This course gives an overview of the basic concepts in time series econometrics, with a particular emphasis on the tools needed to undertake empirical analysis. The final objective is to be able to analyze the evolution of the economic variables (inflation, Gross Domestic Product, Money, interest rate¿), to understand the dynamic relationship between those variables, and to predict them. In macroeconomics context, this is very useful for policy makers; since it helps them take their decision based on better knowledge of how many macroeconomic variables affect each other at different horizons. We will focus on the following topics:
(1) Characteristics of economic time series data: Stochastic processes and time series, stationarity and ergodicity, simple autocorrelation function (ACF) and Partial autocorrelation function (PACF). [Brockwell P.J. and Davis Chapter I + Lecture notes].
(2) Univariate stationary models: Wold decomposition, ARMA processes, Causal models, invertible models, estimation and inference on the mean and the ACF, estimation and inference on the parameter estimates of ARMA models, white noise tests, model selection (information criteria), methodologies for the design of ARMA models, real data examples (interest rates, growth rate of GDP, temperature, etc.) [B&D chapters II, III & V + Lecture notes].
(3) Forecasting: Forecasts computing, forecast evaluation ¿ [B&D chapters II, III & V + Lecture notes].
(4) Regression with autocorrelation: Consequences of the presence of autocorrelated errors, robust inference through HAC standard errors, endogeneity problems (lagged dependent variable), instrumental Variables solution (Two Step Least Squares). [Wooldridge Chapter 12 & 15].
(5) Nonlinear models (TAR, STAR) and ARCH, GARCH models, Estimation, Predictions, extensions of GARCH models. [Hamilton Chapter 21+ Teräsvirta et al. (2010) +Lecture notes].
(6) Vectors Autoregressive Models (VAR): VAR models, structural form, reduced form, identifiability conditions, Granger-Causality analysis, Impulse response function (IRF). [Enders (2004) + Lecture notes].
(7) Non-stationary processes: Non-stationary processes about a trend (vs. integrated processes, unit root Dickey-Fuller test, forecasting with non-stationary models, structural changes, permanent and transitory shocks. [Stock and Watson Chapter 14, Wooldridge Chapter 18 + Lecture notes].
(8) Cointegration: Spurious regressions, Cointegration, Error-Correction models¿ [Stock and Watson Chapter 14, Wooldridge Chapter 18 + Zivot (notes)+ Lecture notes].