Abstract
The development of a flexible family of finite moving-average filters from specified smoothness and fidelity criteria is considered. These filters are based on simple dynamic models operating locally within the span of the filter. They are shown to generalise and extend the standard Macaulay and Henderson filters used in practice. The properties of these filters are determined and evaluated both in theory and in practice.
Keywords
- Good Linear Unbiased Predictor
- Seasonal Adjustment
- Local Linear Model
- Good Linear Unbiased Predictor
- Fidelity Criterion
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References
H. Akaike. Seasonal adjustment by a Bayesian modeling. Journal of Time Series Analysis, 1 (1): 1–13, 1980.
W. Bell. Empirical comparisons of seasonal ARIMA and ARIMA component (structural) time series models. Research Report CENSUS/SRD/RR-93/10, Statistical Research Division, Bureau of the Census, Washington, D.C. 20233–4200, 1993.
R. B. Cleveland, W. S. Cleveland, J. E. McRae, and I. J. Terpenning. STL: A seasonal-trend decomposition procedure based on Loess. Journal of Official Statistics, 6: 3–73, 1990.
W. Gersch and G. Kitagawa. The prediction of time series with trends and seasonalities. Journal of Business and Economic Statistics, 1: 253–264, 1983.
A. G. Gray and P. J. Thomson. Design of moving-average trend filters using fidelity and smoothness criteria. Research Report CENSUS/SRD/RR-96/1, Statistical Research Division, Bureau of the Census, Washington, D.C. 20233–4200, 1996.
A. C. Harvey. Forecasting, structural time series models and the Kalman filter. Cambridge University Press, Cambridge, 1989.
R. Henderson. A new method of graduation. Transactions of the Actuarial Society of America, 25: 29–40, 1924.
P. B. Kenny and J. Durbin. Local trend estimation and seasonal adjustment of economic and social time series. Journal of the Royal Statistical Society, Series A, 145: 1–41, 1982.
M. G. Kendall. Time-Series. Hafner Press, New York, 1973.
D. London. Graduation: The Revision of Estimates. ACTEX, Abington, Connecticut, 1985.
F.R. Macaulay. The Smoothing of Time Series. National Bureau of Economic Research, New York, 1931.
E. Schlicht. A seasonal adjustment principle and a seasonal adjustment method derived from this principle. Journal of the American Statistical Association, 76: 374–378, 1981.
J. Shiskin, A. H. Young, and J. C.Musgrave. The X-11 variant of the Census method II seasonal adjustment program. Technical Paper 15, Bureau of the Census, U.S. Department of Commerce, Washington, D.C., 1967.
E. T. Whittaker. On a new method of graduation. Proceedings of the Edinburgh Mathematical Society, 41: 63–75, 1923.
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© 1996 Springer-Verlag New York, Inc.
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Gray, A., Thomson, P. (1996). Design of Moving-Average Trend Filters using Fidelity and Smoothness Criteria. In: Robinson, P.M., Rosenblatt, M. (eds) Athens Conference on Applied Probability and Time Series Analysis. Lecture Notes in Statistics, vol 115. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2412-9_15
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DOI: https://doi.org/10.1007/978-1-4612-2412-9_15
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94787-7
Online ISBN: 978-1-4612-2412-9
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