Courses

  Overview: This two-day course covers fundamental concepts of time series analysis, both univariate and multivariate, with application to macroeconomic and financial datasets using the EViews econometrics program. 

An essential aspect of economic and financial time series data is that most variables are non-stationary, meaning they do not have constant means or variances. This is most obvious for trended variables; it is not meaningful to refer to the mean of a variables that looks like real GDP, for example.

It is well known that correlation or regression analysis involving trended variables is vulnerable to finding evidence of strong correlations when in fact no relation truly exists.. Early researchers attempted to cope with this problem by "detrending" the data prior to estimating equations involving trended variables. The unit root revolution beginning in the late 1970s called this detrending procedure into question, and led to the quest to develop appropriate procedures for estimation and inference in models containing non-stationary variables.

 
In the first day of this Tools course we will become familiar with different types of stationary and non-stationary variables, consider simple univariate forecasting models, and learn graphical tools and formal tests for non-stationarity.  

 I. Fundamentals Statistical Concepts, Stochastic Simulation and EViews Programming

A. White Noise – Concept and Simulation 

B. Partial Autocorrelation and Autocorrelation Functions; Use of Correlograms

i. Simulated and empirical examples

ii. EViews Programming – Learning by Examples 

II. Univariate Time Series Models: Models of U.S. Inflation 

A. Simulation of ARIMA models

i. Stationary and Non-stationary Stochastic Processes

ii. Graphical identification of ARIMA models

B. Univariate Models: AR Processes

i. Inflation example

ii. Model Selection; general-to-specific modeling

C. Stochastic forecasting using the EViews MODEL object

III. Unit root testing

A. Concepts and motivation; stochastic vs. deterministic trends

B. Augmented Dicky-Fuller test

C. Dickey-Fuller GLS test

D. Applications to macroeconomic and financial data

The advanced materials for days 4 and 5 build on the methods presented in the Econometric Tools course. The first topic provides extensions of the basic vector autoregression model in a quest for greater forecast accuracy. These extensions are evaluated with methods of forecast combination and comparison. 

The standard VAR offers important advantages over traditional structural econometric models, in particular, that all variables are forecast within the model. There is no need to forecast and arbitrarily assume future values of exogenous variables since all variables in the VAR are endogenous. One limitation of the basic VAR is that it is difficult to include a large number of economic variables in a VAR, so that important predictors may be omitted thereby undermining forecast accuracy.

The Factor Augmented VAR provides a framework for incorporating the influence of a large number of economic variables without expanding the dimensions of the VAR to an unmanageable size. This approach has been found to improve forecast accuracy over the simple alternatives.

Cointegration offers a framework for estimating and testing relations between non-stationary variables. If a set of non-stationary variables are tied together in a stationary equilibrium equation, then they are cointegrated. Cointegrated variables are dynamically related by a set of Error correction equations that combine both long run relations and short run dynamics. EViews provides tools for testing and estimating cointegrating equations and error correction models, in either single equation or systems approaches. Systems of error correction equations offer an extension of VARs for forecasting, with the advantage that the forecasted variables must hang together according to the cointegrating equations.

An alternative advanced topic is panel data modeling. EViews provides powerful tools for traditional panel data analysis, including fixed effects and random effects models with various options for handling autocorrelation, heteroscedasticity, and parameters heterogeneity across the panel. In addition, the availability of panel data permits more powerful application of unit root tests and cointegration modeling. Most current applications of panel data analysis fail to recognize the important issues that arise in models with non-stationary data. The ARDL framework for cointegration testing and modeling is easily extended to panel data analysis. 

I. Engle-Granger Single Equation Approach

A. Least  squares estimation

B. Cointegration testing

C. Construction of error correction equations

II. The Autoregressive Distributed Lag (ARDL) Approach

A. ARDL equation as flexible error correction model (ECM)

B. Testing cointegration through tests of error correction mechanism

C. Alternative representations

III. Johansen's Systems Approach

A. Mathematical background: relation between VARs and ECM

B. Johansen's tests of cointegration 

   1. possibility of multiple cointegrating relations

    2. interpretation of estimates of cointegrating equations and ECM

    3. Hypothesis testing.

C. Forecasting

D. Granger causality and impulse response functions.