Econometrics 5: Time Series Flashcards
Are economic time series usually i.i.d.?
No. Economic time series are often dependent and heterogeneously distributed. Observations today usually depend in some way on values yesterday, and trends, structural breaks and seasonality can mean that distributions change over time.
What is a random walk?
A random walk is a special case of an AR(1). It is defined as follows:
yt = a + y_{t-1} + e
State the LLN for weakly stationary processes.
Suppose yt is a weakly stationary process with mean μ and absolutely summable autocovariances such that ∑_{h=0}^∞ |γh|< ∞.
Then,the sample mean ȳ is consistent for µ.
What is a sufficient condition for ergodicity?
∑_{h=-∞}^ ∞ |γh|< ∞.
What is the CLT for stationary AR processes?
Suppose yt is a stationary AR(p) process. Then,
√T(ȳ - µ) -> N[0, ∑γh].
Covariances are summed from -∞ to ∞.
What is a martingale difference sequence?
If E[u|I_{t-1}]=0$, where I_t is the information available at date t (the observations of all current and past values of series), then u_t is a martingale difference sequence.
Does ∑1/t converge? Does ∑1/t^2?
∑1/t does not converge. ∑1/t^2 does, to π^2/6.
Is a time trend model stationary?
No. Its mean is dependent on t.
What does 1/t∑(t/T)^v approach in the limit?
1/(v+1)
If we estimate a time trend model by OLS, is (α,δ) consistent?
Yes, but the two estimators converge at different rates. There is therefore no limiting distribution that standardises this vector in terms of T alone.
