Masanao Aoki

Notes on Economic Time Series Analysis: System Theoretic Perspectives (eBook, PDF)

• Format: PDF

Produktbeschreibung

In seminars and graduate level courses I have had several opportunities to discuss modeling and analysis of time series with economists and economic graduate students during the past several years. These experiences made me aware of a gap between what economic graduate students are taught about vector-valued time series and what is available in recent system literature. Wishing to fill or narrow the gap that I suspect is more widely spread than my personal experiences indicate, I have written these notes to augment and reor ganize materials I have given in these courses and seminars. I have endeavored to present, in as much a self-contained way as practicable, a body of results and techniques in system theory that I judge to be relevant and useful to economists interested in using time series in their research. I have essentially acted as an intermediary and interpreter of system theoretic results and perspectives in time series by filtering out non-essential details, and presenting coherent accounts of what I deem to be important but not readily available, or accessible to economists. For this reason I have excluded from the notes many results on various estimation methods or their statistical properties because they are amply discussed in many standard texts on time series or on statistics.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 249
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642455650
• Artikelnr.: 53139468

Inhaltsangabe

1 Introduction.- 2 The Notion of State.- 3 Time-invariant Linear Dynamics.- 3.1 Continuous time systems.- 3.2 Inverse systems.- 3.3 Discrete-time sequences.- 4 Time Series Representation.- 5 Equivalence of ARMA and State Space Models.- 5.1 AR models.- 5.2 MA models.- 5.3 ARMA models.- Examples.- 6 Decomposition of Data into Cyclical and Growth Components.- 6.1 Reference paths and variational dynamic models.- 6.2 Log-linear models as variational models.- 7 Prediction of Time Series.- 7.1 Prediction space.- 7.2 Equivalence.- 7.3 Cholesky decomposition and innovations.- 8 Spectrum and Covariances.- 8.1 Covariance and spectrum.- 8.2 Spectral factorization.- 8.3 Computational aspects.- Sample covariance Matrices.- Example.- 9 Estimation of System Matrices: Initial Phase.- 9.1 System matrices.- 9.2 Approximate model.- 9.3 Rank determination of Hankel matrices: singular value decomposition theorem.- 9.4 Internally balanced model.- example.- 9.5 Inference about the model order.- 9.6 Choices of basis vectors.- 9.7 State space model.- 9.8 ARMA (input-output) model.- 9.9 Canonical correlation.- 10 Innovation Processes.- 10.1 Orthogonal projection.- 10.2 Kaiman filters.- 10.3 Innovation model.- 10.4 Output statistics Kaiman filter.- 10.5 Spectral factorization.- 11 Time Series from Intertemporal Optimization.- 11.1 Example: dynamic resource allocation problem.- 11.2 Quadratic regulation problems.- 11.3 Parametric analysis of optimal solutions.- 12 Identification.- 12.1 Closed-loop systems.- 12.2 Identifiability of a closed-loop system.- 13 Time Series from Rational Expectations Models 140.- 13.1 Moving Average processes.- 13.2 Autoregressive processes.- 13.3 ARMA models.- 13.4 Examples.- 14 Numerical Examples.- Mathematical Appendices.- References.