Econ 582
Cointegration
Eric Zivot
May 8, 2012
Cointegration
The time series models discussed so far are appropriate for modeling I(0)
data, like asset returns or growth rates of macroeconomic time series.
Economic theory, however, often implies equilibr
Econ 582
Trend-Cycle Decompositions and Unit Root
Tests
Eric Zivot
April 22, 2013
Introduction
A convenient way of representing the levels of an economic time series is
through the so-called trend-cycle decomposition
= +
= deterministic trend
=
random
Estimation and Inference in Cointegration
Models
Economics 582
Eric Zivot
May 17, 2012
Tests for Cointegration
Let the ( 1) vector Y be (1). Recall, Y is cointegrated with 0
cointegrating vectors if there exists an ( ) matrix B0 such that
0 Y
1
.
B0Y =
Econ 582
Introduction to Pooled Cross Section and
Panel Data
Eric Zivot
May 22nd, 2012
Outline
Pooled Cross Section and Panel Data
Analysis of Pooled Cross Section Data
Two Period Panel Data
Multi-period Panel Data
Pooled Cross Section and Panel Data
Box-Jenkins Analysis of ARMA(p,q) Models
Eric Zivot
April 7, 2011
Box-Jenkins Modeling Strategy for Fitting ARMA(p, q) Models
1. Transform the data, if necessary, so that the assumption of covariance
stationarity is a reasonable one
2. Make an initial gue
Econ 582
Univariate Stationary Time Series
Eric Zivot
April 1, 2013
Time Series Concepts
A stochastic process cfw_ is a sequence of random variables indexed by
=1
time :
cfw_ 1 2 +1
A realization of a stochastic process is the sequence of observed data c
Econ 582
Forecasting
Eric Zivot
April 15, 2013
Forecasting
Let cfw_ be a covariance stationary are ergodic process, e.g. an ARMA( )
process with Wold representation
= +
X
~ (0 2)
=0
= + + 11 + 22 +
Let = cfw_ 1 denote the information set available at
Econ 582
Forecast Evaluation
Eric Zivot
April 17, 2013
Forecast Evaluation Statistics
Let cfw_ denote the series to be forecast and let +| denote the out-ofsample forecasts of + based on
Out-of-sample forecasts are typically computed using one of two met
Econ 582
Dynamic Regression Models
Eric Zivot
April 29, 2013
Distributed Lag (DL) Models
Consider the stylized regression model with a single lagged variable
= + 0 + 11 + (0 2)
is covariance stationary and ergodic
is strictly exogenous, [|] = 0 for all