Flashcards in Pinboard Deck (42)

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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