Does not cover block 11 and 12. The rest is covered including the corresponding live sessions. The document is long, but it covers everything mentioned in class.
Table of Contents
Live session 1 ........................................................................................................................................... 3
Definition and conceptual framework......................................................................................................... 5
Extra video ATE ........................................................................................................................................... 6
Designing an event study ............................................................................................................................. 6
Difference calendar and event time....................................................................................................... 7
Stata codes ............................................................................................................................................... 7
Video normal and abnormal returns ......................................................................................................... 12
Stata commands AR and CAR ............................................................................................................ 14
Joint hypothesis problem ........................................................................................................................... 17
Canvas quizzes main points ................................................................................................................. 18
Live session 2 ......................................................................................................................................... 19
Lecture 3 Inference event studies .............................................................................................................. 23
Stata ....................................................................................................................................................... 25
Slides 2: event studies ................................................................................................................................ 26
Lecture 3 heteroscedasticity ....................................................................................................................... 28
Stata ....................................................................................................................................................... 31
Cross sectional correlation ........................................................................................................................ 32
Stata ....................................................................................................................................................... 35
Few events .................................................................................................................................................. 36
Stata few events..................................................................................................................................... 37
Recap quiz ............................................................................................................................................. 38
Live session 3 ......................................................................................................................................... 40
Lecture 4: time series ................................................................................................................................. 46
Trend and seasonality ................................................................................................................................ 47
Dynamic models ......................................................................................................................................... 50
Live session 4 ......................................................................................................................................... 55
Lecture 5: OLS assumptions and time series ............................................................................................ 59
Time series estimation Stata ...................................................................................................................... 64
Extra videos intuition ........................................................................................................................... 64
Live session 5 ......................................................................................................................................... 65
Assignment questions................................................................................................................................. 70
,Lecture 6: serial correlation and strong dependence ............................................................................... 71
Extra video random walk..................................................................................................................... 73
Serial correlation .................................................................................................................................. 73
Serial correlation testing ...................................................................................................................... 79
Stata Breusch-Godfrey ......................................................................................................................... 79
Class quiz summary.............................................................................................................................. 79
Live session 6 – serial correlation and persistent processes .............................................................. 84
Lecture 7 Time series models..................................................................................................................... 87
Time series processes ............................................................................................................................ 87
Selecting the right model ...................................................................................................................... 92
Stata ....................................................................................................................................................... 95
Live session 7.............................................................................................................................................. 96
Assignment for practice notes.................................................................................................................... 96
Lecture 8: Forecasting basics .................................................................................................................... 97
Model selection.................................................................................................................................... 100
Answers to the quiz: ........................................................................................................................... 101
Lecture 9 Stochastic volatility .................................................................................................................. 102
Stylized facts........................................................................................................................................ 102
Stochastic volatility with dice and coins ........................................................................................... 102
GARCH models .................................................................................................................................. 103
GARCH ............................................................................................................................................... 104
Leverage effects................................................................................................................................... 104
GARCH-in-mean model..................................................................................................................... 104
Live session block 8 and 9........................................................................................................................ 105
One step forecast................................................................................................................................. 105
Two step forecast → easy ................................................................................................................... 105
Two step forecast → long route ......................................................................................................... 106
................................ 106
Live session block 10 ................................................................................................................................ 106
Live session Mock exam .......................................................................................................................... 108
EXAM preparation................................................................................................................................... 109
Block 12: Live session .............................................................................................................................. 118
𝐶𝑜𝑣(𝑎, 𝑥) = 0, since a is a constant.
𝐶𝑜𝑣(𝑥, 𝑥) = 𝑉𝑎𝑟(𝑥)
𝐶𝑜𝑣(𝑦, 𝑥) = 𝐶𝑜𝑣(𝑥, 𝑦)
𝐶𝑜𝑣(𝑥, 𝑦)
𝐶𝑜𝑟𝑟(𝑥, 𝑦) =
√𝑉𝑎𝑟(𝑥) ∗ 𝑉𝑎𝑟(𝑦)
- Correlation is NOT a linear operator. This is why it falls between 0 and 1.
OLS
𝑦 = 𝛼 + 𝛽𝑥 + 𝜀
𝐶𝑜𝑣 (𝑥, 𝑦) 𝑉𝑎𝑟(𝑥)
𝛽̂ = = 𝐶𝑜𝑟𝑟(𝑥, 𝑦) ∗ √
𝑉𝑎𝑟(𝑥) 𝑉𝑎𝑟(𝑦)
- Variance of y and x is the same for event studies, so the second formula might be easier to use.
𝜀̂ = 𝐸(𝑦 − 𝛼̂ + ̂𝛽 𝑥) = 0
- Residual for OLS is ALWAYS 0.
𝛼̂ = 𝐸(𝑦) − 𝛽 ∗ 𝐸(𝑥)
Consistent: beta hat approaches beta when the sample size increases.
- Consistency is a property of the estimator but NOT of estimates.
Unbiased: the expected value of beta hat is equal to the true beta.
Differences two estimators of the variance:
- Both are consistent.
- V2 is unbiased but V1 has bias.
o Use V2 for small sample sizes.
- V1 is more efficient than V2.
o Use for large sample sizes.
V1 can never be BLUE, because it is biased.
- BLUE: Best Linear Unbiased Estimator.
, Conditioning: we take a subset of the sample and we take a moment in the subset of the sample.
You have 5 squares with different colors and each square has a color.
- We haven’t computed the risk before knowing the color. We have calculated the average risk
with knowing the color. So, there is still some risk there. As a result, it is an approximation.
We can, however, determine the true value by covering these steps:
Law of total expectation:
𝐸(𝑦) = 𝐸(𝐸(𝑦|𝑥)) = ∑ 𝐸(𝑦|𝑥 = 𝑥𝑖 ) ∗ 𝑃(𝑥 = 𝑥𝑖 )
Law total variance:
𝑉(𝑦) = 𝑉(𝐸(𝑦|𝑥)) + 𝐸(𝑉(𝑦|𝑥))
- Expected idiosyncratic volatility
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