Flashcards in L6: Time series Deck (26)

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1

## What are TS data?

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

2

## How can logs be used with TS data?

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

3

## 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)

4

## 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!)

5

## Note:

### TS data should consider only consecutive, evenly spaced obserlnvations

6

## What is Yt-Y(t-1)?

### First difference

7

## 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)

8

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

### AC or serial correlation

9

## What is the sample autocorrelation?

### An estimate of the population autocorrelation

10

## 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)

11

## 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)

12

## What does it mean if 2 series are jointly stationary?

### Means their joint probability distribution doesn't change over time

13

## What is the main implication of stationarity?

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

14

## 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)

15

## What is the order of an autoregressive model?

### The number of lags used as regressors in an AR model

16

## 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

17

## Difference between predicted values and forecast values?

###
Predicted (fitted) are in-sample

Forecast are out-of-sample (in future)

18

## See

### 'Notation' P2S1 (important!)

19

## Difference between residual and forecast errors?

###
residual is in-sample

forecast error is out-of-sample

20

## See

### Example (cont.) P2S2

21

## 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

22

## 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)

23

## 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!)

24

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

### One with p lags of Y and r lags of X

25

## See

### eg) Philips curve bit

26