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Question 1

What is the primary goal of the OLS method?

Answer 1

To minimize the sum of squared residuals and find the best-fitting line.

Question 2

What is the formula for ß in OLS regression?

Answer 2

ß= Cov(yt,yt-1)/Var(yt)

Question 3

what does it mean for an estimator to be BLUE?

Answer 3

Best Linear Unbiased Estimator: it has the smallest variance among all linear and unbiased estimators

Question 4

why is E[et|yt-1]=0 important in regression

Answer 4

it ensures that the error terms does not systematically vary with the independent variable, making the estimator unbiased

Question 5

what is homoscedasticity, and why is it necessary?

Answer 5

it means constant variance of the error term, necessary for valid standard errors

Question 6

what is the impacy of violating the no-autocorrelation assumption?

Answer 6

it causes inefficient OLS estimators and incorrect inference due to underestimated standard errors

Question 7

why is normality of errors important?

Answer 7

it ensures that finite sampling distribution of the parameters is normal, making hypothesis tesiting valid

Question 8

what are the steps in hypothesis testing?

Answer 8

1. state H0 and H1
2. calculate test statistic
3. determine critical values or p-value
4. Make a decision (reject/fail to reject H0)

Question 9

what does H0: a=0 signify in CAPM?

Answer 9

it tests whether there is an abnormal return (alpha); CAPM implies a=0

Question 10

what do the different values of the Durbin-Watson statistic indicate?

Answer 10

DW = 2: no serial correlation
DW < 2: positive serial correlation
DW > 2: Negative serial correlation

Question 11

how does serial correlation affect OLS estimates?

Answer 11

Makes OLS inefficient, underestimates error variance, and invalidates hypothesis testing

Question 12

what is serial correlation in regression models?

Answer 12

it occurs when residuals et are correlated with et-1 or other lags

Question 13

does serial correlation affect OLS unbiasedness?

Answer 13

No, OLS remains unbiased but looses efficiency and proper inference properties

Question 14

under what conditions does the Gauss-Markov theorm hold?

Answer 14

when assumtions of linearity, no multicollinearity, homoscedasticity, and no autocorrelation are met

Question 15

is normality of errors necessary for large samples?

Answer 15

No, the Central Limit Theory ensures that sampling distribution of OLS estimates is approximately normal

Question 16

why is a t-test used to test a=0 in CAPM?

Answer 16

to determine if the abnormal return (alpha) is significantly different from zero

Question 17

what’s the difference between finite and asymptotic properties of an estimator?

Answer 17

Finite properties apply to small samples, while asymptotic properties apply as sample size approaches infinity

Question 18

how does multicollinarity affect OLS

Answer 18

it does not bias the estimator but inflates standard errors, reducing statistcal significance

Question 19

why must the variance in the OLS be > 0?

Answer 19

without vairance in yt-1, ß cannot be calculated

Question 20

what are the type 1 and type 2 errors in hypothesis testing?

Answer 20

type 1: rejecting H0 when it is truw
type 2: fsiling to reject H0 when it is false

Question 21

what methods cna be used to adjust for serial correlationa?

Answer 21

use roburst standard error(e.g. Newey-west) or models like ARIMA

Question 22

what does a significant alpha in regression imply for investrs?

Answer 22

Evidence of abnormal returns not explained by market risk (ß)

Question 23

how can residual plots help detect serial corrrelation ?

Answer 23

Patterens in residuals, such as trends or cycles, indicated autocorrelation

Question 24

what is the difference between homoscedasticity and heteroscedasticity?

Answer 24

homoscedasticity: constant error variance
heteroscedasticity: error variance depends on the independent variable

Question 25

what are the assumptions needed for OLS to be BLUE?

Answer 25

Linearity, random sampling, no multicollinearity, zero conditional mean, homoscedasticity, no autocorrelation

Question 26

what is the sampling distribution of an estimator?

Answer 26

the distribution of the estimator accross random samples, refecting its variability

Question 27

linear in paramters

Answer 27

the stochastic process follows a linear model

Question 28

No Perfect Collinearity

Answer 28

no idependent variable is a perfect linear combination of the other

Question 29

zero conditional mean of error terms

Answer 29

the expeced value of the error terms, given the explanatory varables for all time periods is 0. error terms is uncorrelated with each explanatory variable in each time period

Question 30

Strict Exogenity

Answer 30

error terms is uncorrelated with each explanatory variable in each time period

Question 31

Weak exogeneity

Answer 31

Weak exogeneity requires the structural error to have zero conditional expectation given the present and past regres- sor values, allowing errors to correlate with future regressor realizations

Question 32

homoscedasticity

Answer 32

conditional on X, the variance et is constant. et and X are independent

Question 33

No serial correlation

Answer 33

Conditional on X, the errors in two different time periods are uncorrelated

Question 34

Autocorrelation

Answer 34

Conditional on X, the error in two different time periods are correlated

Question 35

Normality of error terms

Answer 35

The errors are independent of X and are independently and identically distributed