STATIONARITY

Question 1

What is stationarity? Why is it bad?

Answer 1

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

Question 2

Definition of mean and variance

Answer 2

Mean is the expected value

Variance is the spread around the mean

Question 3

A time series is an example of a…

Answer 3

Stochastic process, the sequence of ransom variables ordered in time however, this is not always the case as trends can be seen.

Question 4

Graphical analysis

Answer 4

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.

Question 5

What is the Augmented DF unit root test? How is it performed?

Answer 5

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

Question 6

What is the null of DF/ADF test?

Answer 6

Null: B3=0 that is the time series is non-stationary (unit root).
Alternative H1: B3=/0 so stationarity.

Question 7

How can we reject the null?

Answer 7

• 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.

Question 8

What is the unit root equation and how do we get there? What if alpha = 1.

Answer 8

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.

Question 9

What are the three versions of the DF/ADF test?

Answer 9

1. Random walk: Change in Yt= B3Yt-1 + Ut
2. Random walk with drift : Change in Yt = B1 + B3Yt-1+ Ut
3. Random walk with drift around deterministic trend: Chnage in Yt = B1 + B2t + B3Yt-1 + Ut

Question 10

What does unit root also mean?

Answer 10

Non-stationary

Question 11

Stata outcome - Long-term memory behaviour

Answer 11

It is positively upwards rising. This shows that the presence of non-stationarity in lY because it has long-term memory behaviour.

Question 12

Stata outcome - Collegram

Answer 12

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.

Question 13

How do you fix the stationarity problem?

Answer 13

Taking the first difference in lags should always create a stationary relationship.
Remove the trend.

Question 14

If t-stat = -3.443 and 5%CV = -3.564 and 10%CV = -3.218 what can we do?

Answer 14

We can reject the null at the 10% level that it’s stationary

Question 15

What is the Phillips Perron test?

Answer 15

Correct for autocorrelation and heteroscedasticity. Makes a non-parametric correction for the t-stat

Question 16

When using the PP test must choose?

Answer 16

1. Include constant
2. Include constant and linear time trend
3. Neither

Question 17

PP method says AC does not affect…

Answer 17

Asymptotic distribution of the t-stat

Question 18

What is the null for PP and how do u test it?

Answer 18

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.

Question 19

What is the Zivot-Andrews test? How is it different from previous tests?

Answer 19

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.

Question 20

What is the null and how do you test it for ZA?

Answer 20

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.

Question 21

When do structural breaks occur?

Answer 21

In non-stationary at the minimum t-stat.

Question 22

What is spurious regression change and how is an easy way to detect it?

Answer 22

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

Question 23

What is the simple DF test?

Answer 23

Tests for stationarity at the first-order level. Assumes no AC.