Quant

Question 1

Machine Learning

Answer 1

Gives a computer the ability to improve its performance of a task over time

Question 2

t-test for r (correlation)

Answer 2

(n-2 df)

t = r*sqrt(n-2)/sqrt(1-r^2)

Question 3

Estimated slope coefficient - least squares

Answer 3

cov (xy) / var (x)

Question 4

Confidence interval for predicted Y-value

Answer 4

y = +- tc * SE of forecast

Question 5

SST, MSR, MSE formulas

Answer 5

SST = RSS + SSE
MSR = RSS/k
MSE = SSE/(n-k-1)

Question 6

Test statistical significant of regression

Answer 6

F = MSR / MSE with k and n-k-1 df (1-tail)

Question 7

SSE

Answer 7

SSE = sqrt(MSE)

Smaller SSE = better fit

Question 8

Coefficient of Determination

Answer 8

R^2 = RSS / SST

% variability of Y explained by Xs; higher R^2 = better fit

Question 9

Heteroskedasticity

Answer 9

Non constant error variance
Detect with Breuch-Pagan test
Correct with White-corrected standard errors

Question 10

Autocorrelation

Answer 10

Correlation among error terms
Detect with durbin-watson test -> positive autocorrelation if DW < dl
Correct by adjusting standard errors using Hansen method

Question 11

Multicollinearity

Answer 11

High correlation between X’s
Detect if F-test significant, t-test insignificant
Correct by dropping X variables

Question 12

Model Misspecification

Answer 12

Omitting a variable
Variable should be transformed
Incorrectly pooling data
Using lagged dependent variable as independent variable
Forecasting the past
Measuring independent variables with error

Question 13

Effects of Misspecification

Answer 13

1. Regression coefficients are biased and inconsistent

2. Lack of confidence in hypothesis tests of the coefficients or the model predictions

Question 14

Supervised machine learning

Answer 14

inputs and outputs are identified

relationships modeled from labeled data

Question 15

Unsupervised machine learning

Answer 15

Algorithm itself seeks to describe the structure of unlabeled data

Question 16

Covariance stationary

Answer 16

mean and variance doesn’t change over time
To determine if a time series is covariance stationary,
1. plot data
2. run an AR model and test correlations
3. Perform Dickey-Fuller test

Question 17

Unit root

Answer 17

coefficient on lagged dependent variable = 1. Series with unit root is not covariance stationary. First differencing will often eliminating the unit root

Question 18

mean reverting level for AR(1)

Answer 18

b0/(1-b1)

Question 19

RSME

Answer 19

square root of average squared error

Question 20

Random walk time series

Answer 20

xt = x(t-1) + error(t)

Question 21

Seasonality

Answer 21

indicated by statistically significant lagged error term. correct by adding lagged term

Question 22

ARCH

Answer 22

detected by estimating:

e^2(t) = a0 + a1*e^2(t-1) + mean(t)

Question 23

Variance of ARCH series

Answer 23

sigma^2(t+1) = ^a0 + ^a1*e(t)^2

Question 24

Risk types

Answer 24

simulations
distribution of risk: continuous
sequential: does not matter
accommodates correlated variables? Yes

scenario analysis
distribution of risk: discrete
sequential: no
accommodates correlated variables? Yes

Decision Trees
distribution of risk: discrete
sequential: yes
accommodates correlated variables? no