L4 - Persistence, Nonstationarity and Spurious Regression Flashcards
What is the general approach to dealing with highly persistent data?
Transform the model back to a stationary process which satisfies weak dependence
Why is a random walk model seen as highly persistent?
Because the variance of a random walk model increases as a linear function of time
What is a unit root process?
A type of time series where the variable tends to return to its mean level after experiencing shocks, but with random fluctuations
ρ = 1 in the classical AR(1) model.
What is the order of intergration?
The number of times the variable has to be differenced to arrive at a weakly dependent process
What are the main features of a stationary I(0) series?
1) Fluctuates around its mean with a finite variance that does not depend upon time
2) Is mean-reverting: tendency to return to its mean
3) Has limited memory; effect of a shock dies out. Autocorrelations die out (fairly) rapidly
What is a nonstationary I(1) series?
1) Wanders widely, no finite (unconditional) mean or variance
2) Has infinitely long memory
3) Estimated autocorrelations decay to zero very quickly
What is trend stationary variable?
In a nonstationary model including a trend, if after removing the trend the resulting variable
becomes stationary
What is the differnece between
Trend Stationary: Achieves stationarity by removing the trend component while preserving other components.
Difference Stationary: Achieves stationarity by taking differences between consecutive observations, effectively removing the trend component
