Pinboard

Question 1

what is a random walk

Answer 1

accumulation of error terms from a stationary series of error terms

Question 2

what is the static model

Answer 2

yt=β0+β1zt+ut

Question 3

what is the finite distributed lag model

Answer 3

yt=β0+β1zt+β2zt-1+…+ut

Question 4

what is a stochastic process

Answer 4

sequence of random variables indexed by time

Question 5

what does weak stationary mean

Answer 5

Mean, variance and covariances are stable. Mean and variance constant over time. Covariance between yt and yt-j depends only on distance between two terms

Question 6

what is an AR(1) model

Answer 6

Autoregressive:

yt=θyt-1+εt

Question 7

what is a MA(1) model

Answer 7

Moving average:

yt=εt+αεt-1

Question 8

what is weak dependence

Answer 8

correlations between time series variables become smaller and smaller. Weakly dependent if Corr(yt,yt-j)->0 as j->∞ (asymptotically uncorrelated)

Question 9

what is the Correlagram equation

Answer 9

ρj=Cov(yt,yt-j)/Var(yt)=γj/γ0

Question 10

what is the variance part of the correlagram equation γ0: (ρj=Cov(yt,yt-j)/Var(yt)=γj/γ0)

Answer 10

Var: γ0=E((yt-μ)^2)

Question 11

what is the autocovariance part of the correlagram equation γj: (ρj=Cov(yt,yt-j)/Var(yt)=γj/γ0)

Answer 11

Autocov: γj=E((yt-μ)(yt-j-μ))

Question 12

what does the fact that E(et^2)=σ^2 mean

Answer 12

the variance where the expected value is 0 (can derive it)

Question 13

what does efficient mean

Answer 13

smallest variance

Question 14

what does consistent mean

Answer 14

plim(αhat)=α

Question 15

what does a unit root mean

Answer 15

yt=θyt-1+et

Unit root: θ=1

Question 16

what is a way of showing et and es are serially uncorrelated when E(et)=0

Answer 16

E(etes)=0 (from Cov(etes) with E(et)=0)

Question 17

what is the stability condition

Answer 17

|θ|<1

Question 18

how do you do the test of order of integration

Answer 18

checking whether weakly stationary -> check whether mean and variance are constant over time -> then check covariance between yt and yt-j

Question 19

what is the test for serial correlation

Answer 19

OLS yt on xt to get β1 -> form residual -> regress uthat on ut-1hat and xt… to get ρ -> F test

Question 20

what is the unit root test

Answer 20

∆yt=c+(θ-1)yt-1+et, (θ-1)=γ -> Dickey-Fuller test against adjusted CVs. DF=γhat/var(γhat)^1/2

Question 21

How do you do the Breusch-Pagan test for homoskedasticity

Answer 21

Null homo H0:E(ui^2|xi)=σ^2, var not fct of explanatory variables, can’t observe ui^2hat so replace by OLS residuals and test H0:δ1=δ2=…=δk=0 in ui^2hat=δ0+δ1x1i+δ2x2i+…+δkxki+ε R^2 in regression of ui^2hat on xi->R^2u^2hat. Bresuch-Pagan stat nR^2u^2hat, n sample size, bull home nR^2u^2hat->d χk^2, null rejected if nR^2u^2hat larger than cv of χk^2 distribution. don’t have to specify an alternative

Question 22

In the Breusch-pagan test do you expect a high or low R^2 under the null of homoskedasticity: (H0:δ1=δ2=…=δk=0 in ui^2hat=δ0+δ1x1i+δ2x2i+…+δkxki+ε)

Answer 22

R^2 small under null because none of var in u explained by regressors

Question 23

what is the definition of heteroskedasticity

Answer 23

conditional variance of the error term in the linear model is different for different values of the explanatory variable
E(ui^2|xi)=Var(yi|xi)=σ^2(xi),
fct of explanatory

Question 24

what is the equation for heteroskedasticity

Answer 24

E(ui^2|xi)=Var(yi|xi)=σ^2(xi),

fct of explanatory

Question 25

what does robust mean

Answer 25

allows for heteroskedasticity

Question 26

what does less noise do

Answer 26

improves efficiency

Question 27

how does the weighted least squares method work (in words)

Answer 27

more noise=less weight
less noise=more weight,
less noise improves efficiency

Question 28

what is the variance (words and equation that matches words)

Answer 28

sum of squared distances of each term from the mean (μ), divided by number of terms in the distribution, from this subtract the square of the mean,
σ^2=(Σ(X-μ)^2)/N = (Σx^2)/N-μ^2

Question 29

what is the variance formula

Answer 29

Var(X)=E((X-E(X))^2) = E(X^2)-(E(X))^2

Question 30

what is homoskedasticity

Answer 30

conditional variance of u given x1,…,xk is constant: Var(u|x1,…,xk)=σ^2

Question 31

what is the total sum of squares (TSS)

Answer 31

Σ(yi-ybar)^2,
measure of total sample variation in the y: how spread out the yi are in the sample.
If we divide the TSS by n-1 we obtain the sample variance

Question 32

what is the model sum of squares (MSS)

Answer 32

Σ(yihat-ybar)^2.

Sample variation in yihat (where we use the fact that ybarhat=ybar)

Question 33

what is the residual sum of squares (RSS or SSR)

Answer 33

Σuihat^2.

RSS measures sample variation in uihat

Question 34

what is the relationship between the RSS the MSS and the TSS

Answer 34

the total variation in y can be expressed as the sum of the explained variation and the unexplained variation.
TSS=MSS+RSS

Question 35

what is the R^2 test

Answer 35

R^2=MSS/TSS = 1 - RSS/TSS

Question 36

if TSS=MSS+RSS what is the F stat that allows for testing whether all parameters, apart from the constant are zero

Answer 36

F = (TSS-RSS)/k / RSS/(n-k-1)

= MSS/k / RSS/(n-k-1)~F(k,n-k-1)

Question 37

what is R^2 a measure of

Answer 37

measure of how much variation in y is explained by variables in model

Question 38

what is the Gauss-Markov property

Answer 38

under the additional assumption of homoskedasticity, the estimator βhat is efficient (smallest variance), and is the BLUE of β, with variance Var(βhat)=σ^2(X’X)^-1

Question 39

what is the covariance equation

Answer 39

Cov(x,y)=E((X-E(X))(Y-E(Y)))

E(XY)-E(X)E(Y)

Question 40

Correlation equation

Answer 40

ρxy=Cov(x,y)/σxσy

Question 41

what is the zero conditional mean assumption

Answer 41

random error u satisfies E(u|x1,…,xk)=0 -> needed for consistency

Question 42

what does no perfect collinearity mean

Answer 42

matrix X full (column) rank