L6: Time series Flashcards
What are TS data?
Data collected on the same observational unit at different points in time
How can logs be used with TS data?
They can simplify them - positive monotonic transformation (compresses data tf easier to interpret coefficients
Main uses of TS data? (4)
Forecasting
Estimation of dynamic causal effects (ie. what is the effect over time of x on y?)
Modelling of risks (eg. FMs)
Non-economic applications (eg. weather forecasting)
What things do and don’t matter with forecasting?
Adjusted R-squared, OVB, coefficient interpretation DONT MATTER
EXTERNAL VALIDITY matters LOTS!!! (ie. model estimated using historical data must hold into (near) future!)
Note:
TS data should consider only consecutive, evenly spaced obserlnvations
What is Yt-Y(t-1)?
First difference
What info does the log(first difference) give? When is this approximation most accurate?
The percentage change of a TS data between periods t-1 and t is approximately 100Δln(Yt)
Most accurate when the %Δ is small (see example bottom of page 1 side 1)
What is the correlation of a series with its own lagged values called?
AC or serial correlation
What is the sample autocorrelation?
An estimate of the population autocorrelation
What is the memory of a series?
How a TS set will often have highly correlated values between its periods (ie. recent yrs inflation rate often tells info on current and future yrs of inflation)
What is a stationary series? And in technical terms?
A series is stationary if its probability distribution does not change over time
ie. if the distribution of (Y(s+1),…,Y(s+T)) does NOT depend on s)
What does it mean if 2 series are jointly stationary?
Means their joint probability distribution doesn’t change over time
What is the main implication of stationarity?
That history is relevant tf is key for external validity of TS regression
What is an autoregressive model?
A regression model in which Yt is regressed against its own lagged values (natural start-point for a forecasting model that wants to use past Y values to predict Yt)
What is the order of an autoregressive model?
The number of lags used as regressors in an AR model
See
Example P2S1 in notes, and the ‘last 10mins of 23rd NOV’ where he explains stationarity in more detail
apparently explains that if the avg. of a series is changing then the series is not stationary
Difference between predicted values and forecast values?
Predicted (fitted) are in-sample
Forecast are out-of-sample (in future)
See
‘Notation’ P2S1 (important!)
Difference between residual and forecast errors?
residual is in-sample
forecast error is out-of-sample
See
Example (cont.) P2S2
How do we test how many lags (AR(p)) to use? (3)
Lag 1, use a t-test to test it is significantly different from 0 (ie. it affects the current value of Y, Yt)
Beyond that, use an F test to test each time you add a new lag!
OR
Determine the order of ‘p’ using an Information Criterion
See slide 37 example
Shows that by increasing the number of lags (ie. 2,3,4) there is an increase in the adjusted R-squared - this may show that adding these additional variables is helping to explain more of the variance (still not that useful though)
What is the ADL model? How does it differ to the ARM model?
Extension of the ARM: AR distributed lag model:
Idea: other variables other than the lagged dependent variables may help to predict Yt tf adds in X’s (and possible lags of X’s too!)
What would an ADL(p,r) model be?
One with p lags of Y and r lags of X
See
eg) Philips curve bit
What is the Granger Causality Test? How is it carried out?
A test of the joint hypothesis that none of the X’s is a useful predictor, up and beyond lagged values of Y
(ie. F-test testing the hypothesis that the coefficients on all the values of the X variables are zero)
