tsdecomp-package: ARIMA-Model-Based Decomposition of Time Series Data

Description

ARIMA-model-based decomposition of a time series.

Arguments

Details

The methods implemented in the package are developed and described (among others) in the references given below. The package is mainly intended for annual, quarterly and monthly time series. The bottom line of the procedure can be summarized as follows. An ARIMA model is fitted to the observed series. Then the pseudo-spectrum of the model is computed and decomposed into partial fractions. This gives ARIMA models for the unobserved components (e.g., trend, seasonal and irregular), which are then used to obtain the weights of double-sided linear filters upon which estimates of the components are obtained.

For practical purposes, the main function provided in the package is ARIMAdec. This function relies on other procedures that implement different stages of the procedure: roots.allocation, pseudo.spectrum, partial.fraction, canonical.decomposition, filtering.

An introduction to the methodology and the package in the form of a vignette is available here:

https://www.jalobe.com/doc/tsdecomp.pdf

References

Box, G. E. P., Hillmer, S. C. and Tiao, G. C. (1978) ‘Analysis and Modeling of Seasonal Time Series’ in Seasonal Analysis of Economic Time Series, Editor Zellner, A. pp. 309-334. U.S. Dept. of Commerce - Bureau of the Census. http://www.nber.org/chapters/c3904.pdf

Brockwell, P. J. and Davis, R. A. (1991) Time Series: Theory and Methods, Second Edition. Springer. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("#1")}10.1007/978-1-4419-0320-4http://doi.org/10.1007/978-1-4419-0320-4doi:\ifelse{latex}{\out{~}}{ }latex~ 10.1007/978-1-4419-0320-4

Burman, J. P. (1980) ‘Seasonal Adjustment by Signal Extraction’. Journal of the Royal Statistical Society. Series A (General), 143(3), pp. 321-337. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("#1")}10.2307/2982132http://doi.org/10.2307/2982132doi:\ifelse{latex}{\out{~}}{ }latex~ 10.2307/2982132

Gómez, V. and Maravall, A. (2001) ‘Programs TRAMO and SEATS. Instructions for the User (Beta Version: June 1997)’. Ministerio de Economía y Hacienda. Dirección General de Análisis y Programación Presupuestaria, Working paper SGAPE-97001. http://www.bde.es/f/webbde/SES/servicio/Programas_estadisticos_y_econometricos/Programas/ficheros/manualdos.pdf

Gómez, V. (2015) ‘SSMMATLAB: A Set of MATLAB Programs for the Statistical Analysis of State Space Models’. Journal of Statistical Software, 66(1), pp. 1-37. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("#1")}10.18637/jss.v066.i09http://doi.org/10.18637/jss.v066.i09doi:\ifelse{latex}{\out{~}}{ }latex~ 10.18637/jss.v066.i09

http://www.sepg.pap.minhap.gob.es/sitios/sepg/en-GB/Presupuestos/Documentacion/Paginas/SSMMATLAB.aspx

Hillmer, S. C. and Tiao, G. C. (1982) ‘An ARIMA-Model-Based Approach to Seasonal Adjustment’. Journal of the American Statistical Association, 77(377), pp. 63-70. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("#1")}10.1080/01621459.1982.10477767http://doi.org/10.1080/01621459.1982.10477767doi:\ifelse{latex}{\out{~}}{ }latex~ 10.1080/01621459.1982.10477767

Maravall, A. and Pierce, D. A. (1987) ‘A Prototypical Seasonal Adjustment Model’. Journal of Time Series Analysis, 8(2), pp.177-193. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("#1")}10.1111/j.1467-9892.1987.tb00431.xhttp://doi.org/10.1111/j.1467-9892.1987.tb00431.xdoi:\ifelse{latex}{\out{~}}{ }latex~ 10.1111/j.1467-9892.1987.tb00431.x

Planas, C. (1997) Applied Time Series Analysis: Modelling, Forecasting, Unobserved Components Analysis and the Wiener-Kolmogorov Filter. Eurostat: Series E, Methods. https://bookshop.europa.eu/en/applied-time-series-analysis-pbCA0897484/

Pollock, D. S. G. (1999) A Handbook of Time-Series Analysis Signal Processing and Dynamics. Academic Press. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("#1")}10.1016/B978-012560990-6/50002-6http://doi.org/10.1016/B978-012560990-6/50002-6doi:\ifelse{latex}{\out{~}}{ }latex~ 10.1016/B978-012560990-6/50002-6