Lecture 5

Question 1

RW Model?

Answer 1

yt = yt-1 + et
shift in et stays in the model (has memory) time dependent mean, variance increasing over time.
RW plus drift has alpha0

Question 2

What is a spurious regression?

Answer 2

Relationship which is not driven by economic indicators (purely random), but the data looks correlated…

In the presence of non stationary variables, might be spurious regression: high R^2 a. t-stat. (significant) w/o economic meaning.

Question 3

For cases for yt and zt

Answer 3

1. Both are stationary –> use classical regress model
2. y and z are integrated by different orders. Regression equations using such variables are meaningless.
3. both nonstationary and integrated with the same order and the residual contains a stochastic trend –> Spurious regression, often recommended that the regression equation be estimated in first differences.
4. nonstationary, integrated by same order, and residual sequence is stationary –> Yt and Zt COINTEGRATED!

Funfact: I(2) usually prices, GDP I(1) so growth rate of GDP is stationary.

Question 4

Dickey Fuller test

Answer 4

Can be used to test for the presence of a unit root. if gamma = 0 yt contains a unit root, =1 RW nonstat.
Normal, with drift, drift + time trend…. test statistics are constructed like the f test.
If a structural change occurs DF will be biased.

Question 5

Selection of lag lengths:

Answer 5

General to specific methodology: use lag lenth p* if t-stat on lag p* is insignificant, reestimate the regression using lag length p*-1 until it is significant. After that use diagnostic checks like AIC or SBC (Model Selection Criteria).

Question 6

Dont use DF test for structural break, which test should be used?

Answer 6

Perrons test for structural change. Need trend shift dummy and level dummy…. Test residuals for WN.