STATIONARITY Flashcards
What is stationarity? Why is it bad?
A critical assumption of time series data is stationarity. This means that the mean and variance of the time series data is consistent. Non-stationary means cannot predict future forecasts nor can generalise the next period. Also, lead to spurious results
Definition of mean and variance
Mean is the expected value
Variance is the spread around the mean
A time series is an example of a…
Stochastic process, the sequence of ransom variables ordered in time however, this is not always the case as trends can be seen.
Graphical analysis
If there is a general trend then it is suggested that the data is non-stationary.
EX - Drifting upwards with a great deal of variance.
What is the Augmented DF unit root test? How is it performed?
The Augmented DF test deals with the correlation of higher error terms. It is used with correlation or lags higher than one is present.
This test generates the dependent variables with the first difference. Uses the unit root test
What is the null of DF/ADF test?
Null: B3=0 that is the time series is non-stationary (unit root).
Alternative H1: B3=/0 so stationarity.
How can we reject the null?
- If t-stat <10% CV then cannot reject the null - non stationary
- if t-stat>10% CV then can reject the null - at the 1%, 5%, or 10% it will be stationary
We can also use p-value where insignificant means non-stationary.
What is the unit root equation and how do we get there? What if alpha = 1.
Start with:
LEXt = B1 + B2t + alphaLEXt-1 + Ut
Subtract LEXT-1 to find first difference.
Change in LEXt = B1 + B2t + (alpha -1)LEXt-1 + Ut where (alpha-1 equals B3).
If alpha = 1 then B3=0 so cannot reject the null - unit root.
What are the three versions of the DF/ADF test?
- Random walk: Change in Yt= B3Yt-1 + Ut
- Random walk with drift : Change in Yt = B1 + B3Yt-1+ Ut
- Random walk with drift around deterministic trend: Chnage in Yt = B1 + B2t + B3Yt-1 + Ut
What does unit root also mean?
Non-stationary
Stata outcome - Long-term memory behaviour
It is positively upwards rising. This shows that the presence of non-stationarity in lY because it has long-term memory behaviour.
Stata outcome - Collegram
Lagged periods are correlated = non-stationary. High AC means correlated and a high Q means high correlation if Prob>Q is significant it means there is a high Q present.
How do you fix the stationarity problem?
Taking the first difference in lags should always create a stationary relationship.
Remove the trend.
If t-stat = -3.443 and 5%CV = -3.564 and 10%CV = -3.218 what can we do?
We can reject the null at the 10% level that it’s stationary
What is the Phillips Perron test?
Correct for autocorrelation and heteroscedasticity. Makes a non-parametric correction for the t-stat
When using the PP test must choose?
- Include constant
- Include constant and linear time trend
- Neither
PP method says AC does not affect…
Asymptotic distribution of the t-stat
What is the null for PP and how do u test it?
Null - same as DF B3=0 (unit root or non-stationary)
Alternative - same as DF that B3 doesn’t equal 0 - stationarity.
Use the same t-stat vs CV test or can use the insignificant p-value to not reject and significant p-value to reject.
What is the Zivot-Andrews test? How is it different from previous tests?
ZA proposed a minimum root test which selects the breakpoints from t-stats.
All previous tests such as ADF and PP are under the assumption of no structural breaks.
What is the null and how do you test it for ZA?
H0: Variables follow a random walk process with no structural change (unit root).
H1: Variables are trend stationery with one-time breaks with precise timing unknown.
When do structural breaks occur?
In non-stationary at the minimum t-stat.
What is spurious regression change and how is an easy way to detect it?
Spurious regression is if series have a meaningful relationship when they clearly should not. Occurs when two non-stationary are regressed on each other.
- If R2>d then suspect spurious regression
What is the simple DF test?
Tests for stationarity at the first-order level. Assumes no AC.
