10. Time series Flashcards
What is the fundamental difference between time series data and cross sectional data?
A time series comes with an ordering and more importantly it is not randomly sampled
What is time series data?
A sequence of observations through time focussing on the same group
What are some of the typical features of time series data (2)?
- Serial correlation
- Non-independence of observations
Why are time series a sequence of random variables?
Because the outcome of economic variables is uncertain and therefore it should be measured as random variables
Why however, despite being made up of random variables, are time series no longer random samples?
Because randomness does not come from sampling a population
What is a sample in time series data?
The one realised path of the time series out of the many possible paths the stochastic process could have taken
What is the notion of serial correlation?
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.
What does stochastic mean?
Random
What does time series analysis focus on?
Modelling the dependency of a variable on its own past, and on the present and past values of other variables
What is a static time series model?
In static time series models, the current value of one variable is modelled as the result of the current values of explanatory variables
How do we know if a model is static?
If t is on both sides of the equation
What is a finite distributed lag model?
In finite distributed lag models, the explanatory vairables are also allowed to influence the dependent variable with a time lag
What is the effect of a transitory shock?
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
What is the effect of a permanent shock
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
What is a transitory shock?
A shock that happens in one period and then gets reversed
What are the 6 time series assumptions?
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
Which of the time series assumptions is the strongest?
TS.3 Zero conditional mean
What is strict exogeneity?
The mean of the error term is uncorrelated to the values of the explanatory variables of all periods
Why is TS.3 important?
Because it rules out feedback from the dependent variable on future values of the explanatory variables; this is often questionable
How do we get to Gauss-Markov conditions where OLS is BLUE again?
Under assumptions TS.1 -TS.5, the OLS estimators have the minimal variance of all linear unbiased estimators of the regression coefficients
What may happen if trending variables are regressed on eachother?
If trending variables are regressed on each other, a spurious relationship may arise if the variables are driven by a common trend
When should a trend be included?
- 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
What will a trend do to the variance of the dependent variable?
Due to the trend, the variance of the dependent variable will be overstated
How should we attempt to remove a trend?
It is better to first detrend the dependent variable and then run the regression on all the independent variables
