Bayesian Decision Analysis For Benchmarking Daily And Monthly Time Series

  1. Sanz-Gómez, Jose-Antonio 1
  2. Rojo-García, José-Luis 1
  1. 1 Universidad de Valladolid
    info

    Universidad de Valladolid

    Valladolid, España

    ROR https://ror.org/01fvbaw18

Revue:
Estudios de economía aplicada

ISSN: 1133-3197,  1697-5731

Année de publication: 2024

Titre de la publication: Advances in Econometric Modeling: Theory and Applications

Volumen: 42

Número: 1

Type: Article

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D'autres publications dans: Estudios de economía aplicada

Résumé

In Business Time Series analysis, daily disaggregation of monthly time series is often needed when adjusting financial series (stock options, swaps, mortgages or other loans). The classical stochastic adjustment methods only allow quarterly or monthly benchmarks to be estimated and can only be applied when high frequency is a regular multiple of low frequency. Thus, they fail to offer solutions for such problems, thereby evidencing the need to develop tools and methods for high-frequency series (daily or weekly ones). This paper obtains the first known method for using daily indicators, taking into account the different number of days for each month. The proposed Bayesian (normal-gamma) method can employ several indicators for the likelihood model, also obtaining an explicit (non iterative) solution for the optimal estimate of high frequency series. It is also important to observe that the model includes a correction mechanism for volatile indicators, as is often found in benchmarking problems for small areas. The methodology, in the line of normal-gamma specifications, allows Bayesian Credibility intervals for the estimated daily series. 

Références bibliographiques

  • Boot, J.C.G. and Feibes, W. (1967). On Glejser's derivation of monthly figures from yearly data. Cahiers Économiques de Bruxelles 36, 539-546.
  • Box, G.E.P. and Tiao, G.C. (1973). Bayesian inference in statistical analysis. Addison Wesley, Boston, MA, USA.
  • Broemeling, L.D. (1985). Bayesian Analysis of Linear Models, Marcel Dekker, New York, NY.
  • Brooks, S.P. and Gelman, A. (1998) General Methods for Monitoring Convergence of Iterative Simulations. Journal of Computational and Graphical Statistics 7:4, 434-455, DOI: 10.1080/10618600.1998.10474787
  • Chow, G.C. and Lin, A.L. (1971) Best Linear Unbiased Interpolation, Distribution and Extrapolation of Time Series by related series. The Review of Economics and Statistics 53(4), 372-375.
  • Dagum, E.B. and Cholette, P.A. (2006) Benchmarking, Temporal Distribution and Reconciliation Methods of Time Series. Springer Science+Business Media. New York.
  • Denton, F.T. (1971). Adjustment of monthly or quarterly series to annual totals: An approach based on quadratic minimization. Journal of the American Statistical Association 66 (333), 99–102. DOI: https://doi.org/10.1080/01621459.1971.10482227
  • di Fonzo, T. (2003). Temporal Disaggregation of Economic Time Series: Towards a dynamic extension (Working Paper), Luxembourg: Office for Official Publication of the European Communities. Retrieved from https://ec.europa.eu/eurostat/documents/3888793/5816173/KS_AN-03-035-EN.
  • di Fonzo, T. and Filosa, R. (1987). Methods of estimation of quarterly national account series: A comparison, in Journée Franco-Italienne de Comptabilité Nationale (Journée de Statistique), Lausanne, Switzerland.
  • Fernández, R.B. (1981). A Methodological note on the estimation of Time Series. The Review of Economics and Statistics 63 (3), 471-478.
  • Gamerman, D. (1997). Markov Chain Monte Carlo: Stochastic simulation for Bayesian inference, Chapman & Hall, London.
  • Gelman, A. and Rubin, D.B. (1992). Inference from Iterative Simulation Using Multiple Sequences. Statistical Sciences 7 (4), 457-511.
  • Geman, S. and Geman, D. (1984) Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images, IEEE Transactions on Pattern Analysis and Machine Intelligence 6 (6), 721-741. DOI:10.1109/TPAMI.1984.4767596
  • Rojo, J.L. and Sanz, J.A. (2001). Una propuesta bayesiana para la distribución de Contabilidades regionales por procedimientos indirectos. In Cambios Regionales en la U.E. y Nuevos Retos Territoriales, AECR, ISBN: 84-607-3322-X, Madrid, 1-19.
  • Rojo, J.L. and Sanz, J.A. (2005). A Bayesian benchmarking method with applications to the Quarterly National Accounts. Luxembourg: Office for Official Publications of the European Communities. Retrieved from https://ec.europa.eu/eurostat/documents/3888793/5836929/KS-DT-05-013-EN.
  • Rojo, J.L. and Sanz, J.A. (2017). Benchmarking and reconciliation of time series. An applied Bayesian method, Methodology 13 (4), 123–134. DOI: https://doi.org/10.1027/1614-2241/a000136.
  • J Rojo, J.L. and Sanz, J.A. (2020). Benchmarking and Reconciliation with Time-varying cross-coefficients, Methodology 16 (4), 316-334. https://doi.org/10.5964/meth.4529
  • Rodríguez-López, A., Fernández-Abascal, A., Maté-García, J.J., Rodríguez-Fernández, J.M., Rojo-García, J.L. and Sanz-Gómez, J.A. (2021). Evaluating Euribor Manipulation: Effects on Mortgage Borrowers. Finance Research Letters, 40, 101795. https://doi.org/10.1016/j.frl.2020.101795.
  • Spiegelhalter, D., Thomas, A., and Best, N. (1999) WinBUGS (Version 1.2) [User Manual]. MRC Biostatistics Unit, Cambridge, United Kingdom.
  • Stram, D. and Wei, W. (1986). A Methodological Note on the Disaggregation of Time Series Totals. Journal of Time Series Analysis 7, S. 293-302
  • Young, M.R. (1996). Robust seasonal adjustment by Bayesian modelling, Journal of Forecasting, 15 (5), 355–367. DOI: https://doi.org/10.1002/(SICI)1099-131X(199609)15:5<355::AID-FOR625>3.0.CO;2-K.
  • Zellner, A. (1971). An Introduction to Bayesian Inference in Econometrics, John Wiley & Sons, New York.
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