Complutense University Library

Modelling an forecasting time series sampled at different frequencies

Casals Carro, José and Jerez Méndez, Miguel and Sotoca López, Sonia (2006) Modelling an forecasting time series sampled at different frequencies. [Working Paper or Technical Report]

[img]
Preview
PDF
563kB

Official URL: http://eprints.ucm.es/7911/

View download statistics for this eprint

==>>> Export to other formats

Abstract

This paper discusses how to specify an observable high-frequency model for a vector of time series sampled at high and low frequencies. To this end we first study how aggregation over time affects both, the dynamic components of a time series and their observability, in a multivariate linear framework. We find that the basic dynamic components remain unchanged but some of them, mainly those related to the seasonal structure, become unobservable. Building on these results, we propose a structured specification method built on the idea that the models relating the variables in high and low sampling frequencies should be mutually consistent. After specifying a consistent and observable high-frequency model, standard state-space techniques provide an adequate framework for estimation, diagnostic checking, data interpolation and forecasting. Our method has three main uses. First, it is useful to disaggregate a vector of low-frequency time series into high-frequency estimates coherent with both, the sample information and its statistical properties. Second, it may improve forecasting of the low-frequency variables, as the forecasts conditional to high-frequency indicators have in general smaller error variances than those derived from the corresponding low-frequency values. Third, the resulting forecasts can be updated as new high-frequency values become available, thus providing an effective tool to assess the effect of new information over medium term expectations. An example using national accounting data illustrates the practical application of this method.

Item Type:Working Paper or Technical Report
Uncontrolled Keywords:State-space models, Kalman filter, Temporal disaggregation, Observability, Seasonality
Subjects:Social sciences > Economics > Econometrics
Series Name:Documentos de Trabajo del Instituto Complutense de Análisis Económico (ICAE)
Volume:2006
Number:0603
ID Code:7911
References:

Amemiya, T. & Wu, R.Y. (1972). The Effect of Aggregation on Prediction in the Autoregressive Model, Journal of the American Statistical Association, 339, 628-632.

Anderson, B.D.O. & Moore, J.B. (1979). Optimal Filtering, Englewood Cliffs (NJ): Prentice-Hall.

Ansley, C.F. & Kohn, R. (1983). Exact Likelihood of Vector Autoregressive-Moving Average Process with Missing or Aggregated Data, Biometrika, 70, 1, 275–278.

Ansley, C. F. & Kohn, R. (1989). Filtering and Smoothing in State Space Models with Partially Diffuse Initial Conditions, Journal of Time Series Analysis, 11, 275–293.

Baffigi, A., Golinelli, R. & Parigi, G. (2004). Bridge Models to Forecast the Euro Area GDP, International Journal of Forecasting, 20, 447-460.

Bitmead, R.R., Gevers, M.R. Petersen, I.R. & Kaye R.J. (1985). Monotonicity and Stabilizability Properties of the Solutions of the Riccati Difference Equation: Propositions, Lemmas, Theorems, Fallacious Conjectures and Counterexamples, System Control Letters, 5, 309-315.

Brewer, K.W. (1973). Some Consequences of Temporal Aggregation and Systematic Sampling for ARMA and ARMAX Models, Journal of Econometrics, 1, 133-154.

Casals, J. Sotoca, S. & Jerez, M. (1999). A Fast and Stable Method to Compute the Likelihood of Time Invariant State-Space Models, Economics Letters, 65, 329-337.

Casals, J. Jerez, M. & Sotoca, S. (2000). Exact Smoothing for Stationary and Nonstationary Time Series, International Journal of Forecasting, 16, 1, 59-69.

Casals, J. Jerez, M. & Sotoca, S. (2002). An Exact Multivariate Model-based Structural Decomposition, Journal of the American Statistical Association, 97, 458, 553-564.

Chow, G.C. & Lin, A.L. (1971). Best Linear Unbiased Interpolation, Distribution and Extrapolation of Time Series by Related Series, The Review of Economics and Statistics, 53, 372-375.

De Jong, P. (1991). The diffuse Kalman filter, The Annals of Statistics, 19, 1073–1083.

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.

Di Fonzo, T. (1990). The Estimation of M Disaggregate Time Series when Contemporaneous and Temporal Aggregates are Known, The Review of Economics and Statistics, 72, 1, 178-182.

Di Fonzo, T. & Marini, M. (2005). Benchmarking Systems of Seasonally Adjusted Time Series, Journal of Business Cycles Measurement and Analysis, 2, 1, 89-123.

Durbin, J. & Quenneville, B. (1997). Benchmarking by State Space Models, International Statistical Review / Revue Internationale de Statistique, 65, 1, 23-48.

Fernández, R.B. (1981). A Methodological Note on the Estimation of Time Series, The Review of Economics and Statistics, 63, 471-476.

Granger, C.W.J. (1990). Aggregation of Time-Series Variables: A Survey, in Disaggregation in Econometric Modelling, eds. T. Barker and M.H. Pesaran, pp. 17-34, Routledge, London.

Granger, C.W.J. & Siklos, P.R. (1995). Systematic Sampling, Temporal Aggregation, Seasonal Adjustment and Cointegration. Theory and Evidence, Journal of Econometrics, 66, 357-369.

Hannan, E. J. & Deistler, M. (1988). The Statistical Theory of Linear Systems. New York: John Wiley, Harvey, A.C. & Pierse, R.G. (1984). Estimating Missing Observations in Economic Time Series, Journal of the American Statistical Association, 79, 385, 125-131.

Harvey, A.C. (1989). Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge (UK): Cambridge University Press.

Jenkins, G.M. & Alavi, A.S. (1981). Some Aspects of Modelling and Forecasting Multivariate Time Series, Journal of Time Series Analysis, 2, 1, 1-47.

Kalman, R.E. (1963). Mathematical Description of Linear Systems, SIAM Journal of Control, 1, 152-192.

Litterman, R.B. (1983). A Random Walk, Markov Model for the Distribution of Time Series, Journal of Business and Economic Statistics, 1, 169-173.

Lütkepohl, H. (1987). Forecasting Aggregated Vector ARMA Processes, Berlin: Springer-Verlag.

Marcellino, M. (1999). Some Consequences of Temporal Aggregation in Empirical Analysis, Journal of Business and Economic Statistics, 1, 129-136.

Nunes, L.C. (2005). Nowcasting Quarterly GDP Growth in a Monthly Coincident Indicator Model, Journal of Forecasting, 24, 575-592.

Onof, C. Wheater, H. Chandler, D. Isham, V. Cox, D.R. Kakou, A. Northrop, P. Oh, L. & RodriguezIturbe, I. (2000). Spatial-Temporal Rainfall Fields: Modelling and Statistical Aspects, Hydrology and Earth System Sciences, 4, 4, 581-601.

Petkov, P.Hr. Christov, N.D. & Konstantinov, M.M. (1991). Computational Methods for Linear Control Systems, Englewood Cliffs (NJ): Prentice-Hall.

Pierse, R.G. & Snell, A.J. (1995). Temporal Aggregation and the Power of Tests for a Unit Root, Journal of Econometrics, 65, 333-345.

Proietti, T. (2006). Temporal Disaggregation by State Space Methods: Dynamic Regression Methods Revisited, Econometrics Journal, 9, 357-372.

Rosenbrock, M.M. (1970). State-Space and Multivariable Theory, New York: John Wiley. Santos-Silva, J.M.C. & Cardoso, F. (2001). The Chow-Lin Method using Dynamic Models, Economic Modelling, 18, 269-280.

Stram, D.O. & Wei, W.W.S. (1986). Temporal Aggregation in the ARIMA Process, Journal of Time Series Analysis, 7, 4, 279-292.

Tiao, G.C. (1972). Asymptotic Behavior of Time Series Aggregates, Biometrika, 59, 521-531.

Terceiro, J. (1990). Estimation of Dynamic Econometric Models with Errors in Variables, Berlin: Springer-Verlag.

Wei, W.W.S. (1978). Some Consequences of Temporal Aggregation in Seasonal Time Series Models” In: Zellner, A. (ed.), Seasonal Analysis of Economic Time Series, Washington DC: Bureau of the Census, 433-448.

Wei, W.W.S. & Stram, D.O. (1990). Disaggregation of Time Series Models, Journal of the Royal Statistical Society, B Series, 52, 3, 453-467.

Deposited On:20 May 2008
Last Modified:06 Feb 2014 07:56

Repository Staff Only: item control page