Frequency Domain Slides

Frequency Domain Slides - NBER Summer Institute Minicourse...

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Lecture 1 1, July 21, 2008 NBER Summer Institute Minicourse – What’s New in Econometrics: Time Series Lecture 1 July 14, 2008 Frequency Domain Descriptive Statistics
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Lecture 1 2, July 21, 2008 Outline 0. Introduction to Course 1. Time Series Basics 2. Spectral representation of stationary process 3. Spectral Properties of Filters (a) Band Pass Filters (b) One-Sided Filters 4. Multivariate spectra 5. Spectral Estimation (a few words – more in Lecture 9)
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Lecture 1 3, July 21, 2008 Introduction to Course Some themes that have occupied time-series econometricians and empirical macroeconomists in the last decade or so: 1. Low-frequency variability: (i) unit roots, near unit roots, cointegration, fractional models, and so forth; (ii) time varying parameters; (iii) stochastic volatility; (iv) HAC covariance matrices; (v) long-run identification in SVAR 2. Identification: methods for dealing with “weak” identification in linear models (linear IV, SVAR) and nonlinear models (GMM). 3. Forecasting: (i) inference procedures for relative forecast performance of existing models; (ii) potential improvements in forecasts from using many predictors
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Lecture 1 4, July 21, 2008 Some tools used: 1. VARs, spectra, filters, GMM, asymptotic approximations from CLT and LLN. 2. Functional CLT 3. Simulation Methods (MCMC, Bootstrap) We will talk about these themes and tools. This will not be a comprehensive literature review. Our goal is present some key ideas as simply as possible.
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Lecture 1 5, July 21, 2008 July 14: Preliminaries and inference 1. Spectral preliminaries and applications, linear filtering theory (MW) 2. Functional central limit theory and structural breaks (testing) (MW) 3. Many instruments/weak identification in GMM I (JS) 4. Many instruments/weak identification in GMM II (JS)
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Lecture 1 6, July 21, 2008 July 15: Methods for macroeconometric modeling 5. The Kalman filter, nonlinear filtering, and Markov Chain Monte Carlo (MW) 6. Specification and estimation of models with stochastic time variation (MW) 7. Recent developments in structural VAR modeling (JS) 8. Econometrics of DSGE models (JS)
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Lecture 1 7, July 21, 2008 July 16: HAC, forecasting-related topics 9. Heteroskedasticity- and autocorrelation consistent (HAC) standard errors (MW) 10. Forecast assessment (MW) 11. Dynamic factor models and forecasting with many predictors (JS) 12. Macro modeling with many predictors (JS)
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Lecture 1 8, July 21, 2008 Time Series Basics (and notation) ( References: Hayashi (2000), Hamilton (1994), … , lots of other books) 1. { Y t }: a sequence of random variables 2. Stochastic Process: The probability law governing { Y t } 3. Realization: One draw from the process, { y t } 4. Strict Stationarity: The process is strictly stationary if the probability distribution of 1 () tt t k YY Y ++ , ,..., is identical to the probability distribution of 1 k Y τ ττ , for all t , , and k. (Thus, all joint distributions are time invariant.) 5. Autocovariances: tk t t k cov Y Y γ ,+ =,
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Lecture 1 9, July 21, 2008 6. Autocorrelations: () tk t t k cor Y Y ρ ,+ =, 7. Covariance Stationarity: The process is covariance stationary if μ t = E ( Y t ) = and γ t,k = k for all t and k .
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Frequency Domain Slides - NBER Summer Institute Minicourse...

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