ECO 341, The Midterm
1. Some General Questions
a. What does it mean for a time series to be variance ergodic?
A: If the series is variance ergodic, then as the sample size approaches innity, the sample variance
converges to the true variance. We cannot te
Introduction: Problems
1. Re-write the following stochastic process using lag operators:
xt = + (1 L + 3 L3 + 4 L4 )xt + (1 + 1 L + 3 L3 )ut
(1)
2. OLS may be appropriate if the temporal component of the data does not matter. For
example, suppose that I r
Introduction: Problems
1. Re-write the following stochastic process using lag operators:
xt = + 1 xt1 + 3 xt3 + 4 xt4 + ut + 1 ut1 + 3 ut3
(1)
2. Suppose that you have a time-series measured annually. Under what conditions might it be
appropriate to simpl
Linear Algebra and Econometric Review: Problems
Consider the following matrices:
A=
3 9
1 4
4 1
B= 1 4 C=
5 3
2 0 7
0 1 3
1. Calculate the following:
a. CB
b. BC
c. A + (CB)
d. A + (BC)
e. A1
f. Det(A)
g. C 1
h. the eigenvalues and eigenvectors of CB
i. t
Economics 318, Advanced Macroeconomics
Winter 2014
Paper Assignment
One-third of the nal class grade depends on a nal paper. The class material is largely theoretical. While you are welcome to write an original theoretical paper (i.e. a new model, this is
Stochastic Processes: Key
Consider the following AR(2) process
xt = + 2 xt2 + ut
(1)
xt2 = + 2 xt4 + ut2
(2)
2
xt = (1 + 2 ) + 2 xt4 + ut + 2 ut2
(3)
1. We may rst re-date (1):
Inserting (2) into (1):
which is an ARMA(4,2). Iterating again yields:
2
3
2
x
Trends and Unit Roots1
As we have discussed, the estimation techniques of this class require that each time series
be stationary. Unfortunately, many time series do not possess this property. These notes thus
demonstrate how we can x non stationary time s
Vector Autoregressions1
We now turn our attention to estimating an entire system of variables through the use of vector
autoregressions. Ultimately, we wish to estimate and forecast how shocks to one variable in the system
may affect others over time. Thi
ECO 341, Fall 2013, Required Homework Assignment #4
Due at 5 PM on Wednesday, October 30
For this assignment, you are to collect a set of time series. These may consist of the variables that
you will use for your nal project or you may use a different set
ECO 341, The Midterm
1. Some General Questions
a. What does it mean for a time series to be variance ergodic?
b. How do econometricians generally deal with correlation between the error term and an independent
variable?
c. Under what conditions does prope