Frequency Domain Analyses of SEATS and X-11/12-ARIMA Seasonal Adjustment Filters for Short and Moderate-Length Time Series

We investigate frequency domain properties, revealed by the squared gain and phase delay functions, of short and moderate-length linear seasonal adjustment filters of the ARIMAmodel-based signal extraction method of SEATS. X-11/12-ARIMA filters are also considered to a limited extent. The focus is on the one-sided (concurrent) and symmetric (central) filters associated with the Box and Jenkins’s airline model for monthly time series of lengths 49 and 109. A Digital Signal Processing perspective on filter properties, favoring interpretability of the filter output, is presented. We show that important features of the finite filters actually used are often not visible in the diagnostics of the infinite filters, such as the Wiener-Kolmogorov symmetric filter gain functions provided by SEATS. For comparing competing adjustments, properties of concurrent filters, especially their phase delays, can be more important than properties of symmetric filters. Our phase delay results illustrate that adjusters who favor smoother seasonal adjustments, or who favor trends for their greater smoothness, must usually reckon with greater delay of turning point and business cycle information for the most recent months. Trend filters are considered briefly. New analytical results are obtained for transfer functions and phase delays.

[1]  A. Izenman,et al.  Fourier Analysis of Time Series: An Introduction , 1977, IEEE Transactions on Systems, Man and Cybernetics.

[2]  G. Huyot,et al.  Analysis of Revisions in the Seasonal Adjustment of Data Using X-11-Arima Model-Based filters , 1986 .

[3]  Genshiro Kitagawa,et al.  A NONSTATIONARY TIME SERIES MODEL AND ITS FITTING BY A RECURSIVE FILTER , 1981 .

[4]  R. Kohn,et al.  Estimation, Prediction, and Interpolation for ARIMA Models with Missing Data , 1986 .

[5]  赤池 弘次,et al.  BAYSEA, a bayesian seasonal adjustment program , 1980 .

[6]  D. Findley,et al.  GENERALIZATIONS OF THE BOX-JENKINS AIRLINE MODEL , 2002 .

[7]  J. Burman.  Seasonal Adjustment by Signal Extraction , 1980 .

[8]  Víctor Gómez,et al.  Seasonal Adjustment and Signal Extraction in Economic Time Series , 1998 .

[9]  B. Anderson,et al.  Optimal Filtering , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[10]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[11]  D. B. Preston.  Spectral Analysis and Time Series , 1983 .

[12]  A. Yaglom,et al.  An Introduction to the Theory of Stationary Random Functions , 1963 .

[13]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[14]  A. Maravall.  Short-term analysis of macroeconomic time series , 1996 .

[15]  E. Dagum.  Spectral properties of the concurrent and forecasting seasonal linear filters of the X‐11‐ARIMA method , 1983 .

[16]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[17]  P. Whittle,et al.  Prediction and Regulation. , 1965 .

[19]  Steven C. Hillmer,et al.  A MATRIX APPROACH TO LIKELIHOOD EVALUATION AND SIGNAL EXTRACTION FOR ARIMA COMPONENT TIME SERIES MODELS , 1988 .

[20]  David F. Findley,et al.  New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program , 1998 .

[21]  C. Planas,et al.  Controlling Revisions in Arima‐Model‐Based Seasonal Adjustment , 2002 .

[22]  C. K. Yuen,et al.  Theory and Application of Digital Signal Processing , 1978, IEEE Transactions on Systems, Man, and Cybernetics.

[23]  B. Fischer,et al.  Large Scale fitting of Regression Models with ARIMA Errors. , 2000 .

[24]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter. , 1991 .

[25]  W. Bell,et al.  Signal Extraction for Nonstationary Time Series , 1984 .

[26]  Siem Jan Koopman,et al.  Stamp 5.0 : structural time series analyser, modeller and predictor , 1996 .

[27]  Siem Jan Koopman,et al.  Computing Observation Weights for Signal Extraction and Filtering , 2003 .

[28]  Víctor Gómez,et al.  Program SEATS 'Signal Extraction in Arima Time Series'. Instructions for the User , 1994 .

[29]  Victor Solo,et al.  Intrinsic random functions and the paradox of l/f noise , 1992 .

[30]  Tucker McElroy,et al.  An iterated parametric approach to nonstationary signal extraction , 2006, Comput. Stat. Data Anal..

[31]  Steven C. Hillmer,et al.  An ARIMA-Model-Based Approach to Seasonal Adjustment , 1982 .

[32]  B. Quenneville,et al.  Seasonal adjustment with the X-11 method , 2001 .

[33]  Donald E. K. Martin,et al.  Computation of asymmetric signal extraction filters and mean squared error for ARIMA component models , 2004 .

[34]  C. Chatfield,et al.  Fourier Analysis of Time Series: An Introduction , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[35]  Chris Chatfield,et al.  The Analysis of Time Series: An Introduction , 1981 .