Module 7: Time series data Flashcards

1
Q

Why are time series data not random samples?

A

Because they are no longer independent of each other

If random: E(y(t)|y(t-1))= E(y(t)) pga de har inget med varandra att göra!

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2
Q

What happens to the expectations of y(t) if it is a random sample (In an AR(1) process?

A

If random: E(y(t)|y(t-1))= E(y(t)) pga de har inget med varandra att göra!

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3
Q

What happens to the E(b2) in an AR(1) process w. lagged dependent vaiable?

A

In an AR(!) process where we have a lagged dependent variable, OLS is biased and consistent so E(b2) will go towards 0 when t goes to infinity

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4
Q

What are the componets of stationarity?

A

E(yt)= μ (does not depent on t)
Var(yt)= σ(sqrd)
Cov(yt, yt-s) depends only on s but not on t, dvs konstant över tid

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5
Q

What is definition of exogeneity in time series model?

A

E(ε| x) is the conditional expectation of yt given all data on the expalatory variable: E(ε| x)=0

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6
Q

What is a static and a dynamic model=

A

The model is static if only observations at time t affect E(yt|x)
If past values can affect then it is dynamic

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7
Q

What is autocorrelation?

What is the formula for error terms with no autocorrelation?

A

It means that the error term are autocorrelated with itself.

Cov(εt, εs)=0 if there is NO autocorrelation

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8
Q

What are GM assumptions for time series data?

A
  • All data is stationary
  • The explanatory variables are exogenous
  • The error terms are homoscedastic
  • There is no autocorrelation
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9
Q

What are the result for a static LRM with GM ?

A

OLS estimator is unbiased, consistent, BLUE and standard errors are consistent.
Inference is correct if errr terms are normal

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10
Q

What are the results for a static LRM with autocorrelation?

A

OLS estimator is unbiased and consistent
OLS estimator s no longer efficient
Variance formula is incorrect ->standard errors are inconsistent and all inference will be misleading

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11
Q

What are White noise errors?

A

ε(t) is independent of all lagged values of y
two distinct error terms are independent
E(εt) = 0 and Var(εt)= sigma(sqrd) (no heteroscedasticity)

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12
Q

What are some results for an AR(1) process with White noise errors?

A

Lagged dependent variables -> GM assumptions cant hold
OLS estimators and standard errors will be consistent
OLS estimator is biased downwads

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13
Q

What is E(y(t)| y(t-1)

A

E(β + ρy(t-1) + ε(t) | y(t-1)) = β +ρy(t1)

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14
Q

If y= β +ρy(t1) + εt has a ρ=1, then we have a unit root. What are the consequences?

A

An AR(1) process with a unit root is non stationary

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15
Q

What is a random walk?

A

It is an AR(1) process with a unit root (ρ = 1)

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16
Q

What is diffrence stationary?

A

It is that the diffrence between y(t)-y(t-1) is stationary