|
Sylvia Kaufmann University
of Basel Master/Doctoral
level FS24
Advanced Time Series Analysis The lecture introduces Bayesian
econometrics, with a particular focus on time series analysis, from
univariate to multivariate high-dimensional. The primary goal in Bayesian inference is
to derive the posterior distribution of an object of interest, being usually
parameters or some latent variables. Therefore, in a first part we define the
basic components specifying the Bayesian setup, the prior and the likelihood,
and discuss principles of posterior updating. As for most econometric models
the posterior distribution is not of a known standard form nor available in
analytical form, the posterior distribution is approximated or estimated by
sampling methods. We introduce two generic samplers based on Markov chain
Monte Carlo (MCMC) simulation methods to estimate the posterior distribution:
Metropolis-Hastings and Gibbs sampling. Bayesian inference inherently lends
itself to a probabilistic interpretation or discussion of model estimates. To
quantify uncertainty, we derive procedures to obtain credible intervals, for
parameters as well as (non)linear transformations of parameters. Finally, we
also discuss approaches to perform model choice or (forecast) evaluation,
like MCMC-based estimation of the marginal likelihood or K-fold
cross-validation. The Bayesian approach circumvents estimation difficulties
when either data is scarce or high-dimensional. To deal with these issues, we
discuss ways of specifying informative prior distributions and prior
distributions that induce shrinkage into parameters. In a last part, we
introduce latent variables which allow extending models to regime-switching
parameters or extracting a small number of common factors from
high-dimensional datasets. The lecture also includes the analytical
discussion of time series models. We derive properties of the time series
process, discuss stationarity and invertibility conditions, derive
conditional and unconditional moments. As single parameters are not of prime
interest, tools like impulse responses and variance decomposition are used to
interpret multivariate time series models. We discuss various strategies of
structural identification. The lecture includes exercise sessions
with applications in time series modelling. Slides
and other material available for download in ADAM University
of Zurich Master
level HS21 Monetary
Policy Analysis: Empirical Modelling The course introduces time series models to
analyse macroeconomic and financial data, with an emphasis on applications in
monetary policy analysis. We discuss various ways of imposing identification
restrictions to obtain a structural interpretation of the model. We introduce
impulse response analysis and variance decomposition to evaluate specific
economic hypotheses. Finally, we discuss various procedures to assess the
forecasting performance of a model. The course is a mix between brief
introductions to models and econometric methods, and practical exercises
implementing and analysing models in software packages, mainly gretl and also Matlab. Students participate actively by presenting and
sharing written solutions to exercises. The students will form teams of
minimum 3 to maximum 5 persons and write a term paper (Seminararbeit,
maximum 20 pages) on an empirical investigation, in which they apply (one of)
the models and the methods discussed during the course. The students are free
to choose the topic of interest and formulate a working hypothesis. After participating, the students should
know about the main econometric issues to address when implementing an
empirical time series model for macroeconomic and financial data. Students
should also be able to implement and analyse simple and small models either
in gretl or Matlab. gretl is available at http://gretl.sourceforge.net/ and Matlab at the repository of the University of Zurich. |