Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

ECONOMETRICS > Time series > Flashcards

Time series Flashcards

1
Q

What are common sources of endogeneity

A

Omitted variables, Simultaneity, measurement error

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What are omitted variables and what are they a source of?

A

When a statistical model leaves out one or more relevant variables. Omits an independent variable that is correlated with both the dependent variable and one or more of the independent variables. Source of endogeneity

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What is simultaneity bias and what can it cause

A

Where the explanatory variable is jointly determined with the dependent variable (X causes Y, Y causes X). Source of endogeneity. Education determines wages but wages also determine future education

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What is measurement error and what can it cause

A

Difference between a measured quantity and its true value. Source of endogeneity.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

2 good examples of omitted variable bias in wage education

A

Education of individual’s parents,

Ability

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Example of measurement error in wage education model

A

Not so much measurement but years does not take into account quality of education

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

what is a chi squared distribution mean and variance

A

mean is the degrees of freedom,

variance is the 2 x degrees of freedom

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

log-level what does β mean

A

100(β1) is the percentage change in y

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

log-log what is β

A

β is the percentage change

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

level-log what is β

A

∆=(β1/100)%∆x

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

what do you need for unbiased estimates

A

linear in parameters,
random sampling,
sample variation in explanatory variable,
zero conditional mean (E(u|x)=0)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

what does unbiased mean

A

E(βhat)=β,

the sampling distribution of βhat is centred around β

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

what are the main assumptions for the main properties of OLS in matrix form

A

data generating process,
random sampling of n observations,
no perfect collinearity: matrix X of full (column) rank, rank k+1,
Zero conditional mean E(u|x1,…,xk)=0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

what does —>p(above) and —>d(above) mean

A
  • –>p is convergence in probability

- –>d is convergence in distribution

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

what is stationarity

A

stationary time series is a process whose probability distributions are stable over time

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

what is significant about the first-order autocovariances for the MA(1) model (yt=εt+αεt-1)

A

only first-oder autocovariance is nonzero

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

what is the strong exogeneity eassumption

A

zero conditional mean assumption E(ut|x)=0, imposes that the error at time t be uncorrelated with each explanatory variable in every time period

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

what can a model with a lagged dependent variable not satisfy

A

model with lagged dependent variable cannot satisfy strong exogeneity

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

what is weakly independent

A

yt and yt-j are ‘almost independent’ as j gets large

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

what is a stable AR(1) process

A

weakly dependent

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

what is serial correlation

A

when homoskedasticity doesn’t hold

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

what happens to OLS in the presence of serial correlation

A

OLS remains consistent, but becomes inefficient and its standard errors need to be adjusted

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

what happens to the Gauss-Markov property under serial correlation

A

Gauss-Markov requires homoskedasticity and serially uncorrelated standard errors, OLS is n longer BLUE in presence of serial correlation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

what’s the difference between the test for serial correlation and the test for serial correlation without strong exogeneity

A

Do OLS regression of uthat on x1t,x2t,… and ut-1hat for all t as opposed to just uthat on ut-1hat

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

how do you adapt the test for serial correlation to tes for higher-order serial correlation (second order ut-2hat)

A

only need to add ut-2hat (,…ut-qhat) to the equation,
uthat=ρ1ut-1+ρ2ut-2+et,
Null: H0:ρ1=ρ2=,…,ρq=0
Then do F test to test joint significance of ρ1 and ρ2 simultaneously

26
Q

In a random walk yt=θyt-1+et what makes it nonstationary

A

whenever |θ|>1, process yt has variance that goes to infinity and is nonstationary

27
Q

where does the term unit root come from

A

called unit root as comes from the fact that θ=1 in AR(1) so t-1 is the root,
strong memory

28
Q

when dealing with a unit root how do you transform it

A

when dealing with a unit root, first differencing turns a unit root process into a weakly dependent process.
It is then integrated of order one or I(1). Also called difference stationary

29
Q

what does difference stationary mean

A

when first differencing turns process (for ex a unit root) into a weakly dependent process

30
Q

what is the order of integration

A

the number of times the variable has to be differenced to arrive at a weakly dependent process

31
Q

what order of integration is a weakly dependent process

A

if process weakly dependent, it is integrated of oder zero I(0)

32
Q

what is the purpose of differencing to get weakly stationary

A

need to keep on differencing until mean, variance and covariance don’t depend on time

33
Q

what does trend stationary mean

A

in a nonstationary model including a trend, if after removing the trend the resulting variable becomes stationary the variable is trend stationary

34
Q

if a model is trend stationary what is the impact of a shock to yt

A

shock to yt over one period and yt returns to its trend value, if no further shocks

35
Q

what is the impact of a shock if a model is difference stationary

A

difference stationary like random walk: a shock in period s has not only an impact on yt but also on yt+1 and yt+2 and so on

36
Q

why can’t you do a t test when testing for unit roots

A

H0: |θ|=1 so process nonstationary so the standard results on the distribution of OLS are no longer valid,
t ratio does not have t distribution

37
Q

what did Dickey and Fuller do

A

discovered unit root hypothesis could still be tested by t-type of statistics provided the critical values are appropriately adjusted

38
Q

what did MacKinnon do

A

MacKinnon used computer simulations to calculate a ‘response surface’ for critical values of the Dickey-Fuller t tests. Can be used to compute critical values for any sample size

39
Q

what’s the adjustment to the model when testing for unit roots with a constant but no trend

A

∆yt = c + γyt-1 + et,

γ=(θ-1)

40
Q

what’s the adjustment to the model when testing for unit roots with a constant and trend

A

∆yt = c + γyt-1 + δt + et,

γ=(θ-1)

41
Q

what is the augmented Dickey-Fuller

A

allows for serial correlation by having lagged first differences which absorb the serial correlation,
∆yt=γyt-1+β1∆yt-1+β2∆yt-2+…+βp∆yt-p+et

42
Q

what are some problems with the Dickey-Fuller test

A 
low power (error of accepting null when alternative true),
'Near' unit root, not good at testing for values such as θ=0.98,
Structural breaks - presence of structural breaks in series, if ignored, lead to null of difference stationary being wrongly accepted
43
Q

what is a spurious regression

A

not what it purports to be, false or fake.

Find statistically significant relationship betw xt and yt which is spurious is xt and yt are unrelated

44
Q

what are the consequences for OLS of heteroskedasticity

A

remains unbiased, consistent and aymptotically normally distributed,
variance different so s.e. that were valid will lead to invalid inference (eg t test not correct size and confidence intervals not correct),
OLS no longer efficient

45
Q

what does the AR(1) correlogram do

A

decay slowly to 0

46
Q

what does the MA(1) correlogram do

A

drops to 0 after one period

47
Q

what does weak dependence say that’s different to weak stationarity

A

adds that correlation goes to 0 as j->∞,

Corr(yt,yt+j) -> 0 as j->∞

48
Q

what does weak dependence allow for

A

contemporaneous exogeneity as opposed to strong, E(ut|xt)=0 only for t, mean of ut doesn’t have to be zero for past values of regressors -> same for variance cst conditional on xt only

49
Q

what is contemporaneous exogeneity

A

E(ut|xt)=0 only for t, mean of ut doesn’t have to be zero for past values of regressors, same for variance cst conditional on xt only

50
Q

when the regressors are lagged so θyt-1 does it satisfy strong exogeneity

A

when regressor lagged it never satisfies strong exogeneity so need weak dependence –> contemporaneous exogeneity needed

51
Q

what is the implication of serial correlation on OLS

A 
consistency preserved (most of the time),
usual standard errors wrong and efficiency lost
52
Q

if strong exogeneity does not hold, what must you do when testing for serial correlation

A

must include all regressors in auxiliary regression

53
Q

what is the main issue with some time series

A

when yt is not stationary and weakly dependent, quite typical for many economic variables

54
Q

what is a leading case of a time series that is not stationary or weakly dependent

A

random walk where var grows over time var(yt)=tσ^2

55
Q

what is another example of a time series that is not stationary or weakly dependent that is not a random walk

A

linear model with a trend, where mean of yt varies over time

56
Q

how do you deal with a linear model with a trend

A

de-trend it

57
Q

what can cause spurious regression

A

nonstationarity

58
Q

what is a random walk (not d)

A

unit root (highly persistent time series)

59
Q

why do we need to difference a unit root process

A

the process is nonstationary and inference based on usual OLS ses is invalid, inference on differenced model is then valid

60
Q

why can’t you use t stat for DF test, why do we have to use different CVs

A

null that λ=0 so θ=1 and there is nonstationarity so OLS doesn’t work

61
Q

what are the assumptions needed for DF

A

error term homoskedastic and not serially correlated

62
Q

how do you deal with serial correlation for DF

A

augmented where introduce lags to absorb serial correlation

ECONOMETRICS (5 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions