Statistics and econometrics software

Several papers

Several papers having to do with the methodology and application of the programs are provided.

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Time series regression with ARIMA noise, missing observations, and outliers (program TRAMO)
- "Seasonal outliers in time series" (468 KB) (with R. Kaiser), Special issue on Time Series, Estadística, Journal of the Inter-American Statistical Institute, 15, 101-142, 2003.
  Presents an extension of TRAMO-SEATS to incorporate seasonal outliers.
- "Missing observations in ARIMA models: skipping approach versus additive outlier approach" (169 KB) (with V. Gómez and D. Peña), Journal of Econometrics 88, 341-364, 1999.
  Develops the alternative algorithms for estimation of missing observations included in TRAMO.
- "Estimation, prediction and interpolation for nonstationary series with the Kalman filter" (1.16 MB) (with V. Gómez), Journal of the American Statistical Association, 89, 611-624, 1994.
  Presents the basic estimation, prediction and interpolation algorithms in TRAMO.
- "Initializing the Kalman Filter with Incompletely Specified Initial Conditions" (2.49 MB) (with V. Gómez), in R. Chen (ed.), Approximate Kalman Filter (Series on Approximation and Decomposition), London: World Scientific Publ. Co., 39-62, 1993.
  The paper addresses the problem of Kalman filtering when initial conditions are incompletely specified (as is the case for nonstationary series). The discussion leads to the "conditional likelihood" approach used in TRAMO.
- "Automatic Identification of RegARIMA models in Large Scale Applications: Program TSW" (483 KB) Mimeo, Bank of Spain, 56 pp, 2009. (A shorter version is contained in Proceedings of the American Statistical Association, Invited Papers, Business and Economic Section, 2009).
  The paper presents an application of program TSW to a set of 500 European monthly trade indicator series. The results of the automatic model identification procedure are analysed and dicussed.
- "Automatic modelling methods for univariate series" (3.53 MB) (with Víctor Gómez). Chapter 7 in A course in Time Series Analysis, D. Peña, D. G. Tiao and R. S. Tsay. (eds.), NY: J. Wiley and Sons, 171-201, 2001.
  The paper presents the methodology behind the automatic model identification and outlier detection and correction in program TRAMO.
Signal extraction in ARIMA time series (program SEATS)
- "Combining Filter Design with Model-Based Filtering: An Application to Business-Cycle Estimation" (272 KB) (with Regina Kaiser), International Journal of Forecasting (followed by discussion) 21, 691-710, 2005.
  Shows a procedure to incorporate "a priori" designed filters into the ARIMA-model-based framework, and presents an application to business-cycle estimation.
- "Stochastic Linear Trends: Models and Estimators" (3.06 MB) Journal of Econometrics, 56, 5-37, 1993. Reprinted in A. Harvey and T. Proietti (eds.), Readings in Unobserved Component Models, Advanced Texts in Econometrics, Oxford University Press, 2005.
  The paper discusses the models implied for stochastic trend-cycle components by "observed" ARIMA models.
- "A Class of Diagnostics in the ARIMA-model-based Decomposition of a Time Series" (119 KB) in Seasonal Adjustment, European Central Bank, 23-36, 2003.
  Suggests a simple and intuitive procedure to derive tests in the ARIMA model-based unobserved -components framework.
- "Estimation Error and the Specification of Unobserved Component Models" (294 KB) (with C.Planas), Journal of Econometrics, 92, 325-353, 1999. Reprinted in P. Newbold and S.J.Leybourne, Recent Developments in Time Series, The International Library of Critical Writings in Econometrics, Cheltenham, UK: Edward Elgar Publ., 2003.
  Analyzes the error in the component preliminary and final estimator in unobserved component models.
- "Seasonal Adjustment and Signal Extraction in Economic Time Series" (244 KB) (with V. Gómez), in D. Peña, G.C. Tiao, and R.S. Tsay (eds.) A Course in Time Series Analysis, Ch.8, 202-247, New York: J. Wiley and Sons, 2001.
  Contains a description of the ARIMA-model-based-signal-extraction methodology enforced in SEATS.
- "Unobserved Components in Economic Time Series" (4.10 MB) in H. Pesaran and M. Wickens (eds.), The Handbook of Applied Econometrics, chap. 1, 12-72. Oxford: Basil Blackwell, 1995.
  Discusses the problem of identification, estimation, diagnostics, and inference in unobserved component models used for economic time series, as well as some implications for standard econometrics practice.
- "Use and Misuse of Unobserved Components in Economic Forecasting" (2.20 MB) Journal of Forecasting, 13, 157-178, 1994.
  Discusses the effect and distorsions that optimal (MMSE) estimation of unobserved components imposes when these estimators are used within an econometric forecasting model.
- "A Prototypical Seasonal Adjustment Model" (1.50 MB) (with D. A. Pierce), Journal of Time Series Analysis, 8, 177-193, 1987. Reprinted in S.Hylleberg (ed.), Modelling Seasonality, Oxford University Press, 1992.
  Details the ARIMA-model-based procedure in the context of a simple (prototypical) model with trend, seasonal, and irregular components.
- "On the Dynamic Structure of a Seasonal Component" (859 KB) Journal of Economic Dynamics and Control, 13, 81-91, 1989.
  The paper discusses the models implied for the seasonal component by "observed" ARIMA models.
- "On Minimum Mean Squared Error Estimation of the Noise in Unobserved Component Models" (89 KB) Journal of Business and Economic Statistics, 5, 115-120, 1987.
  Contains an application that illustrates one of the basic model-based diagnostics in SEATS.
- "A note on minimum mean squared error estimation of signals with unit roots" (410 KB) Journal of Economic Dynamics and Control, 12, 589-593, 1988, North Holland.
  The paper presents a straightforward extension of the Wiener-Kolmogorov filter to non-stationary time series for the case of a doubly infinite realization.
- "Revisions in ARIMA Signal Extraction" (538 KB) Journal of the American Statistical Association, Theory and Methods, 81, 395, 736-740, 1986.
  The paper analizes revisions in the preliminary estimator of the signal in a "signal plus noise" model-based decomposition of an ARIMA time series.
- "An Application of Model-Based Estimation of Unobserved Components" (1.24 MB) International Journal of Forecasting 2, 305-318, 1986.
  The paper illustrates how the decomposition of a series that follows an ARIMA model can be affected by changes in the model specification, and how this sensitivity can be of help when choosing between alternative reasonable specifications.
- "Modeling Considerations in the Seasonal Adjustment of Economic Time Series" (588 KB) (by S. C. Hillmer, W. R. Bell and G. C. Tiao) Conference on the Seasonal Analysis of Economic Time Series, 120-122., U.S. Department of Commerce. Bureau of the Census, 1976.
  The comment suggests an economic consideration that can be of help when assessing the appropriateness of univariate methods for seasonal adjustment.
- "Descomposición de Series Temporales: Especificación, Estimación e Inferencia; con una Aplicación a la Oferta Monetaria en España" (8.17 MB) (followed by discussion), Estadística Española, 114, 11-69, 1987.
  The paper presents the time series decomposition procedure based on signal extraction techniques applied to ARIMA models. The paper addresses the issues of model identification, estimation of the components, diagnostics and inference.
Applications and Extensions
- Applications of the programs
  - "An Application of the TRAMO-SEATS Automatic Procedure; Direct versus Indirect Adjustment" (4.78 MB) Computational Statistics and Data Analysis, 50, 2167-2190, 2006.
    Using Japanese foreign-trade series as example, the paper discusses the direct versus indirect adjustment problem.
  - "An Application of TRAMO-SEATS: Changes in Seasonality and Current Trend-Cycle Assessment" (307 KB) (with R. Kaiser), in ICES II, Proceedings of the Second International Conference on Establishment Surveys (invited papers), Alexandra, VA: American Statistical Association, Washington DC, 731-742, 2001.
    The paper contains an application of TRAMO-SEATS that illustrates the methodology and its use for short-term assessment.
  - "An Application of TRAMO-SEATS: Model Selection and Out-of-sample Performance" (214 KB) (with F.J. Sánchez), in Proceedings in Computational Statistics, Compstat 2000, Heidelberg: Physica-Verlag, 121-131, 2000.
    The paper contains an application of TRAMO-SEATS that deals with model selection and short-term forecasting.
  - "An Application of TRAMO and SEATS" (4.10 MB) in Annali di Statistica: Seasonal Adjustment Procedures. Experiences and Perspectives, 129, X, 20, 271-344, 2000.
    The paper contains an early application of TRAMO-SEATS to a set of Italian macroeconomic series. The series had been selected by an Italian Seasonal Adjustment Research Appraisal Committee composed by members of Academia, of statistical and economic institutions, and of the private sector.
  - "La Desestacionalización de las Series de Agregados Monetarios" (7.52 MB) (with J. Salaverría), Boletín Económico, Banco de España, June 1986, 17-33.
    The paper presents the seasonal adjustment of the Spanish monetary aggregates by means of signal extraction applied to ARIMA models. The standard error of the seasonal and trend-cycle components are derived and some implications for monetary control are discussed.
  - "Application of Program TSW to a Set of Macroeconomic Time Series" (915 KB) Mimeo, Bank of Spain, 136 pp, March 2007.
    The paper presents an application of TRAMO SEATS to a set of national accounts series of Peru. Each series is analized and used to illustrate some particular feature of the programs and how this feature can be of help in solving some specific problem.
- Non-linearity
  - "Unobserved Components in ARCH Models: An Application to Seasonal Adjustment" (1.14 MB) (with G. Fiorentini), Journal of Forecasting, 15, 175-201, 1996.
    The paper contains an application of TRAMO and SEATS to a nonlinear monetary aggregate series. The conditional variance is decomposed into seasonal, trend, and irregular components, and it is seen how this decomposition can be of practical interest in monetary control.
  - "An Application of Nonlinear Time Series Forecasting" (5.83 MB) Journal of Business and Economic Statistic, 1, 66-74, 1983.
    The paper analyses bilinear models in the context of an application to forecasting a monetary aggregate series. It contains a diagnostic for nonlinearity used in TRAMO.
- Business cycle
  - "Temporal Aggregation, Systematic Sampling, and the Hodrick-Prescott Filter" (428 KB) (with Ana del Río), Computational Statistics and Data Analysis, 52, 975-998, 2007.
    The paper presents an intuitive and computationally simple method for deriving Hodrick- Prescott type filters that are consistent under temporal aggregation. It is enforced in the model-based version of the filter that is being incorporated into SEATS.
  - "Estimation of the Business Cycle: A Modified Hodrick-Prescott Filter" (325 KB) (with R. Kaiser), Spanish Economic Review 1, 175-206, 1999.
    Deals with an extension of TRAMO-SEATS to the problem of business-cycle estimation.
  - "Measuring business cycles in economic times series" (1.24 MB) (with Regina Kaiser). Lecture Notes in Statistics, 154, NY: Springer-Verlag, 190 pp., 2001.
    The paper contains a detailed analysis of the Hodrick-Prescott filter to decompose a seasonally adjusted series or trend-cycle component into trend plus cycle. Within a full ARIMA model based approach it is shown how the HP filter can be given a sensible model-based interpretation where the models for the trend and cycle have desirable spectral properties. The model based specification provides further improvements to the standard HP filter application.
- Data quality control
  - "Data Quality Control with ARIMA Filtering" (98 KB) IFC Bulletin, International Statistical Institute Irvin Fischer Committee on Central Bank Statistics, 22, 48-53, 2005.
    Contains an application of the quality control program TERROR to a set of Spanish custom entries for foreign-trade data.
  - "Un Nuevo Método para el Control de Calidad de los Datos en Series Temporales" (78 KB) (with C. Luna), Boletín Económico, Banco de España, May 37-44, 1999.
    The paper presents the program "Tramo for ERRORS" (TERROR) aimed at the detection of errors in data reported to data bases of time series. An application to quarterly series of monetary aggregate components is contained.
- Data revisions and precision of policy
  - "Preliminary Data Error and Monetary Aggregate Targeting" (1.11 MB) (with D.A. Pierce), Journal of Business and Economic Statistics, 1, 179-186, 1983.
    The paper analyses the error in preliminary US monetary aggregate data implied by revisions of the seasonally adjusted series, and the implications for the precision of monetary aggregate monitoring. (Uses the US data for the decade of the 70’s).
  - "The Transmission of Data Noise into Policy Noise in U.S. Monetary Control" (1.83 MB) (with David A. Pierce). Econometrica, Vol. 54, No. 4, 961-979, July 1986.
    The paper provides an estimate of the effect that revisions in the seasonally adjusted monetary aggregate may have had in short-term interest rates policy. (Based on monetary aggregate targeting as enforced by the U.S. Fed during the decade of the 70’s).
- Related methods
  - "Encompassing Univariate Models in Multivariate Time Series: A Case Study" (3.32 MB) (with A. Mathis), Journal of Econometrics, 61, 197-233, 1994. Reprinted in A. Zellner and F. Palm, The Structural Econometric Time Series Analysis Approach, Cambridge: Cambridge University Press, 2004.
    In the context of a multivariate application, the relationship between VAR and ARIMA models is discussed and exploited. In particular, the paper details the spectral factorization routine used in SEATS.
  - "Comment on the X12ARIMA Seasonal Adjustment Method" (231 KB) Journal of Business and Economic Statistics, 16, 155-160, 1998.
    Contains a discussion of the X12ARIMA methodology as enforced in the earlier versions of the program and makes some comparisons with TRAMO-SEATS.
  - "On Structural Time Series Models and the Characterization of Components" (708 KB) Journal of Business and Economic Statistics, 3, 350-355, 1985. Reprinted in Harvey, A. C. (ed.). Time Series, Cheltenham: Edward Elgar Publ., 1994.
    Provides a comparison between the basic X11, the Basic Structural Model of Harvey and Todd, and the default (Airline) TRAMO-SEATS filters.
  - "Identification of the Dynamic Shock Error Model: The Case of Dynamic Regression" (1.56 MB) (with D.J. Aigner) in D.J. Aigner and A.S. Goldberger (eds.), Latent Variables in Socioeconomic Models, Amsterdam: North Holland, 1977.
    The paper derives identification conditions for dynamic models perturbated by ARMA, shocks and errors in the variables.
General comments
- "Notes on Times Series Analysis, ARIMA Models, and Signal Extraction" (628 KB) (with R. Kaiser) Working Paper 0012, Research Department, Bank of Spain, 72 pp., 2000.
  The paper provides an introduction to the field of applied time series analysis for the non-expert user of TRAMO-SEATS.
- "Short-term Analysis of Macroeconomic Time Series" (493 KB) in A. Kirman and L. A. Gérard Varet, eds., Economics: Beyond the Millennium, Oxford: Oxford University Press, 244-272, 1999.
  Contains a reflexion on model based seasonal adjustment, and on the limitations of short-term tools, such as ARIMA models, for long-term inference.
- "Algunas Reflexiones sobre la Utilización del Análisis de Series Temporales en Economía" (1.26 MB) Revista Española de Economía. Vol. 7. Nº 2, 155-170, 2001.
  The paper presents same personal and informal reflexions on the application of time series analysis tools in Economics.
- "Discurso Breve" (79 KB) in I Premio Galicia de Estadística, Instituto Galego de Estadística y Fundación CaixaGalicia, 32-42, 2007.
  The paper contains a brief and anecdotal description of the TRAMO-SEATS gestation.

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