HW #8
1.
A.
B. The 10Y yield changes to 3.279%, from 3.29%. The 3-month yield changes to 0.1755%,
from 0.15%.
C. 24 months prediction out of sample.
2.
A.
B. For the first 5 lags, the probability that all the residuals are uncorrelated is ~0.0000,
which means that some lag is not uncorrelated so this is not a good model.
C. I tried VAR(15) and got a 0.08 probability so we cannot reject the null that all the
residuals are uncorrelated.
D. This model predicts that inflation will go down.
E. CCP_F is the model predicting inflation so it seems to spike in mid-2023 and then fall
back down to pre-2022.
3.
A. The value of Ɣ is 0.8494 and the t-stat is 436.8706. Because stock prices follow a random
walk, the t-stat will not be a good fit on random walks especially with a large sample size.
B. 95% confidence interval for 1-1000: (0.393,0.410)
95% confidence interval for 1000-2000: (1.087,1.127)
95% confidence interval for 2000-3000: (0.844,0.874)
95% confidence interval for 3000-4000: (0.890,0.905)
95% confidence interval for 4000-end: (0.777,0.788)
C. None of the confidence intervals overlap so the estimates are not consistent with each other.
4.
A. Oil futures and oil spot prices are likely cointegrated because, if the spread gets too wide,
there will be the opportunity for arbitrage which will be exploited.
B. Unemployment rates and GDP are not cointegrated because GDP follows a random walk
while unemployment is mean-reverting. They can only be cointegrated when both series
follow a random walk.
C. IBM and GE stock both follow a random walk, but they have no industry-related reason
that would pull the two prices together. Thus, they are likely not cointegrated.
D. Because there is no possibility for easy arbitrage from France to the US, the two gas
prices are not necessarily cointegrated as the spread can get as wide as possible.
E. Because there is the possibility for arbitrage (buying gas in Canada to sell to US), the
spread between the two is mean reverting so the two series are cointegrated.
F. The two series are not cointegrated because the US Debt can increase without causing the
GDP to also increase.
5.
A. GDP Unit root test; this shows that it
follows a random walk, as it is
non-stationary.
PCEC unit root test; this shows that the
PCEC data also follows a random walk.
B. By calculating the series for a difference between the two log prices, we get a probability
of 0.0454, which suggests that the series does not follow a random walk so the two series
are cointegrated.
6.
A. We get that the difference between the log
ask and log bid has a probability of 0.000 in
the unit root test, showing that the two series
are cointegrated and mean-reverting.
The log ask is negative while the log bid is positive,
which makes sense. This is because if the spread is large,
then the ask price will decrease and the bid price will
increase. This will make the two values closer together
and keep the two series cointegrated.
B. The R2 for the VAR(1) is 0.023379 while for the
ECM(1) it is 0.040624, so the error correction
term did help.
C. I calculated using ECM(5) and got a one-step ahead log ask of 3.811936 and log bid of
3.810898.
D. Yes, we expect both the log ask and log bid to
have a positive coefficient with the indicator.
This is because if the indicator is negative
(seller initiated), the bid and ask should both go
down and, if the indicator is positive (buyer
initiated), both the bid and ask should also go
up.
E. This increases the R2 and adjusted R2 from E by
around 0.010-0.015, so it does improve the
model.
F. I chose a GARCH(1,1) model for this series.
The R2 decreased from both previous ECM
models, showing that this model is not a good
fit.