicitly reveal which deterministic functions they annihilate and which they reproduce, directly illustrating very general results of Bell (J Off Stat, 28:441–461, 2012; Center for Statistical Research and Methodology, Research Report Series, Statistics #2015-03, U.S. Census Bureau, Washington, D.C. https://www.census.gov/srd/papers/pdf/RRS2015-03 , 2015). Other formulas express phenomena heretofore lacking such concrete expression, such as the much discussed negative autocorrelation at the first seasonal lag quite often observed in differenced seasonally adjusted series. An innovation that is also applied to airline model seasonal decompositions is the effective use of signs of lag one and first-seasonal-lag autocorrelations (after differencing) to indicate, in a formal way, where smoothness is increased by seasonal adjustment and where its effect is opposite.

Keywords: ARIMA models; Signal extraction smoothness; Timeseries (search for similar items in EconPapers)
JEL-codes: C4 C8 (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13209-016-0139-4

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