β Scribed by Prof. Masanao Aoki (auth.)
No coin nor oath required. For personal study only.
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 reorΒ 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.
Front Matter....Pages N2-IX
Introduction....Pages 1-4
The Notion of State....Pages 5-6
Time-Invariant Linear Dynamics....Pages 7-14
Time Series Representation....Pages 15-21
Equivalence of Arma and State Space Models....Pages 22-32
Decomposition of Data into Cyclical and Growth Components....Pages 33-37
Prediction of Time Series....Pages 38-47
Spectrum and Covariances....Pages 48-59
Estimation of System Matrices: Initial Phase....Pages 60-89
Innovation Processes....Pages 90-105
Time Series from Intertemporal Optimization....Pages 106-131
Identification....Pages 132-139
Time Series from Rational Expectations Models....Pages 140-153
Numerical Examples....Pages 154-177
Back Matter....Pages 178-255
Economic Theory; Statistics for Business/Economics/Mathematical Finance/Insurance
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