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1

what is a random walk

accumulation of error terms from a stationary series of error terms

2

what is the static model

yt=β0+β1zt+ut

3

what is the finite distributed lag model

yt=β0+β1zt+β2zt-1+...+ut

4

what is a stochastic process

sequence of random variables indexed by time

5

what does weak stationary mean

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

6

what is an AR(1) model

Autoregressive:
yt=θyt-1+εt

7

what is a MA(1) model

Moving average:
yt=εt+αεt-1

8

what is weak dependence

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

9

what is the Correlagram equation

ρj=Cov(yt,yt-j)/Var(yt)=γj/γ0

10

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

Var: γ0=E((yt-μ)^2)

11

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

Autocov: γj=E((yt-μ)(yt-j-μ))

12

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

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

13

what does efficient mean

smallest variance

14

what does consistent mean

plim(αhat)=α

15

what does a unit root mean

yt=θyt-1+et
Unit root: θ=1

16

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

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

17

what is the stability condition

|θ|<1

18

how do you do the test of order of integration

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

19

what is the test for serial correlation

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

20

what is the unit root test

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

21

How do you do the Breusch-Pagan test for homoskedasticity

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

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)

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

23

what is the definition of heteroskedasticity

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

24

what is the equation for heteroskedasticity

E(ui^2|xi)=Var(yi|xi)=σ^2(xi),
fct of explanatory

25

what does robust mean

allows for heteroskedasticity

26

what does less noise do

improves efficiency

27

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

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

28

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

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

29

what is the variance formula

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

30

what is homoskedasticity

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