Author	Aoki, Masanao. author
Title	Notes on Economic Time Series Analysis: System Theoretic Perspectives [electronic resource] / by Masanao Aoki
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 1983
Connect to	http://dx.doi.org/10.1007/978-3-642-45565-0
Descript	IX, 249 p. online resource

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 reorยญ 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

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