University of California
Department of Economics
Doug Steigerwald
Advanced Econometrics I
Economics 245B
Lecture Schedule
1
2
3
4
5
Spurious Regression
delayed due to Winter Meetings
Cointegration
Regime Switching
Presentation: Tom Zimmerfaust (January 19
University of California
Department of Economics
D. Steigerwald
Economics 245B
Problem Set V
1.
$
$
If the sample autocorrelations in a series are 1 = .8 and 2 = .5, find asymptotically
efficient estimates of the parameters in an AR(2) model. If the varia
University of California
Department of Economics
D. Steigerwald
Economics 245B
Problem Set VI
1.
Consider the problem of selecting the correct order of a moving average process with a
sample of T observations. If the true order is q*, and the autocovarian
University of California
Department of Economics
D. Steigerwald
Economics 245B
Problem Set VII
1.
For the MA(1) process Yt = t + t-1, where < 1 and t IN(0,2), show how you
would estimate under the following situations:
a. Approximate MLE
b. Exact MLE
c. E
University of California
Department of Economics
D. Steigerwald
Economics 245B
Problem Set VII
1.
For the MA(1) process Yt = t + t-1, where < 1 and t IN(0,2), show how you
would estimate under the following situations:
a. Approximate MLE
b. Exact MLE
c. E
University of California
Department of Economics
D. Steigerwald
Economics 245B
Problem Set VIII
1.
Consider the regression model
yt = 0 + 1yt-1 + t
where cfw_tt=1,.,T is a mean zero white noise process.
$
a. For 1 < 1, find what the OLS estimator of 1 con
University of California
Department of Economics
D. Steigerwald
Economics 245B
Problem Set IX
1.
Given
y t = t + t 1, t = 1, . , T,
where
cfw_t i.i.d., E t = 0 , E 2 = 2 , < 1.
t
a.
b.
Is there measurement error in this problem? If so, where?
c.
What are
University of California
Department of Economics
D. Steigerwald
Economics 245B
Problem Set X
1.
Suppose you have two univariate processes, cfw_yt and cfw_xt.
(a)
Are I(0) and stationary equivalent characterizations of a process? Why or why
not?
(b)
Formal
Regime Switching
joint work with Drew Carter and Ben Hansen
Douglas G. Steigerwald
UC Santa Barbara
November 2010
D. Steigerwald (UCSB)
Regime Switching
November 2010
1 / 15
Roadmap
1
Empirical Use
1
2
2
How to specify models
1
3
what parameters vary over
Economics 245B
Spurious Regressions
Consider the linear regression model
Yt =
+ Xt0 + Ut :
In our previous analysis of the model, we have not mentioned serial correlation
of the regressors and the dependent variable. If both the regressors and the
depende
University of California
Department of Economics
D. Steigerwald
Economics 245B
Problem Set IV
1.
Given a time series yt, t = 1,.,T, where T is an even number, consider its finite Fourier
representation given by the cyclical trend model
(1)
yt =
a0
T
+
2 n
University of California
Department of Economics
D. Steigerwald
Economics 245B
Problem Set IV
1.
Given a time series yt, t = 1,.,T, where T is an even number, consider its finite Fourier
representation given by the cyclical trend model
(1)
yt =
a0
T
+
2 n
University of California
Department of Economics
D. Steigerwald
Economics 245B
Problem Set III
1.
Consider a sequence of observations on a random variable Xt, where t=1,.,T.
(a)
Suppose you are given the power spectral density function for X, fX(),
for [0
University of California
Department of Economics
Doug Steigerwald
Advanced Econometrics II
Economics 245B
Course Goals:
To provide training in frontier econometric methods, and the application of these
methods, at the intersection of computer science, eco
Economics 245B
Cointegration
Consider the linear regression model
Yt =
+ Xt0 + Ut :
We are interested in the behavior of the OLS estimators of
and . Recall
from last time that the degree of dependence in the regressor and dependent
variable play a key rol
Economics 245B
Exercise 2
Consider the regression model
Yt = Xt0 + Ut , t = 1, . . . , n
in which Xt and are K 1 vectors. While the error is mean zero and i.i.d.
unconditionally, Ut exhibits conditional heteroskedasticity of the ARCH form
U t = t Vt ,
wit
Testing for Unobserved Heterogeneity in
Exponential and Weibull Duration Models
JIN SEO CHO
HALBERT WHITE
School of Economics and Finance
Department of Economics
Victoria University of Wellington
University of California, San Diego
P.O. Box 600, Wellingto
Testing for hidden Markov switching
Jin Seo Cho
Victoria University of Wellington
PO Box 600, Wellington, 6001, New Zealand
http:/www.victoria.ac.nz/sef
Robert B Davies
Statistics Research Associates Limited
PO Box 12649, Wellington, 6144, New Zealand
htt
Economics 245B
Nonlinearities in Financial Data
In time-series analysis, one is often interested in forecasting the future value
of a random variable. Consider the rst-order autoregression
Yt = Y t
1
+ Ut ;
where Ut is a white-noise error with EUt2 = 2 .
Optimal Test for Markov Switching Parameters
Marine Carrascoy
Liang Huz
Werner Plobergerx
May 2009
Abstract
This paper proposes a class of optimal tests for the constancy of parameters in
random coe cients models. Our testing procedure covers the class of
University of California
Department of Economics
D. Steigerwald
Economics 245B
Problem Set I
1.
Consider the time-series model
Yt = X t + U t
t = 1, ,n
U t = Vt + 1Vt 1
Vt ~ IN 0, 2
(
)
a.
b.
If we assume that Yt is stationary and V0 = 0 , describe carefu
University of California
Department of Economics
D. Steigerwald
Economics 245B
Problem Set II
1.
Consider the linear regression model with a lagged dependent variable
Yt = 0 + 1Xt + 2Yt-1 + Ut ,
for t = 1,.,T. Now assume that U0 and Y0 are known and let
U
Testing for Regime Switching
joint work with Drew Carter and Ben Hansen
Douglas G. Steigerwald
UC Santa Barbara
August 2010
D. Steigerwald (UCSB)
Regime Switching
August 2010
1 / 37
Roadmap
Null Hypothesis (Ghosh and Sen 1985)
QLR (Cho and White 2007)
1
Q