Module 7: Time series data Flashcards
Why are time series data not random samples?
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!
What happens to the expectations of y(t) if it is a random sample (In an AR(1) process?
If random: E(y(t)|y(t-1))= E(y(t)) pga de har inget med varandra att göra!
What happens to the E(b2) in an AR(1) process w. lagged dependent vaiable?
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
What are the componets of stationarity?
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
What is definition of exogeneity in time series model?
E(ε| x) is the conditional expectation of yt given all data on the expalatory variable: E(ε| x)=0
What is a static and a dynamic model=
The model is static if only observations at time t affect E(yt|x)
If past values can affect then it is dynamic
What is autocorrelation?
What is the formula for error terms with no autocorrelation?
It means that the error term are autocorrelated with itself.
Cov(εt, εs)=0 if there is NO autocorrelation
What are GM assumptions for time series data?
- All data is stationary
- The explanatory variables are exogenous
- The error terms are homoscedastic
- There is no autocorrelation
What are the result for a static LRM with GM ?
OLS estimator is unbiased, consistent, BLUE and standard errors are consistent.
Inference is correct if errr terms are normal
What are the results for a static LRM with autocorrelation?
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
What are White noise errors?
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)
What are some results for an AR(1) process with White noise errors?
Lagged dependent variables -> GM assumptions cant hold
OLS estimators and standard errors will be consistent
OLS estimator is biased downwads
What is E(y(t)| y(t-1)
E(β + ρy(t-1) + ε(t) | y(t-1)) = β +ρy(t1)
If y= β +ρy(t1) + εt has a ρ=1, then we have a unit root. What are the consequences?
An AR(1) process with a unit root is non stationary
What is a random walk?
It is an AR(1) process with a unit root (ρ = 1)
