10. Time series

Question 1

What is the fundamental difference between time series data and cross sectional data?

Answer 1

A time series comes with an ordering and more importantly it is not randomly sampled

Question 2

What is time series data?

Answer 2

A sequence of observations through time focussing on the same group

Question 3

What are some of the typical features of time series data (2)?

Answer 3

• Serial correlation
• Non-independence of observations

Question 4

Why are time series a sequence of random variables?

Answer 4

Because the outcome of economic variables is uncertain and therefore it should be measured as random variables

Question 5

Why however, despite being made up of random variables, are time series no longer random samples?

Answer 5

Because randomness does not come from sampling a population

Question 6

What is a sample in time series data?

Answer 6

The one realised path of the time series out of the many possible paths the stochastic process could have taken

Question 7

What is the notion of serial correlation?

Answer 7

The order of the data is now important. What time series we have temporal ordering of the data, it becomes more and more unrealistic to assume that these data are independent of each other. This is the notion of serial correlation.

Question 8

What does stochastic mean?

Answer 8

Random

Question 9

What does time series analysis focus on?

Answer 9

Modelling the dependency of a variable on its own past, and on the present and past values of other variables

Question 10

What is a static time series model?

Answer 10

In static time series models, the current value of one variable is modelled as the result of the current values of explanatory variables

Question 11

How do we know if a model is static?

Answer 11

If t is on both sides of the equation

Question 12

What is a finite distributed lag model?

Answer 12

In finite distributed lag models, the explanatory vairables are also allowed to influence the dependent variable with a time lag

Question 13

What is the effect of a transitory shock?

Answer 13

If there is a one time shock in a past period, the dependent variable will change temporarily by the amount indicated by the coefficient of the corresponding lag

Question 14

What is the effect of a permanent shock

Answer 14

If there is a permanent shock in a past period, i.e. the explanatory variable permanently increases by one unit, the effect on the dependent variable will be the cumulated effect of all relevant lags. This is a long-run effect on the dependent variable

Question 15

What is a transitory shock?

Answer 15

A shock that happens in one period and then gets reversed

Question 16

What are the 6 time series assumptions?

Answer 16

TS.1 - Linear in parameters
TS.2 - No perfect collinearity
TS.3 - Zero conditional mean
TS.4 - Homoskedasticity
TS.5 - No serial correlation
TS.6 - Normality

Question 17

Which of the time series assumptions is the strongest?

Answer 17

TS.3 Zero conditional mean

Question 18

What is strict exogeneity?

Answer 18

The mean of the error term is uncorrelated to the values of the explanatory variables of all periods

Question 19

Why is TS.3 important?

Answer 19

Because it rules out feedback from the dependent variable on future values of the explanatory variables; this is often questionable

Question 20

How do we get to Gauss-Markov conditions where OLS is BLUE again?

Answer 20

Under assumptions TS.1 -TS.5, the OLS estimators have the minimal variance of all linear unbiased estimators of the regression coefficients

Question 21

What may happen if trending variables are regressed on eachother?

Answer 21

If trending variables are regressed on each other, a spurious relationship may arise if the variables are driven by a common trend

Question 22

When should a trend be included?

Answer 22

• If the dependent variable displays an obvious trending behaviour
• If both the dependent and some independent variables have trends
• If only some of the independent variables have trends; their effect on the dependent variable may only be visible after a trend has been subtracted

Question 23

What will a trend do to the variance of the dependent variable?

Answer 23

Due to the trend, the variance of the dependent variable will be overstated

Question 24

How should we attempt to remove a trend?

Answer 24

It is better to first detrend the dependent variable and then run the regression on all the independent variables