Typos

From Kevin Sheppard

Notes

Chapter 1

pg. 8 Bias should be defined using the estimator, $\gammacorrection{0.75}\mathrm{B}\left(\hat{\boldsymbol{\theta}}\right) = \E\left[\hat{\boldsymbol{\theta}}\right]-\boldsymbol{\theta}_0$ rather than $\gammacorrection{0.75}\mathrm{B}\left(\boldsymbol{\theta}\right) = \E\left[\hat{\boldsymbol{\theta}}\right]-\boldsymbol{\theta}_0$ (Liyan Shi, Matho)

pg. 10 Missing parentheses after $\gammacorrection{0.75}n^{-1}$ in derivation of bias of $\gammacorrection{0.75}\hat{\sigma}^2$ on lines 2, 3 and 4. (Liyan Shi, Matho x2)

pg. 11 Throughout the top 4 lines of math:

$\gammacorrection{0.75}\sum_{i=1}^n \epsilon_i^2$ should be $\gammacorrection{0.75}\sum_{i=1}^n \epsilon_i$

$\gammacorrection{0.75}\hat{\mu}^2 = \left(\mu + n^{-1}\sum_{i=1}^n \epsilon_i^2\right)^2$ should be $\gammacorrection{0.75}\hat{\mu}^2 = \left(\mu + n^{-1}\sum_{i=1}^n \epsilon_i\right)^2$
$\gammacorrection{0.75} = \mu^2 + 2\mu n^{-1}\sum_{i=1}^n \epsilon_i^2+\left(n^{-1}\sum_{i=1}^n \epsilon_i^2\right)^2$ should be $\gammacorrection{0.75}\mu^2 + 2\mu n^{-1}\sum_{i=1}^n \epsilon_i+\left(n^{-1}\sum_{i=1}^n \epsilon_i\right)^2$
$\gammacorrection{0.75}E\left[\hat{\mu}^2\right] = E\left[\mu^2 + 2\mu n^{-1} \sum_{i=1}^n \epsilon_i+\left(n^{-1} \sum_{i=1}^n \epsilon_i^2\right)^2\right]$ should be $\gammacorrection{0.75}E\left[\hat{\mu}^2\right] & = E\left[\mu^2 + 2\mu n^{-1} \sum_{i=1}^n \epsilon_i+\left(n^{-1} \sum_{i=1}^n \epsilon_i\right)^2\right]$
$\gammacorrection{0.75} = \mu^2 + 2\mu n^{-1} E\left[\sum_{i=1}^n \epsilon_i \right]+n^{-2}E\left[\left( \sum_{i=1}^n \epsilon_i^2\right)^2\right]$ should be $\gammacorrection{0.75} = \mu^2 + 2\mu n^{-1} E\left[\sum_{i=1}^n \epsilon_i\right]+n^{-2}E\left[\left( \sum_{i=1}^n \epsilon_i\right)^2\right]$
(Rochi Khemka, Matho x2)

pg. 14 dependant should be dependent (multiple instances). (Maxime Boonen, Typo x2)

pg. 17 Asymptotically normally distribution should be Asymptotically normally distributed (Liyan Shi, Typo)

pg. 18 Rearrangement of Taylor expansion is missing a minus sign on right hand side of equals sign on all lines. (Liyan Shi, Matho x2)

pg. 18 Under the top 4 equations, it should read "where $\gammacorrection{0.75}\mathbf{g}_n(\boldsymbol{\theta}_0) = n^{-1} \sum_{i=1}^n \mathbf{g}_i(\boldsymbol{\theta}_0)$ is the average of the moment conditions. Thus the normalized difference...". This change was needed to clearly define $\gammacorrection{0.75}\mathbf{g}_n(\boldsymbol{\theta}_0)$ (Khushbu Agrawal, Matho)

pg. 22 Information matrix equality is missing a minus sign (Liyan Shi, Matho)

pg. 24-5 Throughout $\gammacorrection{0.75}l(\lambda;\mathbf{y})$ should be $\gammacorrection{0.75}l(\boldsymbol{\theta};\mathbf{y})$ (Liyan Shi, Matho x2)

pg. 34. The definition of P-value should be: The p-value is largest size ( $\gammacorrection{0.75}\alpha$ ) where the null hypothesis cannot be rejected. The p-value can be equivalently defined as the smallest size where the null hypothesis can be rejected. (Rochi Khemka, Matho)

pg. 35 The discussion of power is missing some arguments, and the order of $\gammacorrection{0.75}C_\alpha$ and $\gammacorrection{0.75}\mu_1$ is reversed. Corrected PDF (Maxime Boonen, Matho x2)

pg. 39-40 Mixed references to $\gammacorrection{0.75}i$ and $\gammacorrection{0.75}j$ elements should all be $\gammacorrection{0.75}j$ (Liyan Shi, Matho x2)

pg. 45 $\gammacorrection{0.75}\delta = \sigma^2_{ND} - \sigma^2_{SP}$ , not $\gammacorrection{0.75}\delta = \sigma_{ND} - \sigma_{SP}$ (Liyan Shi, Matho)

Chapter 2

pg. 63, three lines after expression 2.11, it should say “Suppose $\gammacorrection{0.75}\mathbf{A}$ is a $\gammacorrection{0.75}k \, \times \, k$ non-singular matrix” (Gavin Kiel, Matho)

pg. 64 , should be null space of $\gammacorrection{0.75}\mathbf{X}^\prime$ , not null space of $\gammacorrection{0.75}\mathbf{X}$ in definition 2.5. (Gavin Kiel, Matho)

pg. 66, $\gammacorrection{0.75}\mathbf{M}_\iota = \mathbf{I}_n - \boldsymbol{\iota}(\boldsymbol{\iota}'\boldsymbol{\iota})^{-1}\boldsymbol{\iota}'$ rather than $\gammacorrection{0.75}\mathbf{M}_\iota = \boldsymbol{\iota}(\boldsymbol{\iota}'\boldsymbol{\iota})^{-1}\boldsymbol{\iota}'$ , which would be $\gammacorrection{0.75}\mathbf{P}_\boldsymbol{\iota}$ (Gavin Kiel, Matho)

pg. 71 and $\gammacorrection{0.75}\mathbf{C} \neq \left(\mathbf{X}'\mathbf{X}\right)\mathbf{X}'$ should be "...and $\gammacorrection{0.75}\mathbf{C} \neq \left(\mathbf{X}'\mathbf{X}\right)^{-1}\mathbf{X}'$ " (Rochi Khemka, Matho)

pg. 92-93 The term in the Wald statistic should always be $\gammacorrection{0.75}\mathbf{R}\boldsymbol{\Sigma}_{\mathbf{XX}}^{-1}\mathbf{S}\boldsymbol{\Sigma}_{\mathbf{XX}}^{-1}\mathbf{R}'$ so that it is an $\gammacorrection{0.75}m$ by $\gammacorrection{0.75}m$ matrix. (Stephen Caprio, Matho x2)

pg. 120 test for normality of estimated residuals is the Jarque-Beta (JB) test test for normality of estimated residuals is the Jarque-Berra (JB) test (Maxime Boonen, Typo)

pg. 122 and n some cases inconsistent should be and in some cases inconsistent (Maxime Boonen, Typo)

pg. 125 Fortunately bootstrapping is can be used should be Fortunately bootstrapping can be used (Maxime Boonen, Typo)

pg. 128 While this the regression estimates should be While the regression estimates (Maxime Boonen, Typo)

pg. 128 The first issue, which stocks to choose, is difficult and is typically motivated cost of trading and liquidity should be The first issue, which stocks to choose, is difficult and is typically motivated by cost of trading and liquidity (Maxime Boonen, Typo)

pg. 129 $\gammacorrection{0.75}= \left(\sum_{i=1}^n \mathbf{x}_i'\mathbf{x}_i\right)^{-1}\sum_{i=1}^n \mathbf{x}_i'\mathbf{x}_i$ should be $\gammacorrection{0.75}= \left(\sum_{i=1}^n \mathbf{x}_i'\mathbf{x}_i\right)^{-1}\sum_{i=1}^n \mathbf{x}_i'\boldsymbol{\epsilon}_i$ (Khushbu Agrawal, Matho)

pg. 133 [Exercise 2.3] $\gammacorrection{0.75}y_t = \beta_1 x_{it} + \beta_2 x_{2t} + \epsilon_t$ should be $\gammacorrection{0.75}y_t = \beta_1 x_{1,t} + \beta_2 x_{2,t} + \epsilon_t$ (Shawn Loh, Matho)

Chapter 3

pg. 143 A white noise process is also covariance stationarity should be A white noise process is also covariance stationary (Maxime Boonen, Typo)

pg. 152 There is a double equal sign == in eq. 3.29 (Maxime Boonen, Matho)

pg. 152 the stability conditions in a setting with out random shocks. should be the stability conditions in a setting without random shocks.(Maxime Boonen, Typo)

pg. 152 Deriving the autocovariance is straight forward should be Deriving the autocovariance is straightforward (Maxime Boonen, Typo)

pg. 153 (Definition 3.13) A solution ... as a function of only $\gammacorrection{0.75}\{x_i\}_{t=1}^{t}$ , constant and, when $\gammacorrection{0.75}y_t$ has finite history, an initial value $\gammacorrection{0.75}y_0$ . should be A solution ... as a function of only $\gammacorrection{0.75}\{x_i\}_{t=1}^{t}$ , a constant and, when $\gammacorrection{0.75}y_t$ has finite history, an initial value $\gammacorrection{0.75}y_0$ . (Maxime Boonen, Typo)

pg. 153 This is a ???? since it expresses yt as a function should be This is a solution since it expresses yt as a function (Maxime Boonen, Typo)

pg. 157-158 The values used to determine stationarity should all be based on $\gammacorrection{0.75}|c_p|$ , not $\gammacorrection{0.75}|z_p|$ . (Stephen Caprio, Matho x2)

pg. 175 Recall from ???? that maximum likelihood estimates are asymptotically normal, should be Recall from Chapter 1 that maximum likelihood estimates are asymptotically normal, (Maxime Boonen, Typo)

pg. 175 In practice $\gammacorrection{0.75}\mathbf{A}$ is not known should be In practice $\gammacorrection{0.75}\mathcal{I}$ is not known (Maxime Boonen, Matho)

pg. 188 another series which is stationary but with have a larger variance than a correctly detrended series should be another series which is stationary but with a larger variance than a correctly detrended series. (Maxime Boonen, Typo)

pg. 189 Dickey and Fuller considered three sperate specifications for their test should be Dickey and Fuller considered three seperate specifications for their test (Maxime Boonen, Typo)

Chapter 4

pg. 287 In Exercise 4.1 the use of $\gammacorrection{0.75}i$ is incorrect and should be $\gammacorrection{0.75}t$ (Shawn Loh, Matho x x2)

Chapter 6

pg. 368 Sum to should be to $\gammacorrection{0.75}T-1$ not $\gammacorrection{0.75}T+1$ (Shawn Loh, Matho)

Handouts

Financial Econometrics I and II course outline

1.2: Full stop inconsistency (Andreas Jaegle, Typo)

2.6: 'conometrics' (last word) (Andreas Jaegle, Typo)

2.8: Bullet point inconsistency (Andreas Jaegle, Typo)

Week 5 lecture handout

pg. 18 $\gammacorrection{0.75}\mathbf{P}_\mathbf{X} \mathbf{y}_i$ should be $\gammacorrection{0.75}\mathbf{P}_\mathbf{X} \mathbf{y}$ (no i) (Liyan Shi, Matho)

p. 26 The last bullet has a full stop, which is inconsistent with most other slides (Andreas Jaegle, Typo)

p. 28 'heavy tailed' should be 'heavy-tailed' (Andreas Jaegle, Typo)

p. 26, p. 28, p. 29 Different spellings of 'non-singular' (Andreas Jaegle, Typo x2)

p. 34 $\gammacorrection{0.75}\mathbf{Y}$ should be $\gammacorrection{0.75}\mathbf{y}$ in the FOC (Liyan Shi, Matho)

Week 7 lecture handouf

The LM test was missing and n and so should be $\gammacorrection{0.75}LM = n\bar{\tilde{\boldsymbol{s}}}'\hat{\tilde{\boldsymbol{S}}}^{-1}\bar{\tilde{\boldsymbol{s}}}$ (Stephen Caprio, Matho x2)

MATLAB

MATLAB Companion Course

First sentence problem (Andreas Jaegle, Typo)