Advanced topics in Econometrics         Professors: Miguel Jerez; Sonia Sotoca Updated: .

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My Department discontinued the PhD Program

Goal: This course is oriented to graduate students. It reviews the fundamentals of specification, estimation, extrapolation and interpolation of econometric models in state-space. Some important issues treated in this framework are: aggregation, desaggregation and decomposition of time series, errors-in-variables and missing data.

Final grades will depend on the supervised practical work done by the student.

Software: The methods described in this course have been implemented in E⁴, a MATLAB toolbox for time series modeling in state-space. It can be freely downloaded for academic use at E⁴ WEB page.

SECTION I: STATE-SPACE MODELS AND FILTER THEORY.

    1. State-space models.

        1.1. The state-space model (SS) in discrete time.
        1.2. Econometric models in SS.
        1.3. Dynamics implied by the SS model.
        1.4. Practical cases:
                1.4.1. Structural time series models.
                1.4.2. Impulse-response analysis.

        References: Anderson and Moore (1979, chap. 2), Terceiro (1990, chap. 2 and 3).

    2. Filtering, forecasting and smoothing.

        2.1. Problem statement.
        2.2. Filtering.
        2.2. Forecasting.
        2.3. Fixed-interval smoothing.
        2.4. Practical cases:
                2.4.1. Recursive least-squares.
                2.4.2. Goal tracking.

        References: Anderson and Moore (1979, chap. 3, 5 and 7); Jerez (1992); Casals, Jerez and Sotoca (2000).

    3. Time series decomposition.

        3.1. Problem statement.
        3.2. Overview of standard methods.
        3.3. Spectral properties of the structural components and system modes.
        3.4. Classification of the modes and signal extraction.

        References: Casals, Jerez and Sotoca (2002),  Casals, Jerez and Sotoca (2000).

SECTION II: ESTIMATION

    4. Estimation of econometric models in state-space.

        4.1. Computation of the exact gaussian likelihood.
        4.2. The analytical gradient.
        4.3. The Information matrix.
        4.4. Algorithmics.
        4.5. Numerical issues.
                5.5.1. Factorizations.
                5.5.2. Initial conditions for the Kalman filter.
        4.6. Diagnostics.

        References: Terceiro (1990, chap. 4), Casals and Sotoca (2001), Casals, Sotoca and Jerez (1999), De Jong (1988and 1991).

REFERENCES.

• Anderson, B.D.O. and J.B. Moore (1979). Optimal Filtering. Prentice-Hall, Englewood Cliffs (New Jersey).

• Aoki, M. (1990). State Space Modeling of Time Series. Springer-Verlag, Berlín.

• Casals, J. (1997). Métodos de Subespacios en Econometría. Tesis Doctoral. Universidad Complutense de Madrid.

• Casals, J and S. Sotoca (2001). "The exact likelihood for a state-space model with stochastic inputs". Computers and Mathematics with Applications , 42, 199-209.

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

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

• De Jong, P. (1988). "The Likelihood for a State Space Model". Biometrika, 75, 1, 165-169.

• De Jong, P. (1991). "Stable Algorithms for the State Space Model". Journal of Time Series Analysis, 12, 2, 143-157.

• Guerrero, V.M. (1990). "Temporal Disaggregation of Time Series: An ARIMA-based Approach". International Statistical Review, 58, 1, 29-46.

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

• Jerez, M. (1992). "Una Metodología para el Seguimiento de Objetivos Definidos sobre Series Históricas: el Caso del Control Monetario en España". Investigaciones Económicas, XVI, 1, 63-88.

• MATLAB. Reference Guide. The Math Works Inc., Natick, Massachussets.

• MATLAB (1992). The Student Edition of MATLAB™. Student User Guide. Prentice-Hall, Englewood Cliffs (New Jersey).

• Morf, M.; G.S. Sidhuand T. Kailath (1974). "Some New Algorithms for Recursive Estimation in Constant Linear Discrete-time Systems". IEEE Transactions on Automatic Control, AC-19, 4, 315-323.

• Petkov, P.Hr.; N.D. Christovand M.M. Konstantinov (1991). Computational Methods for Linear Control Systems. Prentice-Hall, Englewood Cliffs (New Jersey).

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

• Terceiro, J., J. Casals, M. Jerez, G.R. Serrano and S. Sotoca (2000b). A MATLAB Toolbox for reliable time series modeling and forecasting in state-space.

• Verhaegen M.and P. Van Dooren (1988). "New Insights in the Numerical Reliability Properties of Existing Kalman Filter Implementations". Control and Dynamic Systems, 29, 1-45.

• Wells, C. (1994). "Variable Betas on the Stockholm Exchange 1971-1989". Applied Economics, 4, 75-92.