Week 13: Chapter 18

Question 1

Write the formula for the Dickey-Fuller Test and its hypotheses

Answer 1

yt =α+ρyt−1+et
- H0: ρ=1 against H1: ρ<1
- Basically testing if Yt is I(1)

Question 2

Transform the DF model to allow for the testing of unit root tests, and define the new hypothesis

Answer 2

∆yt =α+θyt−1+et
H0: θ = 0 against H1: θ < 0

Question 3

Whats the benefit of the augmented DF test?

Answer 3

takes care of any remaining serial correlation that may exist even after taking the first difference

Question 4

What happens if we dont account for a time trend in the DF test?

Answer 4

we can mistakenly conclude that a trend stationary
process has a unit root

Question 5

spurious correlation

Answer 5

two variables being related through a correlation with a third variable

Question 6

spurious regression

Answer 6

y and x are not related, but OLS will often indicate a statistically significant relationship

Question 7

What are two problems with spurious regressions

Answer 7

• Spurious regressions will also have a large R2 with a high probability
• If yt and at least one of the regressors is I(1), the results will likely be spurious

Question 8

Write the formula for the Engle-Granger test

Answer 8

notes

Question 9

What does the Engle-Granger enable you to test?

Answer 9

Allows one to test for cointegration by testing for a unit root in the residual ut, by using a DF/ADF test

Question 10

If two variables are not cointegrated, a regression of yt on xt is…

Answer 10

… spurious, there is no long term relationship between x and y BUT the change in x and the change in y CAN be cointegrated
- there can be a long term relationship between ∆yt and ∆xt without there being a long term relationship between y and x

Question 11

What is the benefit of yt and xt being cointegrated?

Answer 11

It allows one to specify more complex dynamics in the model

Question 12

What does the error correction term allow you to study?

Answer 12

The short-term dynamics between y and
x

Question 13

Whats the simplified model for the error correction term?

Answer 13

∆yt =α0+γ0∆xt +δ(yt−1−βxt−1)+ut

Question 14

In the simplified error correction model, if yt−1 > βxt−1 what happens?

Answer 14

y in the previous period overshot the equilibrium and δ works to bring y back to the equilibrium

Question 15

In the simplified error correction model, if yt−1 < βxt−1 what happens?

Answer 15

δ will be positive and will bring y back to equilibrium

Question 16

Write out the steps for estimating the error correction model when 𝛽 is known.

Answer 16

regress ∆yt on ∆xt and st−1 = (yt−1 − βxt−1)

Question 17

Write out the steps for estimating the error correction model when 𝛽 is unknown.

Answer 17

estimate 𝛽 and then use sˆt-1 =(yt-1−βˆxt-1 )

Question 18

Whats the difference between predicted value and forecasted values?

Answer 18

Predicted values: tell you about IN-SAMPLE model fit
Forecasted values: involves uncertainty and tells us about out-of-sample model fit. We want to predict future values that have not yet occured and exist outside the sample

Question 19

What is a loss function?

Answer 19

tells us about how close or how far the forecast was relative to the realized value

Question 20

Squared forecast error equation

Answer 20

notes

Question 21

Write down the VAR model equation

Answer 21

yt =δ0 + α1yt−1 + γ1zt−1 + ut

Question 22

Write the process of F STAT approach

Answer 22

• Start with a model with as many lags of the dependent variable as possible * Test the significance of the last lag
• Do this until the last lag becomes significant at the 95% confidence level
• Then, repeat with other covariates

Question 23

What are the cons of the F stat approach?

Answer 23

• it will sometimes suggest too many lags
• Assume the true AR order is 5, so that the sixth coefficient is zero
• A test using the t-statistic will incorrectly reject the null 5% of the time

Question 24

Whats the formula for BIC

Answer 24

NOTES

Question 25

Whats for formula for AIC

Answer 25

notes

Question 26

whats the formula for z Granger causes y and what do the parameters entail?

Answer 26

E(yt|It−1) ̸= E(yt|Jt−1)
- It-1: Contains past values of both y and z
- Jt-1: Contains past values of ONLY

Question 27

Whats the difference between out-of-sample and in-sample criteria?

Answer 27

• In-sample criteria: how well does the model fit the observations in the sample
• Out-of-sample criteria: how well does the model fit observations outside of the sample

Question 28

What does RSME represent

Answer 28

• the sample standard deviation of the forecast errors
• Want the model with the smallest RSME

Question 29

What does MAE represent (mean absolute error)

Answer 29

• Represents the average of the absolute forecast errors
• We prefer the model with the smallest MAE

Question 30

What happens when you dont control for data with strong seasonality?

Answer 30

Will affect the quality of the forecasts the model produces

Question 31

In the infinite DL model, show how a temp change in z has no long-run effects on y

Answer 31

notes