L6: Time series

Question 1

What are TS data?

Answer 1

Data collected on the same observational unit at different points in time

Question 2

How can logs be used with TS data?

Answer 2

They can simplify them - positive monotonic transformation (compresses data tf easier to interpret coefficients

Question 3

Main uses of TS data? (4)

Answer 3

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)

Question 4

What things do and don’t matter with forecasting?

Answer 4

Adjusted R-squared, OVB, coefficient interpretation DONT MATTER

EXTERNAL VALIDITY matters LOTS!!! (ie. model estimated using historical data must hold into (near) future!)

Question 5

Note:

Answer 5

TS data should consider only consecutive, evenly spaced obserlnvations

Question 6

What is Yt-Y(t-1)?

Answer 6

First difference

Question 7

What info does the log(first difference) give? When is this approximation most accurate?

Answer 7

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)

Question 8

What is the correlation of a series with its own lagged values called?

Answer 8

AC or serial correlation

Question 9

What is the sample autocorrelation?

Answer 9

An estimate of the population autocorrelation

Question 10

What is the memory of a series?

Answer 10

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)

Question 11

What is a stationary series? And in technical terms?

Answer 11

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)

Question 12

What does it mean if 2 series are jointly stationary?

Answer 12

Means their joint probability distribution doesn’t change over time

Question 13

What is the main implication of stationarity?

Answer 13

That history is relevant tf is key for external validity of TS regression

Question 14

What is an autoregressive model?

Answer 14

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)

Question 15

What is the order of an autoregressive model?

Answer 15

The number of lags used as regressors in an AR model

Question 16

See

Answer 16

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

Question 17

Difference between predicted values and forecast values?

Answer 17

Predicted (fitted) are in-sample

Forecast are out-of-sample (in future)

Question 18

See

Answer 18

‘Notation’ P2S1 (important!)

Question 19

Difference between residual and forecast errors?

Answer 19

residual is in-sample

forecast error is out-of-sample

Question 20

See

Answer 20

Example (cont.) P2S2

Question 21

How do we test how many lags (AR(p)) to use? (3)

Answer 21

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

Question 22

See slide 37 example

Answer 22

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)

Question 23

What is the ADL model? How does it differ to the ARM model?

Answer 23

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!)

Question 24

What would an ADL(p,r) model be?

Answer 24

One with p lags of Y and r lags of X

Question 25

See

Answer 25

eg) Philips curve bit

Question 26

What is the Granger Causality Test? How is it carried out?

Answer 26

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)