Week 13: Chapter 18 Flashcards
Write the formula for the Dickey-Fuller Test and its hypotheses
yt =α+ρyt−1+et
- H0: ρ=1 against H1: ρ<1
- Basically testing if Yt is I(1)
Transform the DF model to allow for the testing of unit root tests, and define the new hypothesis
∆yt =α+θyt−1+et
H0: θ = 0 against H1: θ < 0
Whats the benefit of the augmented DF test?
takes care of any remaining serial correlation that may exist even after taking the first difference
What happens if we dont account for a time trend in the DF test?
we can mistakenly conclude that a trend stationary
process has a unit root
spurious correlation
two variables being related through a correlation with a third variable
spurious regression
y and x are not related, but OLS will often indicate a statistically significant relationship
What are two problems with spurious regressions
- 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
Write the formula for the Engle-Granger test
notes
What does the Engle-Granger enable you to test?
Allows one to test for cointegration by testing for a unit root in the residual ut, by using a DF/ADF test
If two variables are not cointegrated, a regression of yt on xt is…
… 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
What is the benefit of yt and xt being cointegrated?
It allows one to specify more complex dynamics in the model
What does the error correction term allow you to study?
The short-term dynamics between y and
x
Whats the simplified model for the error correction term?
∆yt =α0+γ0∆xt +δ(yt−1−βxt−1)+ut
In the simplified error correction model, if yt−1 > βxt−1 what happens?
y in the previous period overshot the equilibrium and δ works to bring y back to the equilibrium
In the simplified error correction model, if yt−1 < βxt−1 what happens?
δ will be positive and will bring y back to equilibrium
Write out the steps for estimating the error correction model when 𝛽 is known.
regress ∆yt on ∆xt and st−1 = (yt−1 − βxt−1)
Write out the steps for estimating the error correction model when 𝛽 is unknown.
estimate 𝛽 and then use sˆt-1 =(yt-1−βˆxt-1 )
Whats the difference between predicted value and forecasted values?
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
What is a loss function?
tells us about how close or how far the forecast was relative to the realized value
Squared forecast error equation
notes
Write down the VAR model equation
yt =δ0 + α1yt−1 + γ1zt−1 + ut
Write the process of F STAT approach
- 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
What are the cons of the F stat approach?
- 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
Whats the formula for BIC
NOTES
Whats for formula for AIC
notes
whats the formula for z Granger causes y and what do the parameters entail?
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
Whats the difference between out-of-sample and in-sample criteria?
- 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
What does RSME represent
- the sample standard deviation of the forecast errors
- Want the model with the smallest RSME
What does MAE represent (mean absolute error)
- Represents the average of the absolute forecast errors
- We prefer the model with the smallest MAE
What happens when you dont control for data with strong seasonality?
Will affect the quality of the forecasts the model produces
In the infinite DL model, show how a temp change in z has no long-run effects on y
notes
